Allied Mathematics

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Allied Mathematics

Publication Date: 01 July, 2006 Available in all formats

Publisher: Vijay Nicole Imprints Private Limited

ISBN: 9789394681071

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ISBN: 9788182091443 Price: INR 425.00

Description

Table of contents

Biographical note

This book adopts a solved problems approach to learning the subject. It is specifically designed to suit the requirements of undergraduate students for the paper on Allied Mathematics. The book covers the syllabus of Madras University in toto.

Description

Table of contents

Cover
Title Page
Copyright Page
Dedication
Contents
Preface
Chapter 1 Algebra
- 1.1 Partial Fraction
  - 1.1.1 Resolving into Partial Fraction
    - Worked Examples
    - Exercise
- 1.2 Binomial Expansion
  - Worked Examples
  - Exercise
  - 1.2.1 Summation of Series Using Binomial Expansion
    - Worked Examples
    - Exercise
  - 1.2.2 Approximation Using Binomial Expansion
    - Worked Examples
    - Exercise
- 1.3 Exponential Series
  - Worked Examples
  - Exercise
  - 1.3.1 Summation of Exponential Series
    - Worked Examples
    - Exercise
- 1.4 Logarithmic Series
  - Worked Examples
  - Exercise
  - 1.4.1 Approximation
    - Worked Examples
    - Exercise
Chapter 2 Theory of Equation
- 2.1 introduction
- 2.2 Imaginary and Irrational Roots
  - Exercise
- 2.3 Relation Between Roots and Coefficient of the Polynomial Equation in x and Symmetric Functions
  - Worked Examples
  - Exercise
- 2.4 Transformation of Equation by Diminishing or Increasing its Roots by a Constant
  - Worked Examples
  - Exercise
- 2.5 Reciprocal Equation
  - Worked Examples
  - Exercise
- 2.6 Finding Approximate Roots by Newton’s Method
  - Worked Examples
  - Exercise
Chapter 3 Matrices
- 3.1 Introduction
  - Worked Examples
  - Exercise
- 3.2 Rank of the Matrix
  - Worked Examples
  - Exercise
  - 3.2.1 Consistency of Equation
    - Worked Examples
    - Exercise
- 3.3 Cayley Hamilton Theorem
  - Worked Examples
  - 3.4 Eigen Values and Eigen Vectors
    - Worked Examples
    - Exercise
Chapter 4 Finite Difference
- 4.1 Difference Operators
  - Worked Examples
  - Worked Examples
- 4.2 Interpolation Formula for Data with Equal Interval of Difference
  - Worked Examples
- 4.3 Lagrange’s Interpolation Formula for Unequal Intervals
  - Worked Examples
  - Exercise
Chapter 5 Trigonometry
- 5.1 Expansion of cosn Ö; sinn 0 in terms of Powers of Cosine and Sine (where n is a Positive Integer)
  - Worked Examples
  - Exercise
- 5.2 Expansion of cosn 6 and sinn 0
  - Worked Examples
  - Exercise
- 5.3 Expansion of sin 0 and cos 6 in terms of powers of 0.
  - Worked Examples
  - Exercise
- 5.4 Hyperbolic Functions
  - Worked Examples
  - 5.4.1 Inverse Hyperbolic Function
    - Worked Examples
    - Exercise
  - 5.5 Logarithm of a Complex Number
    - Worked Examples
    - Exercise
Chapter 6 Differential Calculus
- 6.1 Introduction
- 6.2 Algebra of Derivatives
- 6.3 Application of Derivatives
  - 6.3.1 Radius of Curvature
  - Worked Examples
- 6.3.2 Radius of Curvature in Polar Form
  - Worked Examples
- 6.3.3 Pedal Equation or p - r Equation of a Curve r=f(6)
  - Worked Examples
  - Exercise
- 6.4 Successive Differentiation
  - Worked Examples
  - Exercise
- 6.5 Partial Differentiation
  - Worked Examples
  - 6.5.1 Application of Partial Derivatives
    - Worked Examples
    - Exercise
  - 6.5.2 Maxima and Minima of Functions of Several Variables
    - Worked Examples
  - 6.5.3 Maxima and Minima of Several Variables Under Constraints using Lagrange Multiplier Method
    - Worked Examples
    - Exercise
Chapter 7 Integration
- 7.1 introduction
  - Worked Examples
  - Exercise
- 7.2 Integration by Method of Substitution
  - 7.2.1 Using Trigonometric Substitution
    - Worked Examples
    - Exercise
  - 7.2.2 Integration by Substitution using Following Results
    - Worked Examples
    - Exercise
- 7.3 Integration of Irrational functions
