{"id":66,"date":"2020-08-31T11:57:39","date_gmt":"2020-08-31T06:27:39","guid":{"rendered":"http:\/\/maths.jfn.ac.lk\/?page_id=66"},"modified":"2020-09-29T14:02:29","modified_gmt":"2020-09-29T08:32:29","slug":"applied-mathamatics","status":"publish","type":"page","link":"https:\/\/maths.jfn.ac.lk\/index.php\/applied-mathamatics\/","title":{"rendered":"Applied Mathamatics"},"content":{"rendered":"

Level \u2013 1<\/h3>\n

Course units effective from academic year 2016\/2017 to date<\/h4>\n
\n
<\/span>AMM101G3: Applied Methods I <\/div>
\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Course Code<\/strong><\/td>\nAMM101G3<\/strong><\/td>\n<\/tr>\n
Course Title<\/strong><\/td>\nApplied Methods I<\/td>\n<\/tr>\n
Academic Credits<\/strong><\/td>\n03 (40 hours of lectures and tutorials + 10 hours of practical)<\/td>\n<\/tr>\n
Objectives:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Introduce the fundamentals of vector algebra and vector calculus<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Enable the students to handle field operators and their applications<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Provide various solution methods for solving first order differential equations<\/td>\n<\/tr>\n

Intended Learning Outcomes:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Recall the laws of vector algebra<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Apply vector algebra to geometry<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Solve the first order separable differential equations<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Determine the solution of homogeneous linear differential equations with constant coefficients<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Solve the first order exact differential equations<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Make use of integrating factor method to solve first order linear differential equations<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Compute partial derivatives<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Define field operators (del, curl, and div)<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Relate field operators with physical\/ geometrical properties<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Determine the characteristics (curvature, tangent, normal, binormal, etc.) of space curve<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Compute line integrals<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Familiarize computational techniques for solving ordinary differential equations<\/td>\n<\/tr>\n

Syllabus Outline<\/strong><\/td>\n<\/tr>\n
Contents:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Vector Algebra:<\/strong> Vectors, Scalars, Laws of Vector algebra Unit vectors, Scalar fields, Vector fields, Scalar products, Vector products, Triple products, Reciprocal of Vectors.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 First order Ordinary Differential Equations (ODE): <\/strong>Variable separable, homogeneous equations, exact equations, linear equations and Bernoulli equations.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Vector Calculus:<\/strong> Ordinary derivatives of vectors, Space curves, Differentiation formula, Partial derivatives of vectors, Differential of vectors, Differential Geometry, The vector differential operators, del, Gradient, Divergence, Curl, Formula involving del, Invariance, Ordinary integral of vectors, Line integrals.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Computational Solution of First Order ODE: <\/strong>Getting started with MATLAB, Doing Mathematics using MATLAB. M-Files, MATLAB Interface, Workspace, Working directory, Command window Script m-files and function m-files. The built-in MATLAB commands for solving ordinary differential equation.<\/td>\n<\/tr>\n

Teaching Methods:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Lectures,\u00a0 Tutorials, Handouts, Problem solving, Use of e-resources<\/td>\n<\/tr>\n
Assessment\/ Evaluation Details:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 In-course Assessments\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 25%<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Practical Exam on MATLAB 05%<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 End-of-course Examination\u00a0\u00a0 70%<\/td>\n<\/tr>\n

Recommended Readings:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Vector Analysis, Spiegel. M, Lipschutz. S and Spellman. D., 2nd<\/sup> Edition, Schaum\u2019s outline series, McGraw-Hill Education, 2009.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Introduction to Vector Analysis, Davis. H. F, and Snider. A. D, 3rd<\/sup> Edition, Allyn and Bacon inc, Boston, 1979.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 An Introduction to Ordinary Differential Equations, Earl. A. Coddington, Dover Publication, Inc., New York, 1989.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Elementary Differential Equations and Boundary Value Problems, William E. Boyce, Richard C. Diprima John Wiley & Sons, Inc, 1984.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Elementary Differential Equations with Applications, William R. Derrick, Stanley I. Grossman Addison-Wesley Publishing Company, 1981.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div><\/div>\n

<\/span>AMM102G2: Mechanics I<\/div>
\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Course Code<\/strong><\/td>\nAMM102G2<\/strong><\/td>\n<\/tr>\n
Course Title<\/strong><\/td>\nMechanics I<\/td>\n<\/tr>\n
Academic Credits<\/strong><\/td>\n02 (30\u00a0 hours of lectures and tutorials)<\/td>\n<\/tr>\n
Objectives:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Introduce the fundamentals of particle dynamics and rigid body motion<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Familiarize with equilibrium problems of flexible strings and chains<\/td>\n<\/tr>\n

Intended Learning Outcomes:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Relate the physical quantities in different coordinate system<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Develop equation of motion for varying mass problems<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Solve problems concerning varying mass anddamped motion on a space curve<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Solve problems concerning oblique impact.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Recall the physical quantities associated with the system of particles<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Derive equation of catenary for flexible string\/chain<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Solve the equilibrium problems of flexible chain<\/td>\n<\/tr>\n

Syllabus Outline<\/strong><\/td>\n<\/tr>\n
Contents:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Physical Quantities in Different Co-ordinate Systems: <\/strong>Frame of reference, Inertial frames, Forces, Velocity, Acceleration, Linear momentum, Angular velocity, Angular acceleration, Angular momentum.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Dynamics of a Particle with one Degree of Freedom: <\/strong>Motion in a straight line under variable forces, Motion under gravity in a resisting medium, The rectilinear motion of bodies with variable mass, Particle motion on space curve, Damped harmonic Oscillations, Forced oscillations<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Dynamics of a Particle with two Degrees of Freedom: <\/strong>Oblique impact of elastic bodies.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Moment of Inertia: <\/strong>Moments and product of inertia, Parallel axes theorem, Perpendicular axes theorem for moments and product and product of inertia, Principle axes and principle moments of inertia of a system of particles, Rotating coordinate systems, Infinitesimal rotation.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 The Motion of a System of Particles-general Theorems<\/strong>: The motion of the centre of mass, Motion about the centre of mass, Motion generated by simultaneously applied impulses.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Flexible Chains and Strings: <\/strong>Equation of catenary, Various relations for common catenary, Equilibrium of light string on a smooth plane curve, light string on a rough plane curve, heavy string on a smooth plane curve and heavy string on a rough plane curve.<\/td>\n<\/tr>\n

