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2025 | Buch

Mathematics of Engineering and Science

Practice Problems, Methods, and Solutions

verfasst von: Mehdi Rahmani-Andebili

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Inhaltsverzeichnis

Über dieses Buch

This study guide is designed for students taking courses in engineering mathematics and mathematical methods in science. The textbook includes problems with detailed solutions to teach students the subjects in detail and partially and fully solved exercises with hints to required formulas and answers, enabling students to practice independently and guiding them through problem-solving procedures. The material covered in the book includes complex functions, complex transformations, singularities of complex functions, complex series, Taylor and Laurent series expansions, residue, complex integration, Fourier series, half-domain Fourier sine and cosine series, complex Fourier series, Fourier integral, complex Fourier integral, Fourier transform, half-domain Fourier sine and cosine transform, and partial differential equations.

Offering detailed solutions, multiple problem-solving methods, and clear explanations of concepts, this hands-on tutorial will improve students’ problem-solving skills and foster a solid understanding of engineering mathematics and mathematical methods in science.

Inhaltsverzeichnis

Frontmatter

1. Complex Functions, Equations, Quantities, and Limits: Problems

Abstract

In this chapter, the basic and advanced problems of complex quantities, limit of complex functions, complex equations, and holomorphic functions along with their harmonic conjugate functions are studied. Herein, different types of problems and exercises are presented that are categorized as follows:

Problems with detailed solution: They have been designed to teach students the subjects in detail. Moreover, they have been categorized into different levels based on their difficulty levels (easy, normal, and hard) and calculation amounts (small, normal, and large).
Partially solved exercises: They have been designed to encourage students to practice more problems while guiding them through the problem-solving procedure and hinting the required formulas as well as to help instructors to give tests or quizzes.
Exercises with final answer: They have been designed to encourage students to practice by themselves while hinting them by the final answer.

Mehdi Rahmani-Andebili

2. Complex Functions, Equations, Quantities, and Limits: Solutions of Problems

Abstract

In this chapter, the problems of the first chapter are fully solved, in detail, step-by-step, and with different methods.

Mehdi Rahmani-Andebili

3. Complex Transformations: Problems

Abstract

In this chapter, the basic and advanced problems of complex transformations are presented. The subjects include linear, power, reciprocal, exponential, natural logarithm, hyperbolic sine and cosine, sine and cosine, and linear fractional complex transformation. Herein, different types of problems and exercises are presented that are categorized as follows:

Problems with detailed solution: They have been designed to teach students the subjects in detail. Moreover, they have been categorized into different levels based on their difficulty levels (easy, normal, and hard) and calculation amounts (small, normal, and large).
Partially solved exercises: They have been designed to encourage students to practice more problems while guiding them through the problem-solving procedure and hinting the required formulas.
Exercises with final answer: They have been designed to encourage students to practice by themselves while hinting them by the final answer as well as to help instructors to give tests or quizzes.

Mehdi Rahmani-Andebili

4. Complex Transformations: Solutions of Problems

Abstract

In this chapter, the problems of the third chapter are fully solved, in detail, step-by-step, and with different methods.

Mehdi Rahmani-Andebili

5. Singularities of Complex Functions, Complex series, Taylor and Laurent Series Expansions of Complex Functions, and Residue of Complex Functions: Problems

Abstract

In this chapter, the basic and advanced problems concerned with the singularities of complex functions including poles, removable singularity, and essential singularity; complex series; Taylor and Laurent series expansions of complex functions; and residue of complex functions are presented and studied. Herein, different types of problems and exercises are presented that are categorized as follows:

Problems with detailed solution: They have been designed to teach students the subjects in detail. Moreover, they have been categorized into different levels based on their difficulty levels (easy, normal, and hard) and calculation amounts (small, normal, and large).
Partially solved exercises: They have been designed to encourage students to practice more problems while guiding them through the problem-solving procedure and hinting the required formulas.
Exercises with final answer: They have been designed to encourage students to practice by themselves while hinting them by the final answer as well as to help instructors to give tests or quizzes.

Mehdi Rahmani-Andebili

6. Singularities of Complex Functions, Complex Series, Taylor and Laurent Series Expansions of Complex Functions, and Residue of Complex Functions: Solutions of Problems

Abstract

In this chapter, the problems of the fifth chapter are fully solved, in detail, step-by-step, and with different methods.