  - 7.3.1 Integrals Type I
    - Worked Examples
    - Exercise
  - 7.3.2 Integrals Type II
    - Worked Examples
    - Exercise
  - 7.3.3 Integrals Type III
    - Worked Examples
    - Exercise
  - 7.3.4 Integrals Type IV
    - Worked Examples
    - Exercise
  - 7.3.5 Integrals Type V
    - Worked Examples
    - Exercise
- 7.4 Integration by Parts
  - Worked Examples.
  - Exercise
  - 7.4.1 Bernoulli Formula for Integration by Parts
    - Worked Examples
  - 7.5 Reduction Formula
    - Worked Examples
  - 7.6 Properties of Definite Integral
    - Worked Examples
    - Exercise
Chapter 8 Multiple Integrals
- 8.1 Double Integrals
  - 8.1.1 Evaluation of the Double Integral
    - Worked Examples
    - Exercise
  - 8.2 Change of Order of Integration
    - Worked Examples
    - Exercise
  - 8.3 Triple Integral
    - Worked Examples
    - Exercise
  - 8.4 Application of Double and Triple Integration
    - Worked Examples
  - 8.5 Centroid
    - Worked Examples
    - Exercise
Chapter 9 Fourier Series
- 9.1 Introduction
  - Worked Examples
- 9.2 Half Range Series
  - Worked Examples
  - Exercise
Chapter 10 Differential Equations
- 10.1 Introduction
- 10.2 Equations of First Order and of Higher Degree
  - 10.2.1 Equation Solvable for p
    - Worked Examples
  - 10.2.2 Equation Solvable for y
    - Worked Examples
  - 10.2.3 Equation Solvable for x
    - Worked Examples
  - 10.2.4 Clairaut’s Equation
    - Worked Examples
    - Exercise
- 10.3 Total Differentia!Equation
  - Worked Examples
  - Exercise
- 10.4 Linear Differential Equations of Second Order with Constant Coefficients
  - 10.4.1 To Find Particular Integral for f(x) = eax
    - Worked Examples
  - 10.4.2 To Find Particular Integral for f(x) = sin ax or cos ax
    - Worked Examples
  - 10.4.3 To Find Particular Integral for / (x) = x”
    - Worked Examples
    - Worked Examples
- 10.5 Differential Equation with Variable Coefficient
  - Worked Examples
  - Exercise
Chapter 11 Partial Differential Equations
- 11.1 Introduction
- 11.2 Formation of Partial Differential Equations
  - Worked Examples
  - Exercise
- 11.3 Solving of Partial Differential Equation
  - 11.3.1 Standard I A Differential Equation of the Form F(p,q) = 0
    - Worked Examples
  - 11.3.2 Standard II F(x, p, q) = 0; F(/, p, q) = 0; F(z, p, q) = 0
    - Worked Examples
  - 11.3.3 Standard III F(x,p) = F(y, q)
    - Worked Examples
  - 11.3.4 Standard IV Clairaut’s Form z = px + qy + /’(p, q)
    - Worked Examples
  - 11.3.5 Lagrange’s Partial Differential Equation
    - Worked Examples
- 11.4 Partial Differential Equations Reducible to Standard Forms
  - Worked Examples
  - Exercise
Chapter 12 Laplace Transforms
- 12.1 Introduction
  - 12.1.1 Standard Forms of Laplace Transform
    - Worked Examples
    - Exercise
- 12.2 Inverse Laplace Transform
  - 12.2.1 Inverse of Standard Functions
    - Worked Examples
    - Exercise
- 12.3 Application to Solution of Differential Equations
  - Worked Examples
  - 12.3.1 Solving of Simultaneous Differential Equation
    - Worked Examples
    - Exercise
Chapter 13 Vector Calculus
- 13.1 Introduction
- 13.2 Vector Differentiation
  - Worked Examples
  - Exercise
- 13.3 Differential Operator
  - Worked Examples
  - 13.3.1 Geometrical Interpretation
    - Worked Examples
    - Worked Examples
    - Exercise
  - 13.4 Divergence and Curl of Vector Functions
    - Worked Examples
    - 13.4.1 Properties of Divergence and Curl
      - Worked Examples
      - Exercise
Chapter 14 Vector Integration
- 14.1 Line Integral
  - Worked Examples
  - 14 1.2 Surface Integral
  - 14.1.3 Volume Integral
    - Worked Examples
- 14.2 Integral Theorems (Statement Without Proof)
  - Worked Examples
  - Exercise

Biographical note

A Abdul Rasheed is selection grade lecturer, Department of Mathematics, The New College, Chennai. He has more than 26 years of teaching experience at various levels. He is also the visiting faculty at MEASI Institute of Architecture.

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