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ENGINEERING MATHEMATICS-II 2018

By Genius Publications

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Rs. 250

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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
    1.4.1 Addition of Matrices.
    1.4.2 Properties of Matrix Addition 
    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
    1.8.1 Property of Adjoint 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