MSE617A - Mathematics and Computational Methods

1 Introduction of functions, vectors, matrices 2. Partial Differentiation (Total differentiation, Maximum and minimum: method of Lagrange multipliers, Change of variables: Legendry transformation, Differentiation of integral; Leibniz rule) 3. Multiple Integration (Change of variable: Jacobean, Surface and volume integrals) 4. Vectors (Geometry: Lines and planes, Directional derivative, gradients (fields, equipotential, grad, normal to surface, curl, div), Line integration (conservative fields, potential, exact differentiation), Green, Stokes, Div and Curl theorems 5. Coordinate Transformation (Linear transform, Orthogonal transform, Eigen values: diagonalization of matrix) 6. Ordinary differential equations (Linear first order, Second order: constant coefficient and zero right hand side, Second order: constant coefficient and non zero right hand side) 7. Statistics. Introduction to random experiment, computing probability of an event.