Engineering Mathematics III

At the end of the course, the students should be able to: 1. demonstrate a clear understanding of the

, that is, possess a breadth of knowledge in the area covered; 2. possess an in-depth knowledge upon which a solid foundation can be built in order to demonstrate a depth of understanding in advanced mathematical topics; 3. develop simple algorithms and use computational proficiency; 4. write simple proofs for theorems and their applications; and 5. communicate the acquired mathematical knowledge effectively in speech, writing and collaborative groups. Course Contents Linear Algebra. Elements of Matrices, Determinants, Inverses of Matrices. Theory of Linear Equations. Eigen Values and Eigen Vectors. Analytical Geometry. Coordinate Transformation. Solid Geometry. Polar, cylindrical and spherical coordinates. Elements of functions of several variables. Surface Variables. Ordinary Integrals. Evaluation of Double Integrals, Triple Integrals, Line Integrals and Surface Integrals. Derivation and Integrals of Vectors. The gradient of scalar quantities. Flux of Vectors. The curl of a vector field, Gauss, Greens and Stoke’s theorems and applications. Singular Valued Functions. Multivalued Functions. Analytical Functions. Cauchy Riemann’s Equations. Singularities and Zeroes. Contour Integration including the use of Cauchy’s Integral Theorems. Bilinear transformation. GET 302: Engineering Mathematics IV (3 UnitsC: LH 45) Learning Outcomes At the end of the course, the students should be able to: 1. solve second order differential equations; 2. solve partial differential equations; 3. solve linear integral equations; 4. relate integral transforms to solution of differential and integral equations; 5. explain and apply interpolation formulas; and 6. apply Runge-Kutta and other similar methods in solving ODE and PDEs. Course Contents Series solution of second order linear differential equations with variable coefficients. Bessel and Legendre equations. Equations with variable coefficients. Sturm-Liouville boundary value problems. Solutions of equations in two and three dimensions by separation of variables. Eigen value problems. Use of operations in the solution of partial differential equations and Linear integral equations. Integral transforms and their inverse including Fourier, Laplace, Mellin and Handel Transforms. Convolution integrals and Hilbert Transforms. Calculus of finite differences. Interpolation formulae. Finite difference equations. RungeKutta and other methods in the solutions of ODE and PDEs. Numerical integration and differentiation.