Mathematics-2: As per 2018-2019 GTU 1st Year 2nd Semester
Description
Mathematics-2 has been exclusively designed by completely covering 2018–2019 GTU syllabus, aiming to cater to the needs of the 1st-Year (2nd-Semester) Engineering graduates. This book provides quick conceptual understanding and application capability by its in-depth coverage of the topics. It is a must have book for the students as it contains unique explanation and crystal-clear expression in a step-by-step approach. The pedagogy of this book has been designed in sync with the learning objectives of core mathematics courses. Keeping in mind the learning curve for the students, all the chapters have been organized accordingly.
Table of Contents
Foreword
Expressions of Appreciations
Preface
Acknowledgements
Syllabus
Nomenclature
1 Vector Calculus
1.1 Introduction
1.2 Parametrization of Curves
1.3 Exercises
1.4 Vector and Scalar Fields
1.5 Exercises
1.6 Arc Length of Curve in Space
1.7 Exercises
1.8 Gradient of a Scalar Function
1.9 Exercises
1.10 Divergence and Curl
1.11 Exercises
1.12 Line Integral
1.13 Path Independence and Conservative Field
1.14 Exercises
1.15 Green’s Theorem in the Plane
1.16 Exercises
2 Laplace Transform
2.1 Introduction
2.2 Basic Concepts
2.3 LT of Elementary Functions
2.4 First Shifting Theorem
2.5 Exercises
2.6 Unit Step Function and Second Shifting Theorem
2.7 Exercises
2.8 LT of Derivatives
2.9 LT of Integrals
2.10 Differentiation of LT
2.11 Integration of LT
2.12 LT Using Mixed Formulas
2.13 Exercises
2.14 Dirac’s Delta Function
2.15 LT of Periodic Functions
2.16 Convolution
2.17 Exercises
2.18 ODEs by LT
2.19 System of ODEs
2.20 Exercises
3 Fourier Integral
3.1 Introduction
3.2 Fourier Integrals
3.3 Exercises
4 First-Order ODEs
4.1 Introduction
4.2 Basic Concepts of ODE
4.3 Exact Differential Equation
4.4 Exercises
4.5 Integrating Factors
4.6 Exercises
4.7 Linear Equation
4.8 Bernoulli’s Equation
4.9 Exercises
4.10 First-Order Equations with Higher Degree
4.11 Exercises
5 ODEs of Higher Order
5.1 Introduction
5.2 Basic Concepts of ODE
5.3 Reduction of Order for Solution of DE
5.4 Homogeneous Linear DE with Constant Coefficient
5.5 Exercises
5.6 Non-Homogeneous Linear DE with Constant Coefficient
5.7 Exercises
5.8 Euler–Cauchy Equations
5.9 Method of Variation of Parameters
5.10 Exercises
6 Series Solution and Special Functions
6.1 Introduction
6.2 Classification of Points
6.3 Series Solution
6.4 Power Series Solution
6.5 Frobenius Series Solution
6.6 Some Special Functions and Their Properties
6.7 Exercises
Index