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.