Teaching Methods:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Lecture by Lecturer and small group tutorial discussions by instructor<\/td>\n<\/tr>\n
Assessment\/ Evaluation Details:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 In-course assessment\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 30%<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 End of course Examination\u00a0\u00a0 70%<\/td>\n<\/tr>\n

Recommended Readings:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Introduction to Classical Mechanics, Takwale R.G. and Puranik P.S., Tata-McGraw Hill, 1979.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Classical Mechanics, Goldstein H., Norosa Publishing House, 2000.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Statics: A Text book for the use of the Higher Divisions in Schools and for First Year Students at the Universities, Ramsey A. S., Cambridge University Press, 2009.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div><\/div>\n

<\/span>AMM103G3: Applied Methods II<\/div>
\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Course Code<\/strong><\/td>\nAMM103G3<\/strong><\/td>\n<\/tr>\n
Course Title<\/strong><\/td>\nApplied Methods II<\/td>\n<\/tr>\n
Academic Credits<\/strong><\/td>\n03 (45 hours of lectures and tutorials)<\/td>\n<\/tr>\n
Objectives:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Provide the fundamentals of surface and volume integrals. Enable the students to handle integral theorems<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Introduce integral theorems<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Familiarize curvilinear coordinate systems<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Acquainted with appropriate solution methods of linear differential equations<\/td>\n<\/tr>\n

Intended Learning Outcomes:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Compute surface, and volume integrals<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Characterize conservative and Solenoidal fields<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Recall integral transformation theorems<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Illustrate the integral theorems with examples<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Illustrate the application of integral transformation theorems<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Solve linear homogeneous ordinary differential equations<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Solve first order linear partial differential equations<\/td>\n<\/tr>\n

Syllabus Outline<\/strong><\/td>\n<\/tr>\n
Contents:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Vector Integrals:<\/strong> Surface integrals, Volume integrals.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Integrals Theorems:<\/strong> The divergence theorem of Gauss, Stokes theorem, Green\u2019s theorem in the plane, Related integral theorems, Integral operator form for del.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Curvilinear Coordinates:<\/strong> Transformation of coordinates, Orthogonal curvilinear coordinates, Unit vectors in curvilinear systems, Arc length and volume elements, Gradient, Divergent and Curl, Special orthogonal coordinates systems.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Higher Order Differential Equations:<\/strong> Second order equations with constant coefficients, computation of particular integrals using differential operators, undetermined coefficient method and variation of parameter method.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Partial Differential Equations:<\/strong> Introduction to partial differential equations, Formation and classification of partial differential equations, Solution methods for first order partial differential equations.<\/td>\n<\/tr>\n

Teaching Methods:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Lectures,\u00a0 Tutorials, Handouts, Problem solving, Use of e-resources<\/td>\n<\/tr>\n
Assessment\/ Evaluation Details:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 In-course Assessments\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 30%<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 End-of-course Examination\u00a0 70%<\/td>\n<\/tr>\n

Recommended Readings:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Vector Analysis, Spiegel. M, Lipschutz. S and Spellman. D., 2nd<\/sup> Edition, Schaum\u2019s outline series, McGraw-Hill Education, 2009.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Introduction to Vector Analysis, Davis. H. F, and Snider. A. D, 3rd<\/sup> Edition, Allyn and Bacon inc, Boston, 1979.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 An Introduction to Ordinary Differential Equations, Earl. A. Coddington, Dover Publication, Inc., New York, 1989.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Elementary Differential Equations and Boundary Value Problems, William E. Boyce, Richard C. Diprima John Wiley & Sons, Inc, 1984.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Elementary Differential Equations with Applications, William R. Derrick, Stanley I. Grossman Addison-Wesley Publishing Company, 1981.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div><\/div>\n

<\/span>AMM104G2: Mechanics II<\/div>
\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Course Code<\/strong><\/td>\nAMM104G2<\/strong><\/td>\n<\/tr>\n
Course Title<\/strong><\/td>\nMechanics II<\/td>\n<\/tr>\n
Academic Credits<\/strong><\/td>\n02 (30\u00a0 hours of lectures and tutorials)<\/td>\n<\/tr>\n
Objectives:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Introduce the fundamentals of motion under central force and dynamics of a rigid body<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Familiarize the concept of shearing force and bending moment<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Provide the techniques to compute the deflection of an elastic beam<\/td>\n<\/tr>\n

Intended Learning Outcomes:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Discuss translation\/rotation motion in two dimension<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Classify the equation of angular motion of a rigid body<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Formulate general motion of a rigid lamina in its own plane<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Determine bending moment and shearing force of a straight beam<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Use Bernoulli\u2019s Euler\u2019s law to find the deflection of an elastic beam<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Apply Clapeyron\u2019s equation to find the bending moment of a beam<\/td>\n<\/tr>\n

Syllabus Outline<\/strong><\/td>\n<\/tr>\n
Contents:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Motion under Central Force Polar Coordinate: <\/strong>A central orbit is a plane curve, the angular momentum integral, the theorem of areas.<\/p>\n

