

Unlock a world of knowledge with Vision Publications—where every page brings you closer to your educational goals!
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CONTENTS
1. Integration
1.1 Introduction
Definition of Integration
Indefinite Integration or General Integral
Standard Formulae
1.2 Rules of Integration
Modification of Formulae for Linear Expression (nx + d)
Integration of Simple Rational Function
Integration by Trigonometric Transformation
1.3 Methods of Integration
Integration by Substitution
Important Deductions
Some Standard Substitutions
Integration by Parts and Partial Fraction
2. Definite Integration
2.1 Introduction
2.2 Definition
Rules of Definite Integrals
2.3 Properties of Definite Integrals
3. Application of Definite Integrals
3.1 INTRODUCTION
Tracing of Curves
Area between Two Curves
Volume of Revolution
Centre of Gravity25
Centroid of Plane Lamina
Mean Value OR Average Value
Root Mean Square Value (RMS value)
4. Differential Equation
4.1 INTRODUCTION
Definition
Formation of Differential Equation
4.2 Solution of first order first degree differential Equation
Variable Separable
Equation Reducible to Method of Variables Separable form by suitable substitutions
Homogeneous Differential Equations
Equations Reducible to Homogeneous Form
Linear Differential Equations
Exact differential Equation
4.3 BERNOULLI'S Equations
Non-linear differential equation
5. Application of Differential Equation
5.1 Application of Differential equations
Introduction
Applications of Differential Equations
Kirchhoff’s Laws
Application to LRC Circuits
6. Interpolation
6.1 Introduction
Lagrange’s Interpolation Formula
6.2 Forward and Backward Differences
Forward Differences
Backward Differences
6.3 Newton’s Forward Difference Interpolation Formula
6.4 Newton’s Backward Difference Interpolation Formula
6.5 Concept of Extrapolation
7. Numerical differentiation and integration
7.1 Newton's Forward and Backward Difference Formula for Differentiation
Newton's Forward Difference Formula for Differentiation
Newton's Backward Difference Formula for Differentiation
7.2 Numerical Integration
Trapezoidal Rule
Simpson's One-third Rule
8. Numerical Solution of Ordinary Differential Equation
8.1 Introduction
8.2 Runge-Kutta Method of Second Order
8.3 Runge-Kutta Method for Fourth Order
9. Laplace Transform
6.1 Introduction
6.2 Definition of Laplace Transform
6.3 Laplace Transform of Elementary Functions
Properties of Laplace Transform
First Shifting Property
Second Shifting Property
Multiplication by tn
Division by t Property
Use of Laplace transform in evaluation of certain integrals
6.4 Inverse Laplace Transform
Definition of Inverse Laplace transform
Inverse Laplace Transform of Standard Function
Properties of Inverse Laplace Transform
Inverse Laplace Transform by Method of Partial Fraction
6.5 Convolution Theorem
6.6 Laplace transform of Derivatives
6.7 Solution of Differential Equation using Laplace Transform (upto Second Order Equation)
10. Fourier Series
7.1 Introduction
7.2 Definition of Fourier Series (Euler’s Formula)
7.3 Series Expansion of continuous functions
Series Expansion of continuous Functions in (0, 2p)
Series expansion of continuous functions in (–p,p)
Series expansion of continuous functions in the interval (c, c + 2l)
Fourier Series expansion in (0, 2l)
Fourier Series Expansion in (–l, l)
7.4 Series Expansion of even and odd functions
Fourier Series Expansion of even and odd functions in (–p,p)
Fourier Series Expansion of Even and Odd Functions in (–l, l)
7.5 Half range Expansion
Half range cosine series
Half Range Sine Series
11. Numerical Solution of algebraic equation
8.1 Introduction
8.2 Bisection method
8.3 Regula Falsi method
8.4 Newton-Rapson method
12. Numerical solution of simultaneous equation
9.1 Introduction
9.2 Elimination method – Gauss elimination method
9.3 Gauss-Seidal method (Iterative Method)
9.4 Jacobi’s method
13. Probability
6.1 Introduction
Terms in Probability
Definition
Types of Event
6.2 Definition of Probability of an Event
Addition Theorem of Probability
14. Probability Distribution
7.1 Introduction
7.2 Binomial distribution
7.3 Poisson Distribution
Mean and Variance of Poisson’s Distribution
7.4 Normal distribution
15. Discrete Mathematics
9.1 Relational Algebra
9.2 Definition of a set
Methods for Describing Sets
9.3 Types of Sets
Operations on Set
Counting Principle
Principle of Inclusion - Exclusion
Cartesian Product
Relation
Function
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