i have been trying to follow computer oriented numerical methods in c language for some time now ...

we had lots of maths to cover ... and we lacked proper materials ...

so i had to make notes myself , because most of the text books were lacking the example programs and the maths...

these were the things in my syllabus

mathematical expressions

equations in one variable

equations in two variables

system of 2 equations containing 2 variables

functions in one variable

functions in two variables

differential equations

first order differential equations

second order differential equations

higher order differential equations ...

linear differential equations

separable differential equations

exact differential equations

homogeneous differential equations

non homogeneous differential equations

using the method of undetermined coefficients ...

partial differential equations ...Numerical Methods and errors

Interpolation

Numerical Differentiation

Numerical Integration

Solution of Algebraic and Transcendental Equations

Numerical Solution of a system of Linear Equations

Numerical Solution of Ordinary differential equations

Curve fitting

Numerical Solution of problems associated with Partial Differential EquationsSolution of Algebraic and Transcendental Equation

2.1 Introduction

2.2 Bisection Method

2.3 Method of false position

2.4 Iteration method

2.5 Newton-Raphson Method

2.6 Ramanujan's method

2.7 The Secant Method Finite Differences

3.1 Introduction

3.3.1 Forward differences

3.3.2 Backward differences

3.3.3 Central differences

3.3.4 Symbolic relations and separation of symbols

3.5 Differences of a polynomial Interpolation

3.6 Newton's formulae for intrapolation

3.7 Central difference interpolation formulae

3.7.1 Gauss' Central Difference Formulae

3.9 Interpolation with unevenly spaced points

3.9.1 Langrange's interpolation formula

3.10 Divided differences and their properties

3.10.1 Newton's General interpolation formula

3.11 Inverse interpolation Numerical Differentiation and Integration

5.1 Introduction

5.2 Numerical differentiation (using Newton's forward and backward formulae)

5.4 Numerical Integration

5.4.1 Trapizaoidal Rule

5.4.2 Simpson's 1/3-Rule

5.4.3 Simpson's 3/8-Rule Matrices and Linear Systems of equations

6.3 Solution of Linear Systems – Direct Methods

6.3.2 Gauss elimination

6.3.3 Gauss-Jordan Method

6.3.4 Modification of Gauss method to compute the inverse

6.3.6 LU Decomposition

6.3.7 LU Decomposition from Gauss elimination

6.4 Solution of Linear Systems – Iterative methods

6.5 The eigen value problem

6.5.1 Eigen values of Symmetric Tridiazonal matrix Numerical Solutions of Ordinary Differential Equations

7.1 Introduction

7.2 Solution by Taylor's series

7.3 Picard's method of successive approximations

7.4 Euler's method

7.4.2 Modified Euler's Method

7.5 Runge-Kutta method

7.6 Predictor-Corrector Methods

7.6.1 Adams-Moulton Method

7.6.2 Milne's methodfor example , for a polynomial ...

a solution of a polynomial equation is also called a root of the polynomial ...

a value for the variable that makes the polynomial zero

if you can't find an exact expression, then you can use numerical methods to get approximations ...

with numerical methods you can choose how close to zero you want, and it will give you a value that's at least that close ...The (standard) calculus is broken into two pieces.

i) Differential calculus - which is looking at the instantaneous rates of change of objects with respect to some variables. We have the notion of the derivative of a function.

ii) Integral calculus - which is calculating the area under curves, calculating volumes and so on. This is all given in terms if the (indefinite or definite) integral of a function.

The two notions are tied together via the fundamental theorem of calculus. This says that the derivative and indefinite integral are basically mutual inverses (but not quite).An equation containing the derivatives of one or more dependent variables, with respect to one or more independent variables, is said to be a differential equation

i have managed it this far ...

there were at least 5 books i had to follow ..to understand this properly ...

Peter Selby, Steve Slavin Practical Algebra_ A Self-Teaching Guide

Tom M. Apostol Calculus, Volume I_ One-Variable Calculus, with an Introduction to Linear Algebra

Tom M. Apostol Calculus, Volume II_ Multi-Variable Calculus and Linear Algebra, with Applications to Differential Equations and Probability

Computer oriented numerical methods - N Datta

Computer Fundamentals and Programming in C - J.B. Dixit

at this point of time i am not sure how the alphabets , variables , arrays ... etc ... are declared ??

how do i declare ,

f(x) ... theta , d^2y/dx^2 , (dy/dx)^3 , integral symbol... etc properly in c language ??