Advanced Mathematics for Engineers and Scientists with Worked Examples

Advanced Mathematics for Engineers and Scientists with Worked Examples covers core to advanced topics in mathematics required for science and engineering disciplines. It is primarily designed to provide a comprehensive, straightforward and step-by-step presentation of mathematical concepts to engineers, scientists and general readers. It moves from simple to challenging areas, with carefully tailored worked examples also of different degrees of challenge. Mathematical concepts are deliberately linked with appropriate engineering applications to reinforce their value and are aligned with topics taught in major overseas curriculums.

This book is written primarily for students at levels 3 and 4 (typically in the early stages of a degree in engineering or a related discipline) or for those undertaking foundation, access, Higher National Certificate (HND), International Foundation Year (IFY), and International Year One (IYO) courses with math modules. It is organised into four main parts:

Part I: Trigonometry

Part II: Advanced Mathematics

Part III: Matrices and Vectors

Part IV: Calculus

Each of the above four parts is divided into two or more chapters, and each chapter can be used as a stand-alone guide with no prior knowledge assumed. Further practice material for each chapter is available online.

1. Trigonometric Functions I. 2. Trigonometric Functions II. 3. Trigonometric Identities I. 4. Trigonometric Identities II. 5. Solving Trigonometric Equations. 6. The Binomial Expansion. 7. Partial Fractions. 8. Complex Numbers I. 9. Complex Numbers II. 10. Matrices. 11. Vectors. 12. Fundamentals of Differentiation. 13. Advanced Differentiation. 14. Applications of Differentiation. 15. Indefinite Integration. 16. Definite Integration. 17. Advanced Integration I. 18. Advanced Integration II. 19. Application of Integration. Appendix. Glossary.

Shefiu Zakariyah is a Chartered Engineer (CEng) and a senior member of IEEE (SMIEEE), with over a decade experience in teaching, content development and assessment, and technical training and consulting.