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.