Engineering Mathematics by Example: Vol. I: Algebra and Linear Algebra

✍ Scribed by Robert Sobot

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 313
• 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 cover the subjects of algebra, complex algebra, linear algebra, and calculus of single and multiple argument functions. In addition, the second part of the book covers problems on Convolution and Fourier integrals/sums of typical functions used in signal processing.

• Offers a large collection of progressively more sophisticated mathematical problems on main mathematical topics required for engineers/scientists;
• Provides, at the beginning of each topic, a brief review of definitions and formulas that are about to be used and practiced in the following problems;
• Includes tutorial-style, complete solutions, to all problems.

✦ Table of Contents

Preface
Preface to the Second Edition
Preface to the First Edition
Acknowledgments
Contents
Acronyms
1 Numbers
Problems
1.1 Basic Number Operations
1.2 Fractional Powers and Radicals
1.3 Undefined Forms
1.4 Absolute Numbers and Expressions
Answers
1.1 Basic Number Operations
1.2 Fractional Powers and Radicals
1.3 Undefined Forms
1.4 Absolute Numbers and Expressions
2 Polynomials
Problems
2.1 Polynomial Expansion
2.2 Binomial Theorem (Pascal's Triangle)
2.3 Long Division
2.4 Factorization
2.5 Difference of Squares
2.6 Quadratic Polynomial—Viète Formulas
2.7 Completing the Square
2.8 Factor Theorem
2.9 Partial Fraction Decomposition
Answers
2.1 Polynomials
2.2 Binomial Theorem (Pascal's Triangle)
2.3 Long Division
2.4 Factorization
2.5 Difference of Squares
2.6 Quadratic Polynomial—Viète Formulas
2.7 Completing the Square
2.8 Factor Theorem
2.9 Partial Fraction Decomposition
3 Linear Equations and Inequalities
Problems
3.1 Linear Equations
3.2 System of Linear Equations
3.3 Linear Inequalities
3.4 System of Linear Inequalities
Answers
3.1 Linear Equations
3.2 System of Linear Equations
3.3 Linear Inequalities
3.4 System of Linear Inequalities
4 Logarithmic and Exponential Functions
Problems
4.1 Logarithmic and Exponential Functions
4.2 Simple Logarithmic Calculations
4.3 Exponential Equations
4.4 Logarithmic Equations
4.5 Exponential–Logarithmic Equations
4.6 Exponential Inequalities
4.7 Logarithmic Inequalities
Answers
4.1 Logarithmic and Exponential Functions
4.2 Simple Logarithmic Calculations
4.3 Exponential Equations
4.4 Logarithmic Equations
4.5 Exponential–Logarithmic Equations
4.6 Exponential Inequalities
4.7 Logarithmic Inequalities
5 Trigonometry
Problems
5.1 Trigonometric Definitions
5.2 Basic Calculations
5.3 Basic Identities
5.4 Equations
5.5 Inequalities
Answers
5.1 Trigonometric Definitions
5.2 Basic Calculations
5.3 Basic Identities
5.4 Equations
5.5 Inequalities
6 Complex Algebra
Problems
6.1 Basic Complex Number Forms
6.2 Polar Forms
6.3 Complex Plane
6.4 Euler Identity
6.5 Rational Powers
6.6 Complex Equations
Answers
6.1 Basic Complex Number Forms
6.2 Polar Forms
6.3 Complex Plane
6.4 Euler Identity
6.5 Rational Powers
6.6 Complex Equations
7 Bode Plot
Problems
7.1 Basic Complex Functions
7.2 Bode Plot Examples
Answers
7.1 Basic Complex Functions
7.2 Bode Plot Examples
8 Linear Algebra
Problems
8.1 Vector Definitions
8.2 Vector Operations
8.3 Linear Transformations
8.4 Determinants
8.5 Cramer's Rule
8.6 Vector Space
8.7 Eigenvalues and Eigenvectors
8.8 Matrix Inversion
8.9 Powers of Diagonalizable Matrices
Answers
8.1 Vector Definitions
8.2 Vector Operations
8.3 Linear Transformations
8.4 Determinants
8.5 Cramer's Rule
8.6 Vector Space
8.7 Eigenvalues and Eigenvectors
8.8 Matrix Inversion
8.9 Powers of Diagonalizable Matrices
Bibliography
Index

✦ Subjects

Engineering Mathematics; Linear Algebra; Trigonometry; Functions; Polynomials