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MTH603 : Numerical Analysis

Course Overview

Course Synopsis

Emphasis will be laid, in this course, on learning the Numerical methods to solve the Linear, Non-linear Equations, Interpolation and Different Numerical Methods to solve the problems of Integration, Differentiation and Differential Equations that cannot be solved exactly by the Integration and Differentiation Techniques. So, the use of Numerical Techniques for these sorts of problems will be very handy.

Course Learning Outcomes

At the end of the course, you should be able to:

  • Describe difficulties that can arise because computers usually use finite precision.
  • Grasp the numerical techniques and should be able to use a variety of methods in solving real-life, practical, technical, and theoretical problems which cannot be solved by other methods.
  • Apply the Bisection, Regula Falsi, Newton and Iteration methods to solve a non-linear equation
  • Apply the different method to solve linear Equations
  • Construct Lagrange and Newton forward difference interpolation polynomials for a given set of data.
  • Apply Trapezoidal and Simpson’s rules to find the approximate value of an integral.
  • Describe the basic concepts behind the R-K method and apply specific R-K methods in given problems.

Course Calendar

Errors Computation.2
Bisection Method3
Regula-Falsi Method4
Method of Iteration5
Newton Raphson Method6
Secant Method7
Muller's Method8
Assignment # 01
Gaussian Elimination Method9
Gauss-Jordan Elimination Method10
Jacobi Method11
Gauss-Seidel Iteration Method12
Relaxation Method13
Quiz # 01
Matrix Inversion14
Power Method15
Jacobi's Method16
Jacobi's Method17
Finite Difference Operators18
Finite Difference Operators19
Finite Operators20
GDB # 01
Newton's Forward Difference Formula21
Newton's Backward Difference Formula22
Mid Term Exams
Langrange Interpolation Formula23
Introduction to Divided Differences with examples24
Newton's Divided Difference Interpolation Formula with Error Term25
Differentiation Using Difference Operators26
Differentiation Using Difference Operators (continued)27
Differentiation Using Interpolation28
Assignment # 02
Richardson’s Extrapolation Method29
Newton-Cotes Integration Formulae30
Trapezoidal and Simpsons Rules31
Trapezoidal and Simpsons Rules (continue)32
Rombergs Integration and Double Integration33
Quiz # 2
Taylo's series method34
Euler Method35
Runge-Kutta Method36
Runge-Kutta Method (continued)37
Adam-Moultan’s Predictor-Corrector Method38
Adam-Moultan’s Predictor-Corrector Method39
GDB # 02
Examples of Numerical Differentiation41
An Introduction to MAPLE42
Algorithms for method of Solution of Non-linear Equations43
Non-linear Equations44
Final Term
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