Book description
Engineering Mathematics  II is meant for undergraduate engineering students. Considering the vast coverage of the subject, usually this paper is taught in three to four semesters. The two volumes in Engineering Mathematics by Babu Ram offer a complete solution to these papers.
Table of contents
 Cover
 Title Page
 Contents
 Dedication
 Preface to the Revised Edition

1. Preliminaries
 1.1  Sets and Functions
 1.2  Continuous and Piecewise Continuous Functions
 1.3  Derivability of a Function and Piecwise Smooth Functions
 1.4  The Riemann Integral
 1.5  The Causal and Null Function
 1.6  Functions of Exponential Order
 1.7  Periodic Functions
 1.8  Even and Odd Functions
 1.9  Sequence and Series
 1.10  Series of Functions
 1.11  Partial Fraction Expansion of a Rational Function
 1.12  Special Functions
 1.13  The Integral Transforms

2. Linear Algebra
 2.1  Concepts of Group, Ring, and Field
 2.2  Vector Space
 2.3  Linear Transformation
 2.4  Linear Algebra
 2.5  Rank and Nullity of a Linear Transformation
 2.6  Matrix of a Linear Transformation
 2.7  Changeofbasis Matrix (Transforming Matrix or Transition Matrix)
 2.8  Relation Between Matrices of a Linear Transformation in Different Bases
 2.9  Normed Linear Space
 2.10  Inner Product Space
 2.11  Least Square Line Approximation
 2.12  Minimal Solution to a System of Equations
 2.13  Matrices
 2.14  Algebra of Matrices
 2.15  Multiplication of Matrices
 2.16  Associative Law for Matrix Multiplication
 2.17  Distributive Law for Matrix Multiplication
 2.18  Transpose of a Matrix
 2.19  Symmetric, SkewSymmetric, and Hermitian Matrices
 2.20  Lower and Upper Triangular Matrices
 2.21  Determinants
 2.22  Adjoint of a Matrix
 2.23  The Inverse of a Matrix
 2.24  Methods of Computing Inverse of a Matrix
 2.25  Rank of a Matrix
 2.26  Elementary Matrices
 2.27  Row Reduced Echelon Form and Normal Form of Matrices
 2.28  Equivalence of Matrices
 2.29  Row Rank and Column Rank of a Matrix
 2.30  Solution of System of Linear Equations
 2.31  Solution of NonHomogeneous Linear System of Equations
 2.32  Consistency Theorem
 2.33  Homogeneous Linear Equations
 2.34  Characteristic Roots and Characteristic Vectors
 2.35  The CayleyHamilton Theorem
 2.36  Algebraic and Geometric Multiplicity of an Eigen Value
 2.37  Minimal Polynomial of a Matrix
 2.38  Orthogonal, Normal and Unitary Matrices
 2.39  Similarity of Matrices
 2.40  Diagonalization of a Matrix
 2.41  Triangularization of an Arbitrary Matrix
 2.42  Quadratic Forms
 2.43  Diagonalization of Quadratic Forms
 2.44  Miscellaneous Examples
 Exercises

3. Functions of Complex Variables
 3.1  Basic Concepts
 3.2  DeMoivre's Theorem
 3.3  Logarithms of Complex Numbers
 3.4  Hyperbolic Functions
 3.5  Relations Between Hyperbolic and Circular Functions
 3.6  Periodicity of Hyperbolic Functions
 3.7  Some Basic Concepts
 3.8  Analytic Functions
 3.9  Integration of Complexvalued Functions
 3.10  Power Series Representation of an Analytic Function
 3.11  Zeros and Poles
 3.12  Residues and Cauchy's Residue Theorem
 3.13  Evaluation of Real Definite Integrals
 3.14  Conformal Mapping
 3.15  Miscellaneous Examples
 Exercises

