Allied Mathematics
Author(s): A Abdul Rasheed
Subject(s): Mathematics
ISBN 9789394681071
 Published Date
  Pages 550

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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.

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

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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