Engineering Mathematics II

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Published by Vijay Nicole Imprints Private Limited

Publication Date: Wed Nov 01 00:00:00 UTC 2017 Available in all formats

ISBN: 9789394524248

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ISBN: 9788182094642 Price: INR 575.00

Description

Table of contents

Biographical note

User Reviews

Designed to cater to the requirements of first year engineering students, this book completely covers the latest syllabus of Anna University Regulation 2017.

Cover
About the Author
Title Page
Copyright Page
Contents
Preface
Chapter 1 Matrices
- Introduction
- Rank of a Matrix
  - Simultaneous Linear Equations
  - Rouche’s Theorem
  - Homogeneous System of Linear Equations
  - Linear Independence and Dependence of Vectors
- Eigen Values and Eigen Vectors
  - Introduction
  - Properties of Eigen Values and Eigen Vectors
- Cayley–Hamilton Theorem
- Similar Matrices
  - Diagonalisation of a Matrix
- Orthogonal Matrix
  - Properties
- Quadratic Forms
  - Nature of the Quadratic Form
  - Simultaneous Reduction of Two Quadratic Forms
  - Canonical Forms of Conics
  - Canonical Forms of Quadratics
Chapter 2 Vector Calculus
- Vector Functions
  - Constant Vector
  - Derivative of a Vector Function
  - Velocity of a Particle
- Scalar and Vector Point Functions
  - Scalar Point Function
  - Vector Point Function
  - Level Surface
  - Gradient of a Scalar Point Function
  - Geometric Significance of Grad ϕ
  - Directional Derivative
  - Unit Normal Vector
- Divergence of a Vector Function
  - Physical Significance
  - Solenoidal Vector
  - Curl of a Vector Function
  - Physical Significance
- Line Integral
- Surface Integral
- Volume Integral
- Green’s Theorem in a Plane
- Applications of Green’s Theorem
- Transformation between Line Integral & Surface Integral
- Stoke’s Theorem
- Applications of Stoke’s Theorem
- Gauss Divergence Theorem
- Applications of Gauss Divergence Theorem VC. 133
Chapter 3 Analytic Functions
- Functions of a Complex Variable
  - Definition—Limit of a Function
  - Definition—Continuity of a Function
  - Definition—Derivative of a Function
  - Definition—Analytic Function
- Cauchy-Reimann Equations
  - Necessary Conditions for a Function to be Analytic
  - Sufficient Condition for a Function to be Analytic
  - C-R Equations in Polar Coordinates
- Harmonic Functions
  - Definition—Level Curves
- Milne-Thomson Method
- Conformal Mapping
  - Definition—Conformal Mapping
  - Definition—Isogonal Mapping
  - Transformation ω = z2
  - Transformation ω = ez
- Bilinear Transformation
  - Definition—Fixed Point
  - Definition—Cross Ratio
Chapter 4 Complex Integration
- Definition
- Contour
- Region
  - Open Region
  - Closed Region
  - Connected Region
- Complex Integration
- Cauchy’s Integral Theorem (or) Cauchy’s Fundamental Theorem
  - Extension of Cauchy’s Theorem
  - Cauchy’s Integral Formula
- Taylor’s Series
- Laurent’s Series
- Zeros and Singularities
  - Definition
  - Singularity
  - Singular Point
  - Isolated and Non-Isolated Singularity
  - Kinds of Singularities
  - Test for Singularities
  - Definition of the Residue at a Pole
- Cauchy’s Residue Theorem
  - Calculation of Residues
- Contour Integration
  - Type I—Integration Round the Unit Circle
  - Type II—Evaluation of
  - Cauchy’s Lemma
  - Jordan’s Lemma
  - Type III—Indented Semi-circular Contour
Chapter 5 Laplace Transform
- Existence of the Laplace Transform
  - Laplace Transform of Standard Functions
- First Shifting Theorem
- Transform of Derivatives
- Transforms of Integrals
- Properties
  - Change of Scale
- Derivatives and Integrals of Transforms
- Laplace Transform of Special Function
  - Unit Step Function (or) Heaviside’s Function
- Second Shifting Theorem
  - Dirac-delta Function (or) Unit Impluse Function
  - Laplace Transform of Unit Impluse Function
  - Initial Value Theorem
  - Final Value Theorem
- Inverse Laplace Transforms
  - Type I - Method of Partial Fractions
  - Type II - Using Shifting Theorem
- Convolution Theorem
- Laplace Transform for Periodic Functions
  - Applications of Laplace Transform in Linear Differential Equation
- Integral Equations
- Simultaneous Differential Equations
Two Mark Questions and Answers
- Chapter 1: Matrices
- Chapter 2: Vector Calculus
- Chapter 3: Analytic Functions
- Chapter 4: Complex Integration
- Chapter 5: Laplace Transform
Solved Question Bank
Index

Dr. B. Praba is presently Professor, Department of Mathematics, SSN College of Engineering, Chennai. She is a prolific writer and has more than 30 years of teaching and research experience. She obtained her Ph.D. from Ramanujan Institute for Advanced Mathematics, Chennai. Her books include best sellers on Discrete Maths, Probability and Random Process etc.

