Numerical Analysis (MTCE2063)

Pre-requisite(s)

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%)