The motion of connected particles, two dimensional motion of a projectile in a resisting medium<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 An Introduction to the Dynamics of a Rigid Body: <\/strong>Rotation of a lamina about a fixed axis, Momentum and energy equations for angular motion of a lamina, Compound pendulum, Force exerted on the axis of rotation, Impulse and angular momentum, Relation between the equations of angular motion of a rigid body and the equations of motion of a particle moving in a straight line, Motion of a lamina in its own plane-instantaneous centre of rotation, General motion of a rigid lamina in its own plane.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Bending of Beams: <\/strong>Shearing force of a beam and shearing force diagram, Bending moment of a beam and bending moment diagram, Relation between shearing force and bending moment, Equilibrium of slightly elastic beams, Bending moment of slightly elastic beam, Bernoulli\u2019s Euler\u2019s law for bending moment of slightly elastic beam, Differential equations of equilibrium of thin beams with various types of loads, Clapeyron\u2019s equation of three moments.<\/td>\n<\/tr>\n

Teaching Methods:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Lecture by Lecturer and small group tutorial discussions by instructor<\/td>\n<\/tr>\n
Assessment\/ Evaluation Details:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 In-course assessment\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 30%<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 End of course Examination\u00a0 70%<\/td>\n<\/tr>\n

Recommended Readings:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Classical Mechanics, Taylor J.R., University Science books, 2005.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Engineering Mechanics: Statics, Meriam. L. J. and Kraige. G. L., Willey, 2004. Hibbeler. R.C., Engineering Mechanics:\u00a0Statics, Pearson, 2013.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div><\/div>\n<\/div>\n

Level – 2<\/h3>\n

Course units effective from academic year 2016\/2017 to date<\/h4>\n
\n
<\/span>AMM201G3: Mathematical Methods <\/div>
\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Course Code<\/strong><\/td>\nAMM201G3<\/strong><\/td>\n<\/tr>\n
Course Title<\/strong><\/td>\nMathematical Methods <\/strong><\/td>\n<\/tr>\n
Credit Value<\/strong><\/td>\n03 <\/strong><\/td>\n<\/tr>\n
\u00a0<\/strong><\/p>\n

Hourly Breakdown<\/strong><\/td>\n

Theory<\/strong><\/td>\nPractical<\/strong><\/td>\nIndependent Learning<\/strong><\/td>\n<\/tr>\n
45<\/strong><\/td>\n—<\/strong><\/td>\n105<\/strong><\/td>\n<\/tr>\n
Objectives:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Acquainted with the solution by series method to solve Ordinary Differential Equations and introduce Special Functions<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Introduce the concepts of P.D.E\u2019s and solve linear P.D.E\u2019s<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Imparting the fundamentals and applications of Fourier series, Fourier transform and Laplace transforms<\/td>\n<\/tr>\n

Intended Learning Outcomes:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Solve O.D.E\u2019s by solution of series method<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Recall the elementary special functions<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Solve linear P.D.E\u2019s with constant coefficients<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Determine the Fourier series representation of periodic functions<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Recall the properties of Fourier series<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Define the Fourier transform and inverse transform<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Discuss the fundamental properties of the Fourier transform<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Solve Initial Boundary Value Problems using the Fourier series \/ Fourier transform<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Define the Laplace transform.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Use the Laplace transform \/ techniques to solve Initial Boundary Value Problems<\/td>\n<\/tr>\n

Course Contents:<\/strong><\/td>\n<\/tr>\n
Series solutions for linear differential equations with variable coefficients: <\/strong>Ordinary and singular points, Power series solutions about ordinary and regular singular points, Convergence of power series solutions, Method of Frobenius: Indicial equation, Recurrence relation, General solution.<\/p>\n

Special functions: <\/strong>an Introduction<\/p>\n

Gamma functions, Bessel functions, Legendre polynomials and functions.<\/p>\n

Partial Differential Equations: <\/strong>Introduction of P.D.E: Linear P.D.E, Superpossion of solutions, Auxiliary equation, Complementary function, Particular Integral, Examples and Applications.<\/p>\n

Fourier series and integrals: <\/strong>Fourier series, Half range Fourier sine and cosine series,\u00a0\u00a0 Parseval\u2019s identity, Fourier integrals, Fourier transforms, Properties of Fourier transforms, Applications to Boundary Value Problems.<\/p>\n

Laplace Transforms<\/strong>: Laplace transforms and its properties, Inverse Laplace transforms, Applications to solving ordinary and partial differential equations.<\/td>\n<\/tr>\n

Teaching Methods:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Lectures,\u00a0 Tutorials, Handouts, Problem solving, Use of e-resources<\/td>\n<\/tr>\n
Assessment\/ Evaluation Details:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 In-course Assessments \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a030%<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 End-of-course Examination 70%<\/td>\n<\/tr>\n

Recommended Readings:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 William E. Boyce, Richard C. Diprima, Elementary Differential Equations and Boundary Value Problems, John Wiley & Sons, Inc, 2001.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 M.D.Raisinghania, Advance Differential Equations, Chand & Company Ltd. Ramnagar, New Delhi, 2001.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 A. Donald, Mathematical Methods for Scientists and Engineers, McQuarrie, Univ Science Books; 1st edition, 2003.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 E. Zauderer, Partial Differential Equations of Applied Mathematics, third edition, John Wiley, 2006.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div><\/div>\n

<\/span>AMM202G2: Fluid Dynamics<\/div>
\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Course Code<\/strong><\/td>\nAMM202G2<\/strong><\/td>\n<\/tr>\n
Course Title<\/strong><\/td>\nFluid Dynamics<\/strong><\/td>\n<\/tr>\n
Credit Value<\/strong><\/td>\n02<\/strong><\/td>\n<\/tr>\n
Prerequisites <\/strong><\/td>\nAMM101G3, AMM103G3<\/strong><\/td>\n<\/tr>\n
\u00a0<\/strong><\/p>\n