4. Ordinary Differential Equations
 4.1  Definitions and Examples
 4.2  Formulation of Differential Equation
 4.3  Solution of Differential Equation
 4.4  Differential Equations of First Order
 4.5  Separable Equations
 4.6  Homogeneous Equations
 4.7  Equations Reducible to Homogeneous Form
 4.8  Linear Differential Equations of First Order and First Degree
 4.9  Equations Reducible to Linear Differential Equations
 4.10  Exact Differential Equation
 4.11  The Solution of Exact Differential Equation
 4.12  Equations Reducible to Exact Equation
 4.13  Applications of First Order and First Degree Equations
 4.14  Equations of First Order and Higher Degree
 4.15  Equations which can be Factorized into Factors of First Degree
 4.16  Equations which cannot be Factorized into Factors of First Degree
 4.17  Clairaut's Equation
 4.18  Higher Order Linear Differential Equations
 4.19  Solution of Homogeneous Linear Differential Equation with Constant Coefficients
 4.20  Complete Solution of Linear Differential Equation with Constant Coefficients
 4.21  Application of Linear Differential Equation
 4.22  MassSpring System
 4.23  Simple Pendulum
 4.24  Differential Equation with Variable Coefficients
 4.25  Method of Solution by Changing the Independent Variable
 4.26  Method of Solution by Changing the Dependent Variable
 4.27  Method of Undetermined Coefficients
 4.28  Method of Reduction of Order
 4.29  The CauchyEuler Homogeneous Linear Equation
 4.30  Legendre's Linear Equation
 4.31  Method of Variation of Parameters to Find Particular Integral
 4.32  Solution in Series
 4.33  Bessel's Equation and Bessel's Function
 4.34  FourierBessel Expansion of a Continuous Function
 4.35  Legendre's Equation and Legendre's Polynomial
 4.36  FourierLegendre Expansion of a Function
 4.37  Miscellaneous Examples
 4.38  Simultaneous Linear Differential Equations with Constant Coefficient
 Exercises

5. Partial Differential Equations
 5.1  Formulation of Partial Differential Equation
 5.2  Solutions of a Partial Differential Equation
 5.3  Nonlinear Partial Differential Equations of the First Order
 5.4  Charpit's Method
 5.5  Some Standard Forms of Nonlinear Equations
 5.6  Linear Partial Differential Equations with Constant Coefficients
 5.7  Equations Reducible to Homogeneous Linear Form
 5.8  Classification of Second Order Linear Partial Differential Equations
 5.9  The Method of Separation of Variables
 5.10  Classical Partial Differential Equations
 5.11  Solutions of Laplace Equation
 5.12  Telephone Equations of a Transmission Line
 5.13  Miscellaneous Examples
 Exercises

6. Fourier Series
 6.1  Trigonometric Series
 6.2  Fourier (or Euler) Formulae
 6.3  Periodic Extension of a Function
 6.4  Fourier Cosine and Sine Series
 6.5  Complex Fourier Series
 6.6  Spectrum of Periodic Functions
 6.7  Properties of Fourier Coeffcients
 6.8  Dirichlet's Kernel
 6.9  Integral Expression for Partial Sums of a Fourier Series
 6.10  Fundamental Theorem (Convergence Theorem) of Fourier Series
 6.11  Applications of Fundamental Theorem of Fourier Series
 6.12  Convolution Theorem for Fourier Series
 6.13  Integration of Fourier Series
 6.14  Differentiation of Fourier Series
 6.15  Examples of Expansions of Functions in Fourier Series
 6.16  Method to Find Harmonics of Fourier Series of a Function from Tabular Values
 6.17  Signals and Systems
 6.18  Classification of Signals
 6.19  Classification of Systems
 6.20  Response of a Stable Linear Time Invariant Continuous Time System (LTC System) to a Piecewise Smooth and Periodic Input
 6.21  Application to Differential Equations
 6.22  Application to Partial Differential Equations
 6.23  Miscellaneous Examples
 Exercises

7. Fourier Transform
 7.1  Fourier Integral Theorem
 7.2  Fourier Transforms
 7.3  Fourier Cosine and Sine Transforms
 7.4  Properties of Fourier Transforms
 7.5  Solved Examples
 7.6  Complex Fourier Transforms
 7.7  Convolution Theorem
 7.8  Parseval's Identities
 7.9  Fourier Integral Representation of a Function
 7.10  Finite Fourier Transforms
 7.11  Applications of Fourier Transforms
 7.12  Application to Differential Equations
 7.13  Application to Partial Differential Equations
 Exercises

8. Discrete Fourier Transform
 8.1  Approximation of Fourier Coefficients of a Periodic Function
 8.2  Definition and Examples of DFT
 8.3  Inverse DFT
 8.4  Properties of DFT
 8.5  Cyclical Convolution and Convolution Theorem for DFT
 8.6  Parseval's Theorem for the DFT
 8.7  Matrix Form of the DFT
 8.8  Npoint Inverse DFT
 8.9  Fast Fourier Transform (FFT)
 Exercises
 9. Laplace Transform

