Mathematical Methods in Engineering and Science


Lecture 1 - Introduction


Lecture 2 - Basic Ideas of Applied Linear Algebra


Lecture 3 - Systems of Linear Equations


Lecture 4 - Square Non-Singular Systems


Lecture 5 - Ill-Conditioned and Ill-Posed Systems


Lecture 6 - The Algebraic Eigenvalue Problem


Lecture 7 - Canonical Forms, Symmetric Matrices


Lecture 8 - Methods of Plane Rotations


Lecture 9 - Householder Method, Tridiagonal Matrices


Lecture 10 - QR Decomposition, General Matrices


Lecture 11 - Singular Value Decomposition


Lecture 12 - Vector Space: Concepts


Lecture 13 - Multivariate Calculus


Lecture 14 - Vector Calculus in Geometry


Lecture 15 - Vector Calculus in Physics


Lecture 16 - Solution of Equations


Lecture 17 - Introdcution to Optimization


Lecture 18 - Multivariate Optimization


Lecture 19 - Constrained Optimization: Optimality Criteria


Lecture 20 - Constrained Optimization: Further Issues


Lecture 21 - Interpolation


Lecture 22 - Numerical Integration


Lecture 23 - Numerical Solution of ODE's as IVP


Lecture 24 - Boundary Value Problems, Question of Stability in IVP Solution


Lecture 25 - Stiff Differential Equations, Existence and Uniqueness Theory


Lecture 26 - Theory of First Order ODE's


Lecture 27 - Linear Second Order ODE's


Lecture 28 - Methods of Linear ODE's


Lecture 29 - ODE Systems


Lecture 30 - Stability of Dynamic Systems


Lecture 31 - Series Solutions and Special Functions


Lecture 32 - Sturm-Liouville Theory


Lecture 33 - Approximation Theory and Fourier Series


Lecture 34 - Fourier Integral to Fourier Transform, Minimax Approximation


Lecture 35 - Separation of Variables in PDE's, Hyperbolic Equations


Lecture 36 - Parabolic and Elliptic Equations, Membrane Equation


Lecture 37 - Analytic Functions


Lecture 38 - Integration of Complex Functions


Lecture 39 - Singularities and Residues


Lecture 40 - Calculus of Variations