Hourly Breakdown<\/strong><\/td>\n

Theory<\/strong><\/td>\nPractical<\/strong><\/td>\nIndependent Learning<\/strong><\/td>\n<\/tr>\n
30<\/strong><\/td>\n—<\/strong><\/td>\n70<\/strong><\/td>\n<\/tr>\n
Objectives:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Introduce the fundamental concept of fluid dynamics with special emphasis on pressure equation, circulation, drag and lifts 2D ideal irrotational\u00a0 flow and water waves<\/td>\n<\/tr>\n
Intended Learning Outcomes:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Recall the applied mathematical tools that support fluid dynamics<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Prove the equation of continuity and Euler\u2019s equation of motion<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Apply Bernoulli\u2019s equation to flow problems<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Discuss possible motion and bounding surfaces<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Solve expanding bubble problems<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Discuss 2D ideal irrotational flow<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Determine complex potential in the presence of\u00a0 circular cylinder and long wall<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Applying Blasius\u2019s theorem to compute the net force<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Discuss the water wave problems<\/td>\n<\/tr>\n

Course Contents:<\/strong><\/td>\n<\/tr>\n
Euler\u2019s Equation, Bernoulli\u2019s theorem, vorticity and circulation, Kelvin\u2019s theorem. Irrotational incompressible flow: velocity potential, stream functions and complex potentials for 2D flow, line sources, vortices, superposition, circle theorem, Blasius\u2019s theorem uniform flow past a circular cylinder, flow past a bubble, circulation, drag andlift, flow past a flat wing theorem<\/p>\n

Uniform flow past a circular cylinder, flow past a bubble, circulation, drag andlift, flow past a flat wing.<\/p>\n

Water Waves:<\/strong> 1D free boundary problems, progressive waves, infinite and finite depth, wave speed, dispersion and group velocity.<\/p>\n

Incompressible Newtonian fluids:<\/strong> introduction of concepts, viscosity, Reynolds number and turbulence.<\/td>\n<\/tr>\n

Teaching Methods:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0 Lectures, tutorial discussions and e-learning<\/td>\n<\/tr>\n
Assessment\/ Evaluation Details:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 In-course assessment\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 30%<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 End of course Examination\u00a0\u00a0\u00a0 70%<\/td>\n<\/tr>\n

Recommended Readings:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 M.D. Raisinghana, Fluid Dynamics, 2010.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 J.Williams,Fluid Mechanics, problem solvers, 2014.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 G.K.Batchelor, An introduction to Fluid Dynamics, Cambridge university press, 2000.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 J. Alexandre, Mathematical Introduction to Fluid Mechanics, springer publication, 2000.<\/p>\n

 <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div><\/div>\n

<\/span>AMM203G3: Linear Programming <\/div>
\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Course Code<\/strong><\/td>\nAMM203G3<\/strong><\/td>\n<\/tr>\n
Course Title<\/strong><\/td>\nLinear Programming <\/strong><\/td>\n<\/tr>\n
Credit Value<\/strong><\/td>\n03<\/strong><\/td>\n<\/tr>\n
Prerequisites <\/strong><\/td>\nPMM201G3 and PMM204G2<\/strong><\/td>\n<\/tr>\n
\u00a0<\/strong><\/p>\n

Hourly Breakdown<\/strong><\/td>\n

Theory<\/strong><\/td>\nPractical<\/strong><\/td>\nIndependent Learning<\/strong><\/td>\n<\/tr>\n
40<\/strong><\/td>\n10<\/strong><\/td>\n100<\/strong><\/td>\n<\/tr>\n
Objectives:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Develop a strong knowledge in theoretical concepts of linear programming problems and simplex methods<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Enable the students to solve transportation, assignment and network problems and perform sensitive analysis<\/td>\n<\/tr>\n

Intended Learning Outcomes:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Recall the basic principles in the optimization<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Solve simple linear programming problems by graphical method<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Demonstrate skills in applying simplex methods<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Discuss primal and dual relationships with applications<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Solve real world problems by applying acquired techniques<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Perform sensitivity analysis<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Utilize the special algorithms to solve transportation and assignment problems<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Find the shortest route and maximum flow in Network problems<\/td>\n<\/tr>\n

Course Contents:<\/strong><\/td>\n<\/tr>\n
Preliminaries: <\/strong>optimization under constrains, representation of constrains, geometry of linear programming, extreme points and optimality, basic solutions, efficiency of algorithms.<\/p>\n

Simplex method:<\/strong> un boundedness, degeneracy, big-M method, duality, primal-dual relationship, dual simplex methods, the revised simplex methods, sensitive analysis.<\/p>\n

Transportation and Assignment problems:<\/strong> formulating transportation problems, finding basic solutions, simplex method for transportation problems, assignment problems, transshipment problems and special algorithms.<\/p>\n

Network:<\/strong> shortest route problems, maximum flow problems, project scheduling, spanning trees.<\/td>\n<\/tr>\n

Teaching Methods:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0 Lectures, Tutorial discussions, Practical, Handouts and Self-learning guides.<\/td>\n<\/tr>\n
Assessment\/ Evaluation Details:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 In-course assessment\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 30%<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 End of course Examination 70%<\/td>\n<\/tr>\n

Recommended Readings:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 K.P.C.Edwin and H.Z.Stanislaw, An Introduction to Optimization, Wiley \u2013 Interscience publication, 2001.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 W.L.Winston and M.Venkataramanan, Introduction to Mathematical Programming, Thomson Brooks, 2003.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 V. Steven, Mathematical Programming, Dover Publications Ins.,2009.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 W.L.Walter, Introduction to Mathematical Programming, Pearson Education Company, 1999.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div><\/div>\n

