# Virtual University of Pakistan

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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

 Topic Lecture Resource Page Introduction 1 Errors Computation. 2 Bisection Method 3 Regula-Falsi Method 4 Method of Iteration 5 Newton Raphson Method 6 Secant Method 7 Muller's Method 8 Assignment # 01 Gaussian Elimination Method 9 Gauss-Jordan Elimination Method 10 Jacobi Method 11 Gauss-Seidel Iteration Method 12 Relaxation Method 13 Quiz # 01 Matrix Inversion 14 Power Method 15 Jacobi's Method 16 Jacobi's Method 17 Finite Difference Operators 18 Finite Difference Operators 19 Finite Operators 20 GDB # 01 Newton's Forward Difference Formula 21 Newton's Backward Difference Formula 22 Mid Term Exams Langrange Interpolation Formula 23 Introduction to Divided Differences with examples 24 Newton's Divided Difference Interpolation Formula with Error Term 25 Differentiation Using Difference Operators 26 Differentiation Using Difference Operators (continued) 27 Differentiation Using Interpolation 28 Assignment # 02 Richardson’s Extrapolation Method 29 Newton-Cotes Integration Formulae 30 Trapezoidal and Simpsons Rules 31 Trapezoidal and Simpsons Rules (continue) 32 Rombergs Integration and Double Integration 33 Quiz # 2 Taylo's series method 34 Euler Method 35 Runge-Kutta Method 36 Runge-Kutta Method (continued) 37 Adam-Moultan’s Predictor-Corrector Method 38 Adam-Moultan’s Predictor-Corrector Method 39 GDB # 02 40 Examples of Numerical Differentiation 41 An Introduction to MAPLE 42 Algorithms for method of Solution of Non-linear Equations 43 Non-linear Equations 44 Final Term