Mathematics of Engineering and Science Practice Problems, Methods, and Solutions

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.

1. Complex Functions, Equations, Quantities, and Limits: Problems.- 2. Complex Functions, Equations, Quantities, and Limits: Solutions of Problems.- 3. Complex Transformations: Problems.- 4. Complex Transformations: Solutions of Problems.- 5. Singularities of Complex Functions, Complex series, Taylor and Laurent Series Expansions of Complex Functions, and Residue of Complex Functions: Problems.- 6. Singularities of Complex Functions, Complex series, Taylor and Laurent Series Expansions of Complex Functions, and Residue of Complex Functions: Solutions of Problems.- 7. Complex Integration: Problems.- 8. Complex Integration: Solutions of Problems.- 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.- 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.- 11. Partial Differential Equations: Problems.- 12. Partial Differential Equations: Solutions of Problems.

Dr. Mehdi Rahmani-Andebili is an Assistant Professor with the Department of Electrical and Computer Engineering at the University of Alabama. He received his first M.Sc. and Ph.D. degrees in Electrical Engineering from Tarbiat Modares University and Clemson University in 2011 and 2016, respectively, and his second Ph.D. (2nd M.Sc.) degree in Physics and Astronomy from the University of Alabama in Huntsville in 2019. Moreover, he was a Postdoctoral Fellow at the Sharif University of Technology during 2016-2017. As a professor, he has taught many courses and labs, including Power System Analysis, Electric Machines, Feedback Control Systems Analysis and Design, Signals and Systems, Electromagnetics, Electronics, Digital Logic, Industrial Electronics, Renewable Distributed Generation and Storage, AC Electrical Circuits Analysis, DC Electrical Circuits Analysis, Electrical Circuits and Devices, Fundamental of Electrical Engineering, Essentials of Electrical Engineering Technology, and Algebra and Calculus-Based Physics. Dr. Rahmani-Andebili has over 300 single-author or first-author publications, including journal papers, conference papers, textbooks, books, and book chapters. He is an IEEE Senior Member and a permanent reviewer of many reputable journals. His research areas include Smart Grid, Applications of Artificial Intelligence in Planning and Operation of Power Systems, Integration of Renewables and Energy Storages into Power Systems, Energy Scheduling and Demand-Side Management, Electric Vehicles and Distributed Generation, and Advanced Optimization Techniques in Power System Studies.