<\/span>AMM204G2: Linear Algebra and Analytic Geometry<\/div>
\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Course Code<\/strong><\/td>\nAMM204G2<\/strong><\/td>\n<\/tr>\n
Course Title<\/strong><\/td>\nNumerical Analysis<\/strong><\/td>\n<\/tr>\n
Credit Value<\/strong><\/td>\n02 <\/strong><\/td>\n<\/tr>\n
\u00a0<\/strong><\/p>\n

Hourly Breakdown<\/strong><\/td>\n

Theory<\/strong><\/td>\nPractical<\/strong><\/td>\nIndependent Learning<\/strong><\/td>\n<\/tr>\n
30<\/strong><\/td>\n—<\/strong><\/td>\n70<\/strong><\/td>\n<\/tr>\n
Objectives:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Enable the students to familiarize with fundamental concepts of Numerical Analysis<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Develop knowledge and skills in computer Arithmetic, iterative methods to solve non-linear equations, interpolating techniques to find zeros of polynomials and Numerical Integration methods<\/td>\n<\/tr>\n

Intended Learning Outcomes:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Convert a number from one base to another using Hornor Algorithm<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Determine the quotient and remainder in a polynomial division using Hornor algorithm<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Recall rounding and chopping<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Establish the relationship between the number of real zeros of a polynomial and the Sturm sequence<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Apply bisection method to find roots<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Discuss the convergence of the fixed point iteration<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Establish the convergence of Newton\u2019s iteration<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Apply Newton\u2019s iteration to compute the zero of a given function<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Discuss interpolation methods<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Establish the error bound in interpolation<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Recall Numerical integrating methods<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Evaluate definite integrals using numerical integration methods<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Evaluate error bounds integration methods<\/td>\n<\/tr>\n

Course Contents:<\/strong><\/td>\n<\/tr>\n
Round Off Errors and Computer Arithmetic: <\/strong>Different number bases, Fixed point number representation, Floating point number representation, Rounding, Chopping, Relative error, Absolute error, Error bounds in rounding\/chopping.<\/p>\n

Solution of Equations in one variable: <\/strong>Sturm sequences: Construction, Locating zeros; Bisection Method: Convergence, Error bounds, Fixed Point iteration: Contraction mapping theorem, Existence and uniqueness of fixed point, Convergence; Newton\u2019s method: Convergence, Error bounds; Rate of Convergence: Comparison of rate of convergence, Accelerating the convergence.<\/p>\n

Interpolation and Polynomial Approximation: <\/strong>Interpolation: Existence and Uniqueness, Lagrange Polynomial, Lagrange interpolation, Divided differences, Newton\u2019s interpolation, Error analysis in interpolation.<\/p>\n

Numerical Integration: <\/strong>Trapezoidal rule, Simpson\u2019s rule, Composite Trapezoidal rule, Composite Simpson\u2019s rule, Error Analysis in numerical integration.<\/td>\n<\/tr>\n

Teaching Methods:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0 Lectures, Tutorial discussions, Handouts, Self-learning guides and E-resources<\/td>\n<\/tr>\n
Assessment\/ Evaluation Details:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 In-course Assessments:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 30%<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 End-of-course Examination: 70%<\/td>\n<\/tr>\n

Recommended Readings:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Richard. L. Burden and J. Douglas Fairies, Numerical Analysis, Brooks\/Cole, 2010.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 E. Isaacson and H. B. Keller, Analysis of Numerical Methods, Dover, 1994.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 F. Scheid, Numerical Analysis: Schaum\u2019s Outline Series, McGraw-Hill, 1989.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 H. F. Hildebrand, Introduction to Numerical Analysis, Dover, 1987.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div><\/div>\n<\/div>\n

Level \u2013 3<\/h3>\n

Course units effective from academic year 2016\/2017 to date<\/h4>\n
\n
<\/span>AMM301G3: Mathematical Programming<\/strong> <\/div>
\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Course Code<\/strong><\/td>\nAMM301G3<\/strong><\/td>\n<\/tr>\n
Course Title<\/strong><\/td>\nMathematical Programming<\/strong><\/td>\n<\/tr>\n
Credit Value<\/strong><\/td>\n03 <\/strong><\/td>\n<\/tr>\n
Prerequisites<\/strong><\/td>\nAMM203G3 <\/strong><\/td>\n<\/tr>\n
\u00a0<\/strong><\/p>\n

Hourly Breakdown<\/strong><\/td>\n

Theory<\/strong><\/td>\nPractical<\/strong><\/td>\nIndependent Learning<\/strong><\/td>\n<\/tr>\n
45<\/strong><\/td>\n—<\/strong><\/td>\n105<\/strong><\/td>\n<\/tr>\n
Objectives:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Introduce Mathematical Programming theory and models.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Enable to investigate and apply standard linear and nonlinear programming problems.<\/td>\n<\/tr>\n

Intended Learning Outcomes:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Apply dynamic programming technique to certain types of Mathematical Programming problem<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Solve deterministic programming problems using dynamic programming algorithm<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Construct the goal programming model\u00a0 problems<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Solve goal programming problems using modified simplex method<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Discuss the solution method of unconstrained nonlinear extremum problems<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Apply Lagrangian Multipliers method and Karush-Kuhn-Tucker (KKT) conditions to find local minimizers<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Solve fractional programming problems by modifying them into linear programming problems<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Utilize Wolfe\u2019s algorithm for solving quadratic programming problems<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Apply separable programming algorithm to solve nonlinear programming problems<\/td>\n<\/tr>\n

Course Contents:<\/strong><\/td>\n<\/tr>\n
Introduction to Mathematical Programming: <\/strong>History of Mathematical Programming, standard form, examples, successful applications and utility.<\/p>\n

Dynamic programming:<\/strong> Stage, State, Recursive equation, Developing optimal decision policy, Bellman\u2019s principal of optimality, characteristics of deterministic dynamic programming, solving linear programming problem using dynamic programming approach.<\/p>\n