Mehdi Rahmani-Andebili

7. Complex Integration: Problems

Abstract

In this chapter, the basic and advanced problems of complex integration are presented. The subjects include complex integration of nonholomorphic functions, complex integration of holomorphic functions, and complex integration of functions including a finite number of singular points. Herein, different types of problems and exercises are presented that are categorized as follows:

Problems with detailed solution: They have been designed to teach students the subjects in detail. Moreover, they have been categorized into different levels based on their difficulty levels (easy, normal, and hard) and calculation amounts (small, normal, and large).
Partially solved exercises: They have been designed to encourage students to practice more problems while guiding them through the problem-solving procedure and hinting the required formulas.
Exercises with final answer: They have been designed to encourage students to practice by themselves while hinting them by the final answer as well as to help instructors to give tests or quizzes.

Mehdi Rahmani-Andebili

8. Complex Integration: Solutions of Problems

Abstract

In this chapter, the problems of the seventh chapter are fully solved, in detail, step-by-step, and with different methods.

Mehdi Rahmani-Andebili

9. Fourier Series, Half-Domain Fourier Sine and Cosine Series, Complex Fourier Series, Fourier Integral, Complex Fourier Integral, Fourier Transform, and Half-Domain Fourier Sine and Cosine Transforms: Problems

Abstract

In this chapter, the basic and advanced problems concerned with the Fourier series of periodic functions, half-domain Fourier sine and cosine series of aperiodic functions, complex Fourier series of periodic functions, Fourier integral of aperiodic functions, complex Fourier integral of aperiodic functions, Fourier transform of aperiodic functions, and half-domain Fourier sine and cosine transforms of aperiodic functions are presented and studied. Herein, different types of problems and exercises are presented that are categorized as follows:

Problems with detailed solution: They have been designed to teach students the subjects in detail. Moreover, they have been categorized into different levels based on their difficulty levels (easy, normal, and hard) and calculation amounts (small, normal, and large).
Partially solved exercises: They have been designed to encourage students to practice more problems while guiding them through the problem-solving procedure and hinting the required formulas.
Exercises with final answer: They have been designed to encourage students to practice by themselves while hinting them by the final answer as well as to help instructors to give tests or quizzes.

Mehdi Rahmani-Andebili

10. Fourier Series, Half-Domain Fourier Sine and Cosine Series, Complex Fourier Series, Fourier Integral, Complex Fourier Integral, Fourier Transform, and Half-Domain Fourier Sine and Cosine Transforms: Solutions of Problems

Abstract

In this chapter, the problems of the ninth chapter are fully solved, in detail, step-by-step, and with different methods.

Mehdi Rahmani-Andebili

11. Partial Differential Equations: Problems

Abstract

In this chapter, the basic and advanced problems of partial differential equations are presented. The subjects include determining the type of partial differential equations, updating partial differential equations by new variables, solving partial differential equations by using the techniques used in solving ordinary differential equations, solving partial differential equations by using their characteristics equations, solving partial differential equations by using variables separation method, solving partial differential equations by Laplace transform, and solving partial differential equations in a steady-state condition. Herein, different types of problems and exercises are presented that are categorized as follows:

Problems with detailed solution: They have been designed to teach students the subjects in detail. Moreover, they have been categorized into different levels based on their difficulty levels (easy, normal, and hard) and calculation amounts (small, normal, and large).
Partially solved exercises: They have been designed to encourage students to practice more problems while guiding them through the problem-solving procedure and hinting the required formulas.
Exercises with final answer: They have been designed to encourage students to practice by themselves while hinting them by the final answer as well as to help instructors to give tests or quizzes.

Mehdi Rahmani-Andebili

12. Partial Differential Equations: Solutions of Problems

Abstract

In this chapter, the problems of the 11th chapter are fully solved, in detail, step-by-step, and with different methods.

Mehdi Rahmani-Andebili

Backmatter

Titel: Mathematics of Engineering and Science
verfasst von: Mehdi Rahmani-Andebili
Verlag: Springer Nature Switzerland
Electronic ISBN: 978-3-031-71934-9
Print ISBN: 978-3-031-71933-2
DOI: https://doi.org/10.1007/978-3-031-71934-9

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