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. (C3)
CLO: 2. to analyze complex numbers and variables. (C4)
CLO: 3. to justify his/her analysis of various engineering problems by concepts of Numerical Analysis. (A3)
CLO: 4. to perform simple calculations related to numerical analysis in software (Mat Lab or Mathematica). (C3)

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