Goal programming:<\/strong> Difference between linear programming and Goal programming approach, Model formulation, objectives of pre-emptive and non-pre-emptive programming, Modified Simplex method.<\/p>\n

Nonlinear programming:<\/strong> Fundamentals of optimization, types of problems, Optimality conditions for unconstrained and constrained problems, Lagrangian Multipliers method and Karush-Kuhn-Tucker conditions, Fractional programming, convert the Fractional programming problem into linear programming problem, Quadratic programming, Wolfe\u2019s algorithm, Wolfe\u2019s modified simplex method, Separable programming, separable function, piece wise linear approximation\u00a0of separable nonlinear programming problem, Separable programming algorithm.<\/td>\n<\/tr>\n

Teaching Methods:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Lectures,\u00a0 Tutorials, Handouts, Problem solving, Use of e-resources<\/td>\n<\/tr>\n
Assessment\/ Evaluation Details:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 In-course Assessments \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a030%<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 End-of-course Examination 70%<\/td>\n<\/tr>\n

Recommended Readings:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 W. L. Winston, Introduction of Mathematical Programming Applications and Algorithms, Duxbury press, California, 1995.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 F. S. Hillier and G. J. Lieberman, Introduction to Operations Research, 7th<\/sup> edition, McGrawHill, New York, 2001.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 H. A. Taha, Operations Research an Introduction, 8th<\/sup> edition, Pearson Prentice Hall, New Jersey, 2007.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div><\/div>\n

<\/span>AMM302G3: Classical Mechanics<\/div>
\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Course Code<\/strong><\/td>\nAMM302G3<\/strong><\/td>\n<\/tr>\n
Course Title<\/strong><\/td>\nClassical Mechanics<\/strong><\/td>\n<\/tr>\n
Credit Value<\/strong><\/td>\n03 <\/strong><\/td>\n<\/tr>\n
Prerequisites<\/strong><\/td>\nAMM101G3, AMM102G2, AMM103G3 <\/strong>\u00a0and AMM104G2 <\/strong><\/td>\n<\/tr>\n
\u00a0<\/strong><\/p>\n

Hourly Breakdown<\/strong><\/td>\n

Theory<\/strong><\/td>\nPractical<\/strong><\/td>\nIndependent Learning<\/strong><\/td>\n<\/tr>\n
45<\/strong><\/td>\n—<\/strong><\/td>\n105<\/strong><\/td>\n<\/tr>\n
Objectives:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Impart the principles and laws of classical mechanics<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Enable to derive the governing equations for standard systems, including the Lagrangian and Hamiltonian formulations<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Introduce the application of classical mechanics to standard rigid body problems and rotating systems<\/td>\n<\/tr>\n

Intended Learning Outcomes:<\/strong><\/td>\n<\/tr>\n
\n
    \n
  • Analyze\u00a0 kinematics of the three dimensional particle motion in different coordinate systems<\/li>\n
  • Discuss translational\/ rotational motion in three dimensions<\/li>\n
  • Formulate expressions for velocity and acceleration of a particle in a rotating frame<\/li>\n
  • Discuss motion of a particle moving near earth\u2019s surface<\/li>\n
  • Recall the angular momentum, moments of inertia, principal moment of inertia, moment of inertia tensor<\/li>\n
  • Discuss the motion of a rigid body in three dimensions with angular momentum and moments of inertia<\/li>\n
  • Apply Euler\u2019s equations of motion to rigid body motion<\/li>\n
  • Describe the motion of a mechanical system using Lagrange \/ Hamilton formalism<\/li>\n
  • Utilize \u00a0the canonical transformations<\/li>\n
  • Explain the\u00a0 motion of a spinning top by deriving and solving the equations of motion<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
Course Contents:<\/strong><\/td>\n<\/tr>\n
\u00a0<\/strong><\/p>\n

Motion of a particle: <\/strong>Equation of motion, components of velocity and \u00a0\u00a0acceleration in cylindrical coordinates and in spherical polar coordinates, Finite displacements, Infinitesimal displacements, rate of change of displacement referred to rotating axes and motion relative to earth.<\/p>\n

Motion of a rigid body: <\/strong>Definitions of moments of inertia and products of inertia, Radius of gyration, Moment of inertia with respect to a variable line, The momental ellipsoid , Principal axes and principal moments of inertia, Equations of motion of a rigid body, Euler\u2019s equation of motion and applications.<\/p>\n

Lagrange\u2019s equations:<\/strong> Degrees of freedom, Generalized coordinates, Generalized velocity, Holonomic and non-Holonomic systems, virtual displacement, virtual work, D\u2019Alembert\u2019s principle, Generalized force,\u00a0 Expression for Lagrangian, solving Lagrange\u2019s equations of motion, Application.<\/p>\n

Lagrange\u2019s equations for impulsive motion: <\/strong>Formulation and elementary applications.<\/p>\n

Hamilton\u2019s Equations: <\/strong>Equations of motion, Applications, Canonical transformations.<\/p>\n

Motion of spinning top:<\/strong> Eulerian angles, type of motions \u2013 Precession, Nutation and\u00a0\u00a0 Spin, Equations of motion.<\/td>\n<\/tr>\n

Teaching Methods:<\/strong><\/td>\n<\/tr>\n
\n
    \n
  • Lectures, Tutorials, Handouts, Problem solving, e-resources.<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
Assessment\/ Evaluation Details:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 In-course Assessments \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a030%<\/p>\n

\u00a0<\/strong><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 End-of-course Examination 70%<\/td>\n<\/tr>\n

