Engineering Mathematics with MATLAB

This textbook takes a streamlined, practical approach, designed to make engineering mathematics accessible and manageable for undergraduate students and instructors alike. Students will gain a fundamental understanding within the scope of a two-semester course. This textbook introduces students to the fundamental principles of engineering mathematics through concise explanations, systematically guiding them from the basics of first-order, second-order, and higher-order ordinary differential equations (ODEs), Laplace transforms, and series solutions of ODEs. It then transitions to more advanced topics, including linear algebra, linear system of ODEs, vector differential calculus and vector integral calculus, Fourier analysis, partial differential equations (PDEs), and concludes with complex numbers, complex functions, and complex integration. The book presents fundamental principles systematically with concise explanations. It features categorized key concepts, detailed solutions, and alternative methods to connect material to prior knowledge. Exercises are thoughtfully organized, balancing problem-solving practice with real-world applications in fields like mechanical engineering, electrical engineering, chemical engineering, and so on. Notably, this book incorporates MATLAB® to enhance understanding. MATLAB-based examples simplify complex calculations, offering visualizations that connect theory and practice. Chapters also include optional advanced topics, providing deeper insights for motivated learners. Designed with practicality in mind, this book offers a balanced approach to mastering engineering mathematics, with a manageable workload aligned to academic schedules. It is an invaluable resource for instructors seeking effective teaching tools and for students aiming to build strong mathematical foundations that they can apply to their own engineering discipline.

Chul Ki Song is an Emeritus Professor in the School of Mechanical Engineering, Gyeongsang National University, Korea. He earned his Ph.D. degree from Seoul National University, Korea. He previously worked for KIA Motors. Jong-Ryeol Kim is Professor in the Department of Electrical Engineering, Sejong University, Korea. He earned his Ph.D. degree from KAIST, Korea. He previously worked for Samsung Electronics.

Contents Preface 1. First Order Ordinary Differential Equations 2. Second Order Ordinary Differential Equations 3. Higher Order Ordinary Differential Equations 4. Laplace Transforms 5. Series Solutions of Ordinary Differential Equations 6. Linear Algebra: Matrices, Determinants, and Eigenvalue Problems 7. Linear System of Ordinary Differential Equations 8. Vector Differential Calculus: Grad, Div, and Curl 9. Vector Integral and Integral Theorems 10. Fourier Analysis 11. Partial Differential Equations 12. Complex Numbers and Functions 13. Complex Integration References Appendix A Appendix B