Computational Techniques

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2 STUDENTS

Contents:
Introduction : Motivation and applications.

Computation and Error Analysis : Accuracy and precision; Truncation and round-off errors; Binary Number System; Error propagation.

Linear Systems and Equations : Matrix representation; Cramer’s rule; Gauss Elimination; Matrix Inversion; LU Decomposition; Iterative Methods; Relaxation Methods; Eigen Values.

Algebraic Equations : Bracketing methods: Bisection, Reguli-Falsi; Open methods: Secant, Fixed point iteration, Newton-Raphson; Multivariate Newton’s method.

Regression and Curve Fitting : Linear regression; Least squares; Total Least Squares; Interpolation; Newton’s Difference Formulae; Cubic Splines.

Numerical Differentiation : Numerical differentiation; higher order formulae.
Integration and Integral Equations : Trapezoidal rules; Simpson’s rules; Quadrature.

ODEs: Initial Value Problems : Euler’s methods; Runge-Kutta methods; Predictor-corrector methods; Adaptive step size; Stiff ODEs.

ODEs: Boundary Value Problems : Shooting method; Finite differences; Over/Under Relaxation (SOR).
PDEs : Introduction to Partial Differential Equations.

Course Curriculum

Mod-01 Lec-01 Introduction Details 53:53
Mod-02 Lec-02 Computational and Error Analysis Details 51:31
Mod-03 Lec-03 Linear Equations Part 1 Details 53:48
Mod-03 Lec-04 Linear Equations Part 2 Details 54:46
Mod-03 Lec-05 Linear Equations Part 3 Details 57:48
Mod-03 Lec-06 Linear Equations Part 4 Details 57:2
Mod-03 Lec-07 Linear Equations Part 5 Details 57:9
Mod-03 Lec-08 Linear Equations Part 6 Details 57:21
Mod-04 Lec-09 Non Linear Algebraic Equations Part 1 Details 1:5:18
Mod-04 Lec-10 Non Linear Algebraic Equations Part 2 Details 1:1:46
Mod-04 Lec-11 Non Linear Algebraic Equations Part 3 Details 50:36
Mod-04 Lec-12 Non Linear Algebraic Equations Part 4 Details 41:1
Mod-04 Lec-13 Non Linear Algebraic Equations Part 5 Details 52:55
Mod-04 Lec-14 Non Linear Algebraic Equations Part 6 Details 52:38
Mod-05 Lec-15 Regression and Interpolation Part 1 Details 51:56
Mod-05 Lec-16 Regression and Interpolation Part 2 Details 48:21
Mod-05 Lec-17 Regression and Interpolation Part 3 Details 56:2
Mod-05 Lec-18 Regression and Interpolation Part 4 Details 50:55
Mod-05 Lec-19 Regression and Interpolation Part 5 Details 57:10
Mod-06 Lec-20 Differentiation and Integration Part 1 Details 57:15
Mod-06 Lec-21 Differentiation and Integration Part 2 Details 53:4
Mod-06 Lec-22 Differentiation and Integration Part 3 Details 55:19
Mod-06 Lec-23 Differentiation and Integration Part 4 Details 54:57
Mod-06 Lec-24 Differentiation and Integration Part 5 Details 57:48
Mod-07 Lec-25 Ordinary Differential Equations (initial value problems) Part 1 Details 50:30
Mod-07 Lec-26 Ordinary Differential Equations (initial value problems) Part 2 Details 49:31
Mod-07 Lec-28 Ordinary Differential Equations (initial value problems) Part 4 Details 50:52
Mod-07 Lec-29 Ordinary Differential Equations (initial value problems) Part 5 Details 56:30
Mod-07 Lec-30 Ordinary Differential Equations (initial value problems) Part 6 Details 53:8
Mod-07 Lec-31 Ordinary Differential Equations (initial value problems) Part 7 Details 54:58
Mod-07 Lec-32 Ordinary Differential Equations (initial value problems) Part 8 Details 52:51
Mod-07 Lec-33 Ordinary Differential Equations (initial value problems) Part 9 Details 54:29
Mod-07 Lec27 Ordinary Differential Equations (initial value problems) Part 3 Details 54:7
Mod-08 Lec-34 Ordinary Differential Equations (boundary value problems) Part 1 Details 51:45
Mod-08 Lec-35 Ordinary Differential Equations (boundary value problems) Part 2 Details 50:10
Mod-08 Lec-36 Ordinary Differential Equations (boundary value problems) Part 3 Details 48:9
Mod-09 Lec-37 Partial Differential Equations Part 1 Details 50:45
Mod-09 Lec-38 Partial Differential Equations Part 2 Details 56:16
Mod-09 Lec-39 Partial Differential Equations Part 3 Details 51:39
Mod-09 Lec-40 Partial Differential Equations Part 4 Details 51:53

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