Recommended Readings:<\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 C. E. Easthope, Three Dimensional Dynamics, 2nd<\/sup> edition, Butterworth & Co. Ltd., London, 1964.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 R. Douglas Gregory, Classical Mechanics, Cambridge University Press, 2006.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 H. Goldstein, C. Poole and J. Safko, Classical Mechanics, 3rd<\/sup> edition, Addison Wesley, 2000.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 D. A. Wells, Lagrangian Dynamics, Schaum\u2019s outline series, McGraw-Hill, Inc., 1967.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div><\/div>\n

<\/span>AMM303G2: Numerical Methods<\/div>
\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Course Code<\/strong><\/td>\nAMM303G2<\/strong><\/td>\n<\/tr>\n
Course Title<\/strong><\/td>\nNumerical Methods<\/strong><\/td>\n<\/tr>\n
Credit Value<\/strong><\/td>\n02<\/strong><\/td>\n<\/tr>\n
Prerequisites\u00a0 <\/strong><\/td>\nNone<\/strong><\/td>\n<\/tr>\n
\u00a0<\/strong><\/p>\n

Hourly Breakdown<\/strong><\/td>\n

Theory<\/strong><\/td>\nPractical<\/strong><\/td>\nIndependent Learning<\/strong><\/td>\n<\/tr>\n
30<\/strong><\/td>\n—<\/strong><\/td>\n70<\/strong><\/td>\n<\/tr>\n
Objectives:<\/em><\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Acquaint with the numerical methods for solving large systems of linear equations<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Familiarize the underlying mathematical concepts of computer aided numerical algorithms<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Enable to solve differential equations by using numerical methods<\/td>\n<\/tr>\n

Intended Learning Outcomes:<\/em><\/strong><\/td>\n<\/tr>\n
\n
    \n
  • Outline the fundamental concepts in numerical linear algebra<\/li>\n
  • Apply the matrix factorization algorithms to solve system of linear equations<\/li>\n
  • Determine bounds for relative error in the solution of a system of linear equations<\/li>\n
  • Examine the convergence of iterative methods for solving system of linear equations<\/li>\n
  • Use iterative methods to solve a system of linear equations<\/li>\n
  • Apply the numerical methods for certain types of differential equations<\/li>\n
  • Discuss the convergence of a numerical method applied to a differential equation<\/li>\n
  • Formulate basic algorithms in mathematical software<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n
Course Contents: <\/strong><\/td>\n<\/tr>\n
Elimination Methods:<\/em><\/strong> Linear algebra Review, Gaussian Elimination, LU factorization, Operations count, Pivoting, PLU factorization, types of solutions<\/p>\n

Error Analysis:<\/em><\/strong> Vector and Matrix norms, perturbation, perturbation bounds, residual, residual bounds, iterative refinement<\/p>\n

Iterative Methods:<\/em><\/strong> Construction of iterative algorithms, Jacobi Method, Gauss Seidel Method, convergence, conditioning<\/p>\n

Numerical Methods for Differential Equations:<\/em><\/strong> Differential Equations Review, Initial Value problems, Euler Methods, Linear Multistep methods, order, consistency, convergence, stability.<\/td>\n<\/tr>\n

Teaching Methods:<\/em><\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Lectures,\u00a0 Tutorials, Handouts, Problem solving, \u00a0e-resources<\/td>\n<\/tr>\n
Assessment\/ Evaluation Details:<\/em><\/strong><\/td>\n<\/tr>\n
\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 In-course Assessments\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 30%<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 End-of-course Examination\u00a0\u00a0\u00a0 70%<\/td>\n<\/tr>\n

Recommended Readings:<\/em><\/strong><\/td>\n<\/tr>\n
\n
    \n
  • N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM, 1997.<\/li>\n
  • G. Golub and V. L. Charles, Matrix Computations, John Hopkins University Press, 1996.<\/li>\n
  • R. Dormand, Numerical Methods for Differential Equations: A computational Approach, Taylor and Francis, 1996.<\/li>\n
  • D. Griffiths and D. Higham, Numerical Methods for Ordinary Differential Equations, Springer, 2010.\u00a0 <\/em><\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div><\/div>\n
    <\/span>AMM304G2: Fluid Dynamics II<\/div>
    \n
    \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
    Course Code<\/strong><\/td>\nAMM304G2<\/strong><\/td>\n<\/tr>\n
    Course Title<\/strong><\/td>\nFluid Dynamics II<\/strong><\/td>\n<\/tr>\n
    Credit Value<\/strong><\/td>\n02<\/strong><\/td>\n<\/tr>\n
    Prerequisites <\/strong><\/td>\nAMM101G3, AMM103G3 and AMM202G2 <\/strong><\/td>\n<\/tr>\n
    \u00a0<\/strong><\/p>\n

    Hourly Breakdown<\/strong><\/td>\n

    		Theory<\/strong><\/td>\nPractical<\/strong><\/td>\nIndependent Learning<\/strong><\/td>\n<\/tr>\n
    30<\/strong><\/td>\n—<\/strong><\/td>\n70<\/strong><\/td>\n<\/tr>\n
    Objectives:<\/strong><\/td>\n<\/tr>\n
    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Introduce the fundamentals of Hydrostatics and its applications<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Formulate the constitutive equations of Hydrodynamics<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Provide the solution methods for fluid mechanics problems<\/td>\n<\/tr>\n

    Intended Learning Outcomes:<\/strong><\/td>\n<\/tr>\n
    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Define the center of pressure<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Determine center of pressure and pressure on immersed bodies<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Recall the elements of Hydrodynamics<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Outline the laws of thermodynamics<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Formulate the constitutive equations of Fluid motion<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Explain the driven flows and rotating flows<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Analyze the fundamentals of water waves<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Discuss the nature of incompressible Newtonian turbulent flows<\/td>\n<\/tr>\n

