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      Basic Applied Mathematics
      Basic Applied Mathematics

      Basic Applied Mathematics

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      Applied Mathematics

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      EU3234363840424446USXX5XSSMLXLXXLXXLArm Length6161,56262,56363,56464,5Bust Circumference8084889296101106111Waist Girth6165697377828792Hip Circumference87919599103108113118

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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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