# Applied Numerical Methods for EC Engineers (BEC306D)

## Applied Numerical Methods for EC Engineers

### Module-1:

Errors in computations and Root of the equations Approximations and Round Off -Errors in computation: Error definitions, Round-Offerrors, Truncation errors and the Taylor series-The Taylor series, Error Propagation, Total numerical error,Absolute,Relative and percentage errors,Blunders, Formulation errors and data uncertainty. Roots of equations: Simple fixed point iteration methods. Secant Method, Muller’s method, and Graeffe’s Roots Squaring Method. Aitkin’s Method. (8 hours) (RBT Levels: L1, L2 and L3)

### Module-2:

Solution of System of Linear Equations Rank of the matrix, Echelon form, Linearly dependent and independent equations, Solutions for linear equations, Partition method, Croute's Triangularisation method. Relaxation method. Solution of non-linear simultaneous equations by Newton-Raphson method. Eigen Values and properties, Eigen Vectors, Bounds on Eigen Values, Jacobi’s method, Given’s method for symmetric matrices. (8 hours) (RBT Levels: L1, L2 L3) @#12102023 @#12102023

### Module-3:

Curve Fitting Least-Squares Regression: Linear Regressions, Polynomial regressions, Multiple Linear regressions, General Linear Least squares, Nonlinear Regressions, QR Factorization. Curve Fitting with Sinusoidal Functions Introduction to Splines,Linear Splines, Quadratic Splines, Cubic Splines. Bilinear Interpolation. (8 hours) (RBT Levels: L1, L2 L3)

### Module-4:

Numerical integration, Difference equations and Boundary Value Problems Romberg’s method, Euler-Maclaurin formula, Gaussian integration for n = 2 and n=3. Numerical double integration by trapezoidal and Simpson’s 1/3 rd rule. Solution of linear difference equations. Boundary-Value Problems, Introduction. The Shooting Method, Finite-Difference Methods (8 hours) (RBT Levels: L1, L2 and L3)

### Module-5:

Numerical solution of partial differential equations Classifications of second-order partial differential equations,Finite difference approximations to partial derivatives. Solution of:Laplace equation, Poisson equations, one-dimensional heat equation and wave equations. (8 hours) (RBT Levels: L1, L2 and L3)

#### Suggested Learning Resources: Books

1. Steven C. Chapra & Raymond P. Canale: “Numerical Methods for Engineers and Scientists”, McGraw Hill, 8th Edition, 2020.
2. Steven C. Chapra: “Applied Numerical Methods with MATLAB for Engineers and Scientists”, McGraw Hill, Fifth Edition, 2023.
3. B. S. Grewal: “Numerical Methods in Engineering & Science with programs in C, C++ and MATLAB”, Khanna Publishers, 10 h Ed., 2015.

#### Reference Books:

1.John H. Mathews & Kurtis D. Frank: “Numerical Methods Using MATLAB”, PHI Publications, 4th Edition, 2005.
2.Won Young Yang, Wenwu Cao, Tae Sang Chung, John Morris: “Applied Numerical Methods Using MATLAB” , WILEY Interscience, Latest Edition, 2005.