Description
This book is written for the undergraduate students of all Engineering disciplines. It offers comprehensive coverage of all topics with step by step problem solving procedures. This book gives the instructors maximum flexibility in selecting the material and tailoring it to their needs. The modern approach in this book will prepare the students for the future tasks. The material lays a good foundation of Engineering Mathematics that will help the students in their careers and in further studies.
• Pedagogy includes solved examples and exercise problems.
• Numerous specific examples clarifying the essence of the topics and methods for solving problems and equations along with real time applications.
• Concise and coherent survey of the most important definitions, formulae, equations, methods and theorems.
Table of Content
Chapter 1 Differential Calculus
1.1 Representation of Functions
1.1.1 Representing a Function Numerically
1.1.2 Representing a Function Graphically
1.1.3 Piece wise Functions
Solved Problems (Problem 1.1 to 1.11)
1.1.4 Types of Function
Exercise 1.1
1.2 Limit of a Function
Solved Problems (Problem 1.12 to 1.50)
1.3 Continuity of a Function
Solved Problems (Problem 1.51 to 1.55)
Exercise 1.2
1.4 Derivatives
Solved Problems (Problem 1.56 to 1.69)
Exercise 1.3
Solved Problems (Problem 1.70 to 1.126)
Exercise 1.4
1.5 Test for Derivatives
Solved Problems (Problem 1.127 to 1.181)
Miscellaneous Problems
Exercise 1.5
Chapter 2 Functions of Several Variables
2.1 Partial Differentiation
Solved Problems (Problem 2.1 to 2.8)
2.2 Euler’s Theorem for Homogeneous Functions
Solved Problems (Problem 2.9 to 2.13)
Exercise 2.1
2.3 Partial Differentiation of Implicit Functions
Solved Problems (Problem 2.14 to 2.32)
Exercise 2.2
Solved Problems (Problem 2.33 to 2.47)
Exercise 2.3
Solved Problems (Problem 2.48 to 2.59)
Exercise 2.4
Solved Problems (Problem 2.60 to 2.71)
Exercise 2.5
Solved Problems (Problem 2.72 to 2.83)
Exercise 2.6
Chapter 3 Integral Calculus
3.1 Indefinite Integral and Definite Integral
3.1.1 Fundamental Theorem of Calculus
3.1.2 Riemann Sum
Solved Problems (Problem 3.1 to 3.6)
Exercise 3.1
3.2 Method of Substitution (Change of the Independent Variables)
Solved Problems (Problem 3.7 to 3.13)
3.3 Integration of Rational Function using Partial Fraction
3.3.1 Proper and Improper Functions
Solved Problems (Problem 3.14 to 3.20)
Exercise 3.2
Solved Problems (Problem 3.21)
3.4 Integration by Parts
Solved Problems (Problem 3.22 to 3.26)
Exercise 3.3
3.5 Trigonometric Integrals
Solved Problems (Problem 3.27 to 3.30)
Exercise 3.4
3.5.1 Trigonometric Substitutions
Solved Problems (Problem 3.31 and 3.32)
3.5.2 Integration of Special Functions
Solved Problems (Problem 3.33 to 3.38)
Exercise 3.5
3.6 Rational Function
Solved Problems (Problem 3.39 to 3.44)
3.7 Integration of Irrational Function
Solved Problems (Problem 3.45 to 3.48)
Exercise 3.6
3.8 Improper Integrals
Solved Problems (Problem 3.49 to 3.62)
Exercise 3.7
Chapter 4 Multiple Integrals
4.1 Double Integration in Cartesian Coordinates
Solved Problems (Problem 4.1 to 4.18)
Exercise 4.1
4.2 Double Integration in Polar Coordinates
Solved Problems (Problem 4.19 to 4.25)
Exercise 4.2
4.3 Change of Order of Integration
Solved Problems (Problem 4.26 to 4.35)
4.4 Change of Variables
Solved Problems (Problem 4.36 to 4.41)
Exercise 4.3
4.5 Area Enclosed by Plane Curves =
Solved Problems (Problem 4.42 to 4.49)
4.5.1 Polar Coordinates
Solved Problems (Problem 4.50 to 4.58)
Exercise 4.4
4.6 Triple Integration in Cartesian Coordinates
Solved Problems (Problem 4.59 to 4.76)
Exercise 4.5
Chapter 5 Ordinary Differential Equation
5.1 Differential Equation
5.1.1 Linear Differential Equations with Constant Coefficients
Solved Problems (Problem 5.1 to 5.49)
Exercise 5.1
Solved Problems (Problem 5.50 to 5.62)
5.1.2 Legendre’s Linear Equation
Solved Problems (Problem 5.63 to 5.68)
Exercise 5.2
5.1.3 Simultaneous First Order Linear Equation with Constant Coefficients
Solved Problems (Problem 5.69 to 5.78)
Exercise 5.3
5.2 Method of Variation of Parameters
Solved Problems (Problem 5.79 to 5.91)
Exercise 5.4
5.3 Method of Undetermined Coefficients
Solved Problems (Problem 5.92 to 5.100)
• Appendix A Solved Question Papers
• Appendix B Formulas and Theorems for Reference
• Appendix C Formulas (to differential equations)
About The Authors
Dr. C. Vijayalakshmi is Associate Professor, Mathematics Division, School of Advanced Sciences, Vellore Institute of Technology, Chennai. She has 23 years of experience teaching both undergraduates and postgraduates.
Dr. K. SIVASELVAN is Associate Professor, Jeppiaar Engineering college, Chennai. He has 16 years of experience teaching both undergraduates and postgraduates.
Dr. R. SUBRAMANI is Assistant Professor, Kristu Jayanti Collge, Bengaluru. His area of specilisation includes Advanced Optimization Techniques and Stochastic Processes.
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