Engineering Mathematics by Example: Vol. II: Calculus

✍ Scribed by Robert Sobot

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 511
• Edition: 2
• Category: Library

✦ Synopsis

This textbook is a complete, self-sufficient, self-study/tutorial-type source of mathematical problems. It serves as a primary source for practicing and developing mathematical skills and techniques that will be essential in future studies and engineering practice. Rigor and mathematical formalism is drastically reduced, while the main focus is on developing practical skills and techniques for solving mathematical problems, given in forms typically found in engineering and science. These practical techniques are split into three separate books: the topics of algebra, complex algebra, and linear algebra (Vol. I), calculus of single and multiple argument functions (Vol. II), and continues and discrete Convolution and Fourier integrals/sums of typical functions used in signal processing, in addition to Laplace transform examples (Vol. III).

✦ Table of Contents

Preface
Preface to the Second Edition
Preface to the First Edition
Acknowledgments
Contents
Acronyms
1 Limits
Problems
1.1 Simple Limits
1.2 Limits to Infinity
1.3 Limits Involving Radicals
1.4 The Squeeze Theorem
1.5 Limits Based on [x] Function
1.6 Limits Based on the Constant e
1.7 Limits Involving Trigonometric Functions
1.8 Limits of Piecewise Functions
1.9 Asymptotes
Answers
1.1 Simple Limits
1.2 Limits to Infinity
1.3 Limits Involving Radicals
1.4 The Squeeze Theorem
1.5 Limits Based on [x] Function
1.6 Limits Based on the Constant e
1.7 Limits Involving Trigonometric Functions
1.8 Limits of Piecewise Functions
1.9 Asymptotes
2 Derivatives
Problems
2.1 Basic Derivatives
2.2 Product Rule
2.3 Quotient Rule
2.4 Chain Rule
2.5 Taylor Polynomial
2.6 L'Hôpital's Rule
Answers
2.1 Basic Derivatives
2.2 Product Rule
2.3 Quotient Rule
2.4 Chain Rule
2.5 Taylor Polynomial
2.6 L'Hôpital's Rule
3 Function Analysis
Problems
3.1 Polynomial Functions
3.2 Rational Functions
3.3 Radical Functions
3.4 Exponential and Log Functions
3.5 Trigonometric Functions
3.6 Composite Functions
3.7 Orthogonal Functions
Answers
3.1 Simple Polynomial Functions
3.2 Rational Functions
3.3 Radical Functions
3.4 Exponential and Log Functions
3.5 Trigonometric Functions
3.6 Composite Functions
3.7 Orthogonal Functions
4 Multivariable Functions
Problems
4.1 Domains of Typical 3D Surfaces
4.2 Multivariable Limits
4.3 Partial Derivatives
4.4 Multivariable Integrals
Answers
4.1 Domains of Typical 3D Surfaces
4.2 Multivariable Limits
4.3 Partial Derivatives
4.4 Multivariable Integrals
5 Integrals
Problems
5.1 Simple Integrals
5.2 Integration by Change of Variables
5.3 Integration by Parts
5.4 Trigonometric Substitutions
5.5 Rational Functions
5.6 Definite Integrals
5.7 Area Integral
5.8 Volume of a Solid of Revolution
5.9 Line Integral
5.10 Mean of a Function
5.11 Improper Integrals
Answers
5.1 Simple Integrals
5.2 Integration by Change of Variables
5.3 Integration by Parts
5.4 Trigonometric Substitutions
5.5 Rational Functions
5.6 Definite Integrals
5.7 Area Integral
5.8 Volume of a Solid of Revolution
5.9 Line Integral
5.10 Mean of a Function
5.11 Improper Integrals
6 Differential Equations
Problems
6.1 First Order, Separable Variables
6.2 First Order, Homogeneous
6.3 First Order, Function Coefficients
6.4 Linear Equations, Constant Coefficients
Answers
6.1 First Order, Separable Variables
6.2 First Order, Homogeneous
6.3 First Order, Function Coefficients
6.4 Linear Equations, Constant Coefficients
Bibliography
Index

✦ Subjects

Engineering Mathematics; Calculus; Function Analysis; Limits; Derivatives; Integrals; Differential Equations