COURSE OBJECTIVES

• To introduce various techniques for solving (i) linear, non-linear, and difference equations using various numerical methods and (ii) complex numbers and variables.
• To apply gained knowledge to solve practical problems.

COURSE LEARNING OUTCOMES (CLO)

CLO: 1. To solve problems of non-linear equations, interpolation, numerical differentiation/integration and linear simultaneous equations.
CLO: 2. To analyze complex numbers and variables.
CLO: 3. To justify his/her analysis of various engineering problems by concepts of Numerical Analysis.
CLO: 4. To perform simple calculations related to numerical analysis in software (Mat Lab or Mathematica).

COURSE CONTENTS

1. Solution of Non-Linear Equations
• Bisection method
• Newton’s method
• Secant method
• Method of false position
• Method of successive approximation
2. Interpolation
• Basic idea
• Taylor’s polynomial
• Lagrange’s formula of interpolation
3. Numerical Differentiation and Integration
• Numerical differentiation
• Review of integration concept and their physical significance for Engineering
• Trapezoidal and Simpson’s rule numerical integration techniques
4. Solution of Linear Simultaneous Equations
• Gaus Elimination and Gaus-Jordan methods
• Numerical solution of differential equations
• Euler and modified Euler methods
• Runge-Kutta methods
5. Complex Numbers
• Basic operations
• Graphical representations
• Polar and exponential forms of complex numbers
• De’moivre’s theorem with applications
6. Complex Variables
• Limit, continuity, zeros and poles
• Cauchy-Reimann Equations
7. Use of Softwares
• Matlab
• Mathmatica