10. Inverse Laplace Transform
 10.1  Definition and Examples of Inverse Laplace Transform
 10.2  Properties of Inverse Laplace Transform
 10.3  Partial Fractions Method to Find Inverse Laplace Transform
 10.4  Heaviside's Expansion Theorem
 10.5  Series Method to Determine Inverse Laplace Transform
 10.6  Convolution Theorem
 10.7  Complex Inversion Formula
 10.8  Miscellaneous Examples
 Exercises
 11. Applications of Laplace Transform

12. The Ztransform
 12.1  Some Elementary Concepts
 12.2  Definition of Z transform
 12.3  Convergence of Ztransform
 12.4  Examples of Ztransform
 12.5  Properties of the Ztransform
 12.6  Inverse Ztransform
 12.7  Convolution Theorem
 12.8  The Transfer Function (or System Function)
 12.9  Systems Described by Difference Equations
 Exercises

13. Elements of Statistics and Probability
 13.1  Introduction
 13.2  Measures of Central Tendency
 13.3  Measures of Variability (Dispersion)
 13.4  Measure of Skewness
 13.5  Measures of Kurtosis
 13.6  Covariance
 13.7  Correlation and Coefficient of Correlation
 13.8  Regression
 13.9  Angle Between the Regression Lines
 13.10  Probability
 13.11  Conditional Probability
 13.12  Independent Events
 13.13  Probability Distribution
 13.14  Mean and Variance of a Random Variable
 13.15  Binomial Distribution
 13.16  Pearson's Constants for Binomial Distribution
 13.17  Poisson Distribution
 13.18  Constants of the Poisson Distribution
 13.19  Normal Distribution
 13.20  Characteristics of the Normal Distribution
 13.21  Normal Probability Integral
 13.22  Areas Under the Standard Normal Curve
 13.23  Fitting of Normal Distribution to a Given Data
 13.24  Sampling
 13.25  Level of Significance and Critical Region
 13.26  Test of Significance for Large Samples
 13.27  Confidence Interval for the Mean
 13.28  Test of Significance for Single Proportion
 13.29  Test of Significance for Difference of Proportion
 13.30  Test of Significance for Difference of Means
 13.31  Test of Significance for the Difference of Standard Deviations
 13.32  Sampling with Small Samples
 13.33  Significance Test of Difference Between Sample Means
 13.34  Chisquare Distribution
 13.35  X2Test as a Test of Goodnessoffit
 13.36  Snedecor's Fdistribution
 13.37  Fisher's Zdistribution
 13.38  Miscellaneous Examples
 Exercises

14. Linear Programming
 14.1  Linear Programming Problems
 14.2  Formulation of an LPP
 14.3  Graphical Method to Solve LPP
 14.4  Canonical and Standard Forms of LPP
 14.5  Basic Feasible Solution of an LPP
 14.6  Simplex Method
 14.7  Tabular Form of the Solution
 14.8  Generalization of Simplex Algorithm
 14.9  Twophase Method
 14.10  Duality Property
 14.11  Dual Simplex Method
 14.12  Transportation Problems
 14.13  Matrix Form of the Transportation Problem
 14.14  Transportation Problem Table
 14.15  Basic Initial Feasible Solution of Transportation Problem
 14.16  Test for the Optimality of Basic Feasible Solution
 14.17  Degeneracy in Transportation Problem
 14.18  Unbalanced Transportation Problems
 Exercises

15. Basic Numerical Methods
 15.1  Approximate Numbers and Significant Figures
 15.2  Classical Theorems used in Numerical Methods
 15.3  Types of Errors
 15.4  General Formula for Errors
 15.5  Solution of Nonlinear Equations
 15.6  Linear System of Equations
 15.7  Finite Differences
 15.8  Error Propagation
 15.9  Interpolation
 15.10  Interpolation with Unequal Spaced Points
 15.11  Newton's Fundamental (Divided Difference) Formula
 15.12  Lagrange's Interpolation Formula
 15.13  Curve Fitting
 15.14  Numerical Quadrature
 15.15  Ordinary Differential Equations
 15.16  Numerical Solution of Partial Differential Equations
 Exercises
 Statistical Tables
 Copyright
Product information
 Title: Engineering Mathematics, Volume II, Second Edition
 Author(s):
 Release date: May 2012
 Publisher(s): Pearson India
 ISBN: 9788131785034
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