WEBVTT

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Welcome to the e-Learning of the course numerical analysis.

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I am from Prof. Mudumangal Pal from Vidyasagar University.

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I will teaching the numerical analysis.

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This is also known as numerical methods.

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A problem particularly a mathematical problem can be solved in to

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three different methods and gives three different types of solutions.

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The first method is known as analytical method

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and it gives analytical or compact solution.

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The second method is known as series solution and it gives

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solution is in infinite series form.

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The third method is known as numerical method.

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The analytical method gives analytical solution or compact solution,

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that means the solution in our conventional form.

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The main advantage of this method is that this method gives exact solution

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that mean there is no error

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but the main drawback of this method is that,

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the method is complicated for some particular type of problems

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and needs lot of complicated mathematical formula.

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If the analytical method is not suitable or complicated to solve a particular problem,

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then we will go to series solution method.

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But the main drawback of this method is that

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the solution obtained by this method

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is valid only for the integral of convergence of The Infinite series.

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If the method is not suitable for a particular type of problems,

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then we will go to the last method that means the numerical method.

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The numerical method is very simple to use to solve a particular problem

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for example to find the integration of a function.

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There is a very simple formula, algebric formula

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to find the integration of that particular function

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and this formula gives the solution

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of almost all kind of function in a simple way.

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But the main drawback of numerical method is the method gives

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erroneous solution.

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Thus to solve a problem first we apply the analytical method.

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If the method is not suitable or complicated for a particular problem

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then we shall go to the series solution method

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and if this method is also complicated for a particular problem,

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then we will go to the last method that means to the numerical method.

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The numerical method gives erroneous solution even then

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this method is widely used by mathematicians, computer scientist,

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statisticians, engineers and many other people.

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The numerical method is mainly used

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to solve a particular problem with the help of computer.

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Thus the numerical method is a multidisciplinary method.

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Now I coming to the distribution of the course the entire course is

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divided into 9 chapters and 36 modules.

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In 1st chapter you will learn different sources of errors,

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causes of errors and type of errors.

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In Chapter 2 you will learn

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different beautiful and interesting method of interpolation.

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Chapter 3 is devoted for approximation of functions.

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In chapter 4 you will study different method to solve

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a nonlinear equations.

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Chapter 5 is devoted to solve

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system of linear equation by various interesting methods.

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You will learn different methods to find eigenvalues and eigenvectors

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in Chapter 6.

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In Chapter 7 you will learn the numerical derivative methods

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and numerical integration.

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In chapter 8 is devoted to solve ordinary Differential Equation

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by different methods.

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In chapter 9 you will learn finite difference method

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to solve partial differential equations.

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Lot of C programs are given to sort certain problems.

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This is a four credit course.

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To study this course you have to learn

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or you have to know the basic ideas of Calculus

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and algebra of undergraduate standard.

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Also to understand the C programs

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the basic knowledge of C programming is required.

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I believe that after finishing this course,

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you will be able to solve lot of mathematical problems,

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with the help of numerical methods

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as well as with the help of computers.

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At the end of each module there is a self-assessment containing MCQ,

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true and false type question, fill in the blanks

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& long answer type question.

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Hope you will learn and enjoy the course numerical analysis

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by these series of lectures.