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i have been trying to narrow it down .. because we lacked proper texts and materials to learn it properly ...

the whole thing sort of looked a bit like this ...

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 Equations

Solution 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 method

i was wondering about the difference between a differential equations and functions like f(x,y) =

??