In this course, we will investigate the mathematical methods and techniques that are largely used in engineering sciences and related fields. This is an interdisciplinary subject motivated by engineers’ needs of using mathematical approaches in terms of practical and theoretical considerations for analyzing and solving problems of relevance. This second semester of engineering mathematics will be dealt with Fourier series as well as integral and transforms, boundary-value problems, partial differential equations (PDE), and complex analysis.

Course Contents: 1. Orthogonal functions and Fourier series 2. Sturm-Liouville theorem 3. Fourier integral 4. Fourier transform * 1st midterm examination 5. Boundary-value problems and partial differential equations (in rectangular and other coordinates) 6. PDE Wave equation 7. PDE Heat equation 8. PDE Laplace equation * 2nd midterm examination 9. Complex analysis: functions of a complex variable 10. Complex analysis: integration in the complex plane 11. Complex analysis: series and residues * 3rd midterm examination

1. D. G. Zill, Advanced Engineering Mathematics, 7th Ed., Jones & Bartlett Learning, Burlington, 2022.

2. E. Kreyszig, Advanced Engineering Mathematics, 10th Edition, John Wiley & Sons, Inc., New York, 2011. 3. P. V. O’Neil, Advanced Engineering Mathematics, 7th Edition, Brooks/Cole Publishing Company, London, 2011. 4. M. D. Greenberg, Advanced Engineering Mathematics, 2nd Ed., Prentice Hall, 1998.