Mathematical Methods in Engineering and Science

Dasgupta, B. (Bhaskar)

Preliminary Backgroung ; Matrices and Linear Transformations ; Operational Fundamentals of Linear Algebra ; System of Linear Equations ; Gausss Elimination Family of Methods ; Special Systems and Special Methods ; Numerical Aspects in Linear Systems; Eigenvalues and Eigenvectors ; Diagonalization and Similarity Transformations ; Jacobi and Givens Rotation Methods ; householder Transformation and Tridiagonal Matrices ; QR Decomposition Method; Eigenvalue Problem of General Matrices; singular Value Decomposition; Vector Spaces: Fundamental Concepts; Multivariate Calculus; Vactor Analysis: Curves and Surfaces; Scalar and Vector Fields; Polynomial Equations; Solution of Nonlinear Equations and SYstems; Optimization Introduction; Multivariate Optimization; Methods of Nonlinear Optimization; Constrained Optimization; Linear and Quadratic Programming Problesm; Interpolation and Approximation; Basic Methods of Numerical Interpolation; Advanced Topics in Numerical Intergration; Numerical Solution of Ordinary Differential Equations; ODE Solutions Advanced Issues; Existence and Uniqueness Theory; First Order Ordinary Differential Equations; Second Order Linear Homogeneous Equations ; Second Order Linear Homogeneous and Non-Homogeneous ODE's ; Higher Order Linear ODE's ; Laplace Transform ; ODE systems ; Stability of Dynamic Systems; Series Solutions and Special Functions ; Sturm-Liouville theory; Fourier Series and Integrals; Fourier Transforms ; Minimax Approximation; Partial Differential Equations; Analytic Functions; Integrals in the Complex Plane; Singularities of Complex Functions;

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National Programme on Technology Enhanced Learning (NPTEL)

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