None

### Recommended Book(s)

Numerical Analysis, Scheid, Schaum Series, Latest Edition

### Reference Book(s)

Complex Variables, Murray R. Spiegel, Schaum Series, Latest Edition

## COURSE OBJECTIVES

1. To introduce various techniques for solving linear, non-linear, and difference equations using various numerical methods.

2. To apply gained knowledge to solve practical problems.

## COURSE LEARNING OUTCOMES (CLO)

CLO:1              Learn solution of non-linear equations.

CLO:2              Understand finite difference.

CLO:3              Be able to do numerical integration.

CLO:4              Solve linear simultaneous equations.

CLO:5              Recognize complex variables.

## COURSE CONTENTS

### Solution Of Non-Linear Equations

• Bisection method
• Newton’s method
• Secant method
• Method of false position
• Method of successive approximation

### Finite Differences

• Finite differences
• Difference operators and tables
• Differences of polynomials
• Newton’s and Gauss interpolating techniques for equally spaced data
• Simple theorems on divided differences
• Newton’s formula for unequal intervals
• Lagrange’s formula of interpolation
• Numerical differentiation

### Numerical Integration

• Review of integration concept and their physical significance for Engineering
• Trapezoidal and Simpson’s rule numerical integration techniques

### Solution Of Linear Simultaneous Equations

• Jacobi’s method, Gauss-Seidal method
• Sparse matrices, Solution of differential equation
•  Euler and modified Euler methods
• Runge-Kutta method

### Complex Variables

• Limit, continuity, zeros and poles
• Cauchy-Reimann Equations
• Conformal transformation
• Contour integration

## MAPPING OF CLOs TO PROGRAM LEARNING OUTCOMES

 CLO’s CLO-1 (Learn  non-linear equation) CLO-2  (Understand Finite Differences) CLO-3  (Able to do Numerical Integration) CLO-4 (Solving Linear Simultaneous Equations) CLO-5 (Recognizing Complex Variables) PLO’s PLO-1 (Engineering Knowledge) PLO-2 (Problem Analysis) PLO-3 (Design/Development of Solutions) √ √ √ PLO-4 (Investigation) √ √ PLO-5 (Modern Tool Usage) PLO-6 (The Engineer and Society) PLO-7 (Environment and Sustainability) PLO-8 (Ethics) PLO-9 (Individual and Team work) PLO-10 (Communication) PLO-11 (Project Management) PLO-12 (Lifelong Learning)

## MAPPING OF CLOs TO ASSESSMENT MODULES

 CLOs CLO:1 CLO:2 CLO:3 CLO:4 CLO:5 Assessment Modules Assignments (20-25%) √ √ √ √ Quizzes (15-20%) √ √ √ √ Midterm Exam (20%) √ √ √ Final Exam (40-45%) √ √ √ √ √