    Course Contents:<\/strong><\/td>\n<\/tr>\n
    Hydrostatics:<\/strong><\/p>\n

    Definition of center of pressure, Formula for finding center of pressure, Center of pressure on certain type of objects and illustrative examples, effect of further immersion, Liquids more than one, The center of pressure of a plane area lies vertically beneath the center of the superincumbent fluid.<\/p>\n

    Hydrodynamics:<\/strong><\/p>\n

    Fundamentals of fluid mechanics: Microscopic and macroscopic properties of liquids and gases, the continuum hypothesis, review of thermodynamics, general equations of motion, surface gravity waves, buoyancy \u2013 driven flows, rotating flows.<\/p>\n

    Water Waves: 1D free boundary problems, progressive waves, infinite and finite depth, wave speed, dispersion and group velocity.<\/p>\n

    Incompressible Newtonian fluids: introduction of concepts, viscosity, Reynolds number and turbulence.<\/td>\n<\/tr>\n

    Teaching Methods:<\/strong><\/td>\n<\/tr>\n
    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Lectures, tutorial discussions and e-resources<\/td>\n<\/tr>\n
    Assessment\/ Evaluation Details:<\/strong><\/td>\n<\/tr>\n
    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 In-course Assessments \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a030%<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 End-of-course Examination \u00a0\u00a0\u00a070%<\/td>\n<\/tr>\n

    Recommended Readings:<\/strong><\/td>\n<\/tr>\n
    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 M. D. Raisinghana, Fluid Dynamics, S. Chand Publishing, 2003.<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 J. Williams, Fluid Mechanics, problem solvers, George Allen & Unwin Ltd, 1974.<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 J. Alexandre, A mathematical Introduction to Fluid Mechanics, Springer, 1993.<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 M. Ray and H. S. Sharma, A text book of Hydrostatics Sultan Chand & Company, 2000.<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 P. Kundu and I. Cohen, Fluid mechanics, Academic Press, 2011.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div><\/div>\n

    <\/span>AMM305G2: Mathematical Modeling<\/div>
    \n
    \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
    Course Code<\/strong><\/td>\nAMM305G2<\/strong><\/td>\n<\/tr>\n
    Course Title<\/strong><\/td>\nMathematical Modeling <\/strong><\/td>\n<\/tr>\n
    Credit Value<\/strong><\/td>\n02<\/strong><\/td>\n<\/tr>\n
    Prerequisites<\/strong><\/td>\nNone<\/strong><\/td>\n<\/tr>\n
    \u00a0<\/strong><\/p>\n

    Hourly Breakdown<\/strong><\/td>\n

    		Theory<\/strong><\/td>\nPractical<\/strong><\/td>\nIndependent Learning<\/strong><\/td>\n<\/tr>\n
    30<\/strong><\/td>\n—<\/strong><\/td>\n70<\/strong><\/td>\n<\/tr>\n
    Objectives:<\/strong><\/td>\n<\/tr>\n
    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Provide knowledge and skills to build mathematical models of real-world problems, analyze them and make predictions about behavior of problems taken from physics, biology, chemistry, economics and other fields.<\/td>\n<\/tr>\n
    Intended Learning Outcomes:<\/strong><\/td>\n<\/tr>\n
    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Recall the modeling techniques for real world problems<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Describe the mathematical model for given word problems<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Sketch the solution of the formulated model problems involving Differential equations<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Analyze the solution and behavior of Differential equation models<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Modify the simple models for the change of environment<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Solve single species population models<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Discuss interacting two species population models<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Analyze selected Models and Case studies<\/td>\n<\/tr>\n

    Course Contents:<\/strong><\/td>\n<\/tr>\n
    Introduction:<\/strong> Basic approach of Mathematical Modeling, its needs, types of models and limitations, setting up mathematical models for simple problems in words.<\/p>\n

    Differential Equations:<\/strong> Direction field, solution sketch, phase portrait, equilibrium solution, stability.<\/p>\n

    Single species population models:<\/strong> Basic concepts, Exponential growth model, formulation, solution, interpretation and limitations, Compensation and dispensation, Logistic growth model, formulation, solution, interpretation and limitations.<\/p>\n

    Two species population models:<\/strong> Types of interaction between two species. Lotka-Volterra prey-predator model, formulation, solution, interpretation and limitations. Lotka-Volterra model of two competing species, formulation, solution, interpretation and limitations.<\/p>\n

    Selected Models and Case studies:<\/strong> Models from Biology\/Medicine\/Social Science\/Engineering\/Physics – Especially epidemic model, SIR model, diffusion model, combat model, discrete models, election model.<\/td>\n<\/tr>\n

    Teaching Methods:<\/strong><\/td>\n<\/tr>\n
    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0 Lectures, Tutorial discussions, Handouts and e-resources.<\/td>\n<\/tr>\n
    Assessment\/ Evaluation Details:<\/strong><\/td>\n<\/tr>\n
    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 In-course assessment\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a030%<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 End of course Examination\u00a0\u00a0\u00a0\u00a0 70%<\/td>\n<\/tr>\n

    Recommended Readings:<\/strong><\/td>\n<\/tr>\n
    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 M. Braun, C. S. Coleman, and D. A. Drew, Vol. 1, Vol. 2 and Vol.3 – Differential Equation Models, Springer-Verlag, New York, 1983.<\/p>\n

     <\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 W. Meyer, Concepts of Mathematical Modeling, McGraw Hill, New York, 1994.<\/p>\n

     <\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Moghadas, S. M. and Douraki, M. J., Mathematical Modeling: A Graduate Textbook, Wiley, 2018.<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Tung, K. K., Topics in Mathematical Modeling, illustrated edition, Princeton University Press, 2007.<\/p>\n

    \u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Meerschaert, M. M., Mathematical Modeling, 2nd<\/sup> edition, Academic Press, 1999.<\/p>\n

     <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

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