Engineering Mathematics I

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ISBN 9789394524095

Publication Date Tue Aug 01 00:00:00 UTC 2017

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Table of contents

Biographical note

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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 Authors
Title Page
Copyright Page
Contents
Preface
Unit - I Differential Calculus
- Limit, Continuity and Differentiability
  - Introduction
- Limit of a Function
- Properties of Limits
- Left and Right Limits
- Infinite Limits
- Continuity
- Properties of Continuous Functions
- The Derivative
- Higher Derivatives
- Mean Value Theorem
  - Rolle’s Theorem
- Mean Value Theorem (Lagrange’s)
- Alternative Form of Lagrange’s Mean Value Theorem
- Cauchy’s Mean Value Theorem
- Alternative Form of Cauchy’s Mean Value Theorem
Unit - II Functions of Several Variables
- Partial Derivatives
  - Definition
  - Total Differentiation
  - Derivatives of Implicit Functions
  - Euler’s Theorem for Homogeneous Functions
- Total Differential Coefficient
- Functions of Functions and Implicit Functions
- Taylor’s Theorem
- Jacobians
  - Properties
- Maxima and Minima of Functions of Two variables
  - Definition—Maximum
  - Definition—Minimum
  - Working Rule for Finding the Extreme Values of f(x, y)
  - Constrained Maxima and Minima
  - Lagrange Method of Multipliers
Unit - III Integral Calculus
- Integral Calculus
  - Definite Integral
  - Proper Integral
  - Improper Integral
- Definite Integral
- Riemann Sum
  - Riemann Integral
- Examples of Riemann Integration From Definition
  - Definition
  - (I) Algebraic Formulae
  - (II) Trigonometry Formulae
- Riemann Sum Practice Problems
- Fundamental Theorem of Integral Calculus
- Integration By Parts
- Cancellation of Integrals
- Integration By Parts in the Case of Definite Integrals
- Integration of Partial Fractions
  - Rational Function
  - Partial Fractions
  - Method of Finding the Constant Quantities
- Miscellaneous Solved Examples
- Integration of Rational Functions
  - Definition
- Integration of Irrational Algebraic Fractions
  - Integrations of Rational Functions of x and (ax + b)1/n
- Reduction Formulae
- Walli’s Formula
Unit - IV Multiple Integrals
- Introduction
  - Double Integrals
  - Evaluation of Double Integrals
  - Beta and Gamma Function
  - Relation between Beta and Gamma Functions
  - Area as Double Integral
  - Changing the Order of Integration
  - Application of Beta Gamma Functions to Multiple Integrals
- Transformation from Cartesian Coordinates to Polar Coordinates
- Triple Integrals
  - Evaluation of Triple Integrals
  - Cartesian Coordinator Triple Integrals
  - Volume as Triple Integral
- Change of Variables
- Jacobian
  - Two Important Results Regarding Jacobians
  - Change of Variable in the Case of Two Variables
  - Change of Variables in the Case of Three Variables
  - Transmission from Cartesian to Polar Coordinates
  - Transformation from Cartesian to Polar Coordinates
Unit - V Differential Equations
- Table of Integration Formulas
- Procedural Rules
- Basic Formulas
- Ordinary Differential Equations
- Linear differential Equations with Constant Coefficients
- Simultaneous First Order Linear Equations with Constant Coefficient
- Linear Equations with Variable Coefficients
- Cauchy’s and Legendre’s Linear Equations
- The Method of Variation of Parameters
- Method of Undetermined Coefficients for Finding the Particular Integral
Two Marks Questions and Answers
Solved Question Bank
Index

B Praba is presently Associate Professor, Department of Mathematics, SSN College of Engineering, Chennai. She has 22 years of research and teaching experience and has written books on Discrete Mathematics, Statistics, Random Process and Queuing Theory and Statistics for Management. She has obtained her Ph.D., from Ramanujan Institute for Advanced Study in Mathematics, Chennai.

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.

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