Essential Science and Engineering Mathematics

Linear Algebra, Differential Equations and Complex Variables
Erscheinungsjahr 2027
ISBN: 978-3-032-42924-7
Verlag: Springer

Buch, Englisch, 354 Seiten, Format (B × H): 155 mm x 235 mm

provides a structured introduction to the mathematical techniques commonly encountered in undergraduate engineering and applied science courses. Designed for early-stage engineering students, the book integrates linear algebra, ordinary differential equations, mathematical modeling, and foundational complex analysis into a coherent learning framework. The text begins with matrices, systems of linear equations, vector spaces, and eigenvalue problems, laying the groundwork for modern engineering analysis. It then introduces ordinary differential equations through practical solution methods, including separable equations, Bernoulli equations, variation of parameters, and Cauchy-Euler equations. Throughout the book, mathematical modeling examples demonstrate how differential equations can be used to represent and analyze engineering and scientific systems. The book concludes with an accessible treatment of complex numbers and selected topics in complex analysis, supporting applications in electrical engineering, signal processing, physics, and related disciplines. Carefully sequenced explanations, worked examples, and progressively challenging exercises help students develop confidence in analytical reasoning.

Balancing mathematical rigor with accessibility, this textbook is designed for undergraduate courses in engineering mathematics, applied mathematics, physical sciences, computer science, data science, and related STEM fields. It also serves as a valuable resource for independent learners seeking a clear, practical foundation in essential mathematical methods and their engineering applications.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Al Ali, Ahmad

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Algebra
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Preface.- Matrices.- Vector Spaces and Subspaces.- Eigenvalues and Eigenvectors.- Ordinary Differential Equations.- Complex Analysis and Their Applications.- Appendix: Solutions to Exercises.

Über Autor(innen)

Ahmad Al Ali, Ph.D., is Professor of Applied Mathematics and Vice-Chancellor of Emirates Aviation University, Dubai. He earned his Ph.D. in Applied Mathematics from City University of London and holds MSc and BSc degrees in Mathematics from the University of London. Before joining Emirates Aviation University, he served as Associate Dean for Research in the Faculty of Mathematics at United Arab Emirates University, where he taught and conducted research in applied mathematics. His research interests include mathematical modeling, numerical methods, and asymptotic analysis. Throughout his academic leadership career, he has contributed to the development of industry-oriented higher education programs in engineering, aviation, and applied sciences. Teaching has remained central to his academic career, with extensive experience in mathematics and engineering mathematics education. His teaching focuses on helping students understand complex mathematical concepts and connect mathematical theory with practical engineering applications. Drawing on extensive experience in curriculum development and engineering mathematics education, he is committed to presenting complex mathematical concepts through clear, structured, and accessible explanations that support student understanding and effective learning.