S Kalavathy is Professor, Department of Mathematics, RMD Engineering College, Chennai. She has over 23 years of experience in teaching Mathematics and has written several books including best sellers on Engineering Mathematics and Operational Research.

Comments should not be blank

Rating

Description

Designed to cater to the requirements of first year engineering students, this book completely covers the latest syllabus of Anna University Regulation 2017.

Table of contents

Cover
About the Author
Title Page
Copyright Page
Contents
Preface
Chapter 1 Matrices
- Introduction
- Rank of a Matrix
  - Simultaneous Linear Equations
  - Rouche’s Theorem
  - Homogeneous System of Linear Equations
  - Linear Independence and Dependence of Vectors
- Eigen Values and Eigen Vectors
  - Introduction
  - Properties of Eigen Values and Eigen Vectors
- Cayley–Hamilton Theorem
- Similar Matrices
  - Diagonalisation of a Matrix
- Orthogonal Matrix
  - Properties
- Quadratic Forms
  - Nature of the Quadratic Form
  - Simultaneous Reduction of Two Quadratic Forms
  - Canonical Forms of Conics
  - Canonical Forms of Quadratics
Chapter 2 Vector Calculus
- Vector Functions
  - Constant Vector
  - Derivative of a Vector Function
  - Velocity of a Particle
- Scalar and Vector Point Functions
  - Scalar Point Function
  - Vector Point Function
  - Level Surface
  - Gradient of a Scalar Point Function
  - Geometric Significance of Grad ϕ
  - Directional Derivative
  - Unit Normal Vector
- Divergence of a Vector Function
  - Physical Significance
  - Solenoidal Vector
  - Curl of a Vector Function
  - Physical Significance
- Line Integral
- Surface Integral
- Volume Integral
- Green’s Theorem in a Plane
- Applications of Green’s Theorem
- Transformation between Line Integral & Surface Integral
- Stoke’s Theorem
- Applications of Stoke’s Theorem
- Gauss Divergence Theorem
- Applications of Gauss Divergence Theorem VC. 133
Chapter 3 Analytic Functions
- Functions of a Complex Variable
  - Definition—Limit of a Function
  - Definition—Continuity of a Function
  - Definition—Derivative of a Function
  - Definition—Analytic Function
- Cauchy-Reimann Equations
  - Necessary Conditions for a Function to be Analytic
  - Sufficient Condition for a Function to be Analytic
  - C-R Equations in Polar Coordinates
- Harmonic Functions
  - Definition—Level Curves
- Milne-Thomson Method
- Conformal Mapping
  - Definition—Conformal Mapping
  - Definition—Isogonal Mapping
  - Transformation ω = z2
  - Transformation ω = ez
- Bilinear Transformation
  - Definition—Fixed Point
  - Definition—Cross Ratio
Chapter 4 Complex Integration
- Definition
- Contour
- Region
  - Open Region
  - Closed Region
  - Connected Region
- Complex Integration
- Cauchy’s Integral Theorem (or) Cauchy’s Fundamental Theorem
  - Extension of Cauchy’s Theorem
  - Cauchy’s Integral Formula
- Taylor’s Series
- Laurent’s Series
- Zeros and Singularities
  - Definition
  - Singularity
  - Singular Point
  - Isolated and Non-Isolated Singularity
  - Kinds of Singularities
  - Test for Singularities
  - Definition of the Residue at a Pole
- Cauchy’s Residue Theorem
  - Calculation of Residues
- Contour Integration
  - Type I—Integration Round the Unit Circle
  - Type II—Evaluation of
  - Cauchy’s Lemma
  - Jordan’s Lemma
  - Type III—Indented Semi-circular Contour
Chapter 5 Laplace Transform
- Existence of the Laplace Transform
  - Laplace Transform of Standard Functions
- First Shifting Theorem
- Transform of Derivatives
- Transforms of Integrals
- Properties
  - Change of Scale
- Derivatives and Integrals of Transforms
- Laplace Transform of Special Function
  - Unit Step Function (or) Heaviside’s Function
- Second Shifting Theorem
  - Dirac-delta Function (or) Unit Impluse Function
  - Laplace Transform of Unit Impluse Function
  - Initial Value Theorem
  - Final Value Theorem
- Inverse Laplace Transforms
  - Type I - Method of Partial Fractions
  - Type II - Using Shifting Theorem
- Convolution Theorem
- Laplace Transform for Periodic Functions
  - Applications of Laplace Transform in Linear Differential Equation
- Integral Equations
- Simultaneous Differential Equations
Two Mark Questions and Answers
- Chapter 1: Matrices
- Chapter 2: Vector Calculus
- Chapter 3: Analytic Functions
- Chapter 4: Complex Integration
- Chapter 5: Laplace Transform
Solved Question Bank
Index

Biographical note

User Reviews

Comments should not be blank

Rating