Introduction to programming in MATLAB, examples. Error definitions, Taylor series and error propagation. (6hrs)

Roots of equations – Bisection method, fixed point iteration, Newton-Raphson method, secant method, systems of nonlinear equations. Numerical linear algebra – Gauss elimination, LU decomposition, matric inversion, power method for finding eigen values, QR factorisation. (11 hrs)

Curve Fitting – Linear regression, polynomial regression, nonlinear regression, Newton’s divided difference interpolation, Lagrange interpolation. (8 hrs)

Numerical Integration and Differentiation – Trapezoidal rules, Simpson’s rules, Newton-Cotes algorithm, Gauss quadrature, high accuracy differentiation formulas, Richardson extrapolation, partial derivatives. (8 hrs)

Objectives

• To familiarize different numerical methods to solve engineering problems.
• To write computer programs and use toolboxes in the software packages.
• To select a specific numerical method to solve practical problems.

Course Outcomes

• CO1: Solve linear and nonlinear algebraic equations and systems of nonlinear equations using numerical. techniques.
• CO2: Use regression and interpolation methods for curve fitting.
• CO3: Select and apply numerical schemes for differentiating and integrating complicated functions
• CO4: Apply computational schemes for solving systems of ordinary differential equations.
• CO5: Solve PDEs by numerical methods

CO – PO Mapping

Textbook(s)

• Numerical Methods for Engineers, Steven Chapra and Raymond Canale, 7^th Edition, McGraw Hill, 2015.
• Applied Numerical Analysis, LaureneFausett, 2^nd Edition, Pearson, 2008.
• Advanced Engineering Mathematics, Erwin Kreyszig, 10^th Edition, Wiley, 2015.

Evaluation Pattern