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## ENGINEERING MATHEMATICS-II 2018

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### Specifications of ENGINEERING MATHEMATICS-II 2018

#### Book Details

• 978-93-83644-76-6
• English
• 2018
• Paper Back
• 500

#### Contents

• .1. Linear Algebra-Matrices

1.1 Introduction
1.2 Definition of a Matrix
1.3 Types of Matrices
1.4 Algebra of Matrices
1.4.3 Subtraction of Matrices
1.4.4 Scalar Multiple of a Matrix
1.4.5 Product of Two Matrices
1.4.6 Properties of Matrix Multiplication
1.4.7 Positive Integral Powers of Matrices
1.5 Determinants
1.6 Minors and Cofactors
1.7 Properties of Determinants
1.8 Adjoint of a Square Matrix
1.9 Singular and Non-Singular Matrices
1.10 Inverse of a Matrix
1.11 Submatrix of a Matrix
Excercise 1.1
1.12 Rank of a Matrix
1.13 Elementary Transformation ....................................................... 1.201.14 Echelon Form of a Matrix
1.15 Normal Form of a Matrix
viii
1.16 Inverse of a Matrix by Elementary Transformations
1.17 System of Linear Simultaneous Equations
1.17.1 Solution of System of n Simultaneous Non-
Homogeneous Linear Equations in n Unknowns
1.17.2 System of Linear Homogeneous Equations
1.18 Vectors: Linearly Dependent and Linearly Independent
Exercise 1.2
1.19 Eigenvalues and Eigenvectors
1.19.1 Eigenvalues or Characteristic Roots
1.19.2 Eigenvectors or Characteristic Vectors
1.20 Cayley-Hamilton Theorem
1.20.1 Inverse by Cayley-Hamilton Theorem
1.21 Diagonalization of a Matrix
1.21.1 Powers of a Matrix A
1.22 Orthogonal Matrix
Exercise 1.3
2. Fourier Series
2.1 Introduction
2.2 Orthogonal Functions
2.3 Fourier Series
2.4 Dirichlet’s Conditions
2.5 Even and Odd Functions
2.6 Fourier Series for Even and Odd Functions
Illustrative Examples
Exercise 2.1
2.7 Fourier Series in Arbitrary Interval (0, 2l) or (–l, l)
2.8 Half-range Series
Illustrative Examples
Exercise 2.2
ix
2.9 Harmonic Analysis
Exercise 2.3
3. Differential Equations
3.1 Introduction
3.3 Differential Equation of First Order and First Degree
3.4 Variables Separable Form
3.5 Homogeneous Equations3.6 Equation Reducible to Homogeneous Form
3.7 Linear Differential Equation Exercise 3.1
3.8 Equation Reducible to Linear Form
Exercise 3.2
3.9 Exact Differential Equations
Illustrative Examples
Exercise 3.3
3.10 Equations Reducible to Exact Form
Illustrative Examples
Exercise 3.4
4. Differential Equation of Higher Order with
Constant Coefficient
4.1 Introduction
4.2 Obtaining C.F. of f(D)y= Q or General Solution of f(D)y =
Exercise 4.1
4.3 Particular Integral of f(D)y = Q......
4.4 To find P.I. when Q = eax, where ‘a’ is any Constant and
f(a)  0
4.5 To Find P.I. when Q = eax and f (a)= 0
4.6 To Find P.I. when Q = sin ax or cos ax and f(–a2)  0
4.7 To Find P.I. when Q = sinax or cosax and f(–a2) = 0
4.8 To Find P.I. when Q =xm, where m is a Positive Integer
Illustrative Examples
Exercise 4.2
4.9 To Find P.I. when Q = eaxV where V is any function of x
4.10 To Find P.I. when Q = xv, where v is any Function of x
Illustrative Examples
Exercise 4.3
4.11 Simultaneous Linear Differential Equations
4.11.1 Method of Solving Simultaneous Linear Differential Equations
4.11.2 Solution of Simultaneous Equations of the type
Exercise 4.4
5. Second Order Differential Equation
5.1 Introduction
5.2 Homogeneous Linear Differential Equation or Euler-Cauchy
Differential Equation
Illustrative Examples
Exercise 5.1
5.3 Exact Differential Equation
5.4 Integrating Factor
Illustrative Examples
Exercise 5.2
5.5 When a Part of C.F is Known
5.6 Rules for Finding the Complementary Function
Exercise 5.3
5.7 Reduction to Normal Form (Removal of first Derivative or
Change of Dependent Variable)
5.8 Finding the Solution of Differential Equation by Changing
the Independent Variable
Exercise 5.5
5.9 Method of Variation of Parameters
Exercise 5.6
5.10 Method of Undetermined Coefficients
Illustrative Examples
Exercise 5.7
6. Partial Differential Equations
6.1 Introduction
6.2 Formation of Partial Differential Equations
6.3 Definitions .
6.4 Linear Partial Differential Equations of First Order
Exercise 6.1
6.5 Special Methods of Solution to First Order P.D.E.
Exercise 6.2
6.6 Charpit’s Method for Solving General P.D.E.
Exercise 6.3
7. Separation of Variables-Boundry Value Problems
7.1 Introduction
7.2 Classification of Partial Differential Equations of Second Order
7.3 Method of Separation of Variables .............................................. 7.2
7.4 Solution of Wave Equation in One Dimension
7.5 Solution of One-Dimensional Heat Equation
(Or Diffusion Equation)
7.5.1 Solution to One-Dimensional Heat Equation When
Boundary Conditions are Non-Homogeneous
7.6 Solution of Laplace’s Equations in two Dimension
7.6.1 Laplace's Equation in Polar Coordinates
Illustrative Examples
Exercise