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)
Author(s): Robert Sobot
Edition: 2
Publisher: Springer
Year: 2023
Language: English
Commentary: Publisher PDF | Published: 15 November 2023
Pages: xiv, 217
City: Cham
Tags: Engineering Mathematics; Series; Elementary Special Functions; Time Convolution; Fourier Transform; Laplace Transformation
Preface
Preface to the Second Edition
Preface to the First Edition
Acknowledgments
Contents
Acronyms
1 Series
Problems
1.1 Sequence Notation
1.2 Finite Series
1.3 Infinite Series
1.4 Geometric Series
1.5 Mathematical Induction
Answers
1.1 Sequence Notation
1.2 Finite Series
1.3 Infinite Series
1.4 Geometric Series
1.5 Mathematical Induction
2 Elementary Special Functions
Problems
2.1 Basic Special Functions
2.2 Derivatives and Integrals with Special Functions
2.3 Special Functions Relations
Answers
2.1 Basic Special Functions
2.2 Derivatives and Integrals with Special Functions
2.3 Special Functions Relations
3 Continuous Time Convolution
Problems
3.1 Basic Function Transformations
3.2 Function Synthesis and Decomposition
3.3 Continuous Time Convolution
3.4 Energy and Power
Answers
3.1 Basic Function Transformations
3.2 Function Synthesis and Decomposition
3.3 Continuous Time Convolution
3.4 Energy and Power
4 Discrete Time Convolution
Problems
4.1 Discrete Signal Convolution
4.2 Discrete Signal Energy and Power
Answers
4.1 Discrete Signal Convolution
4.2 Discrete Signal Energy and Power
5 Continuous Time Fourier Transform
Problems
5.1 Special Functions
5.2 Composite Functions
5.3 Fourier Series
Answers
5.1 Special Functions
5.2 Composite Functions
5.3 Fourier Series
6 Discrete-Time Fourier Transform
Problems
6.1 Simple Seqences
6.2 Fourier Series
6.3 Inverse Discrete Time FT
6.4 Fast Fourier Transform
Answers
6.1 Simple Seqences
6.2 Fourier Series
6.3 Inverse Discrete Time FT
6.4 Fast Fourier Transform
7 Laplace Transformation
Problems
Problems
7.1 Basic Laplace Transformations
7.2 Basic Properties
7.3 Inverse Laplace Transformation
7.4 Differential Equations
Answers
7.1 Basic Laplace Transformations
7.2 Basic Properties
7.3 Inverse Laplace Transformation
7.4 Differential Equations
Bibliography
Index
