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Course Name: CSU0032 Engineering Mathematics 工程數學 (Fall 2026)
Instructor: Chao Wang 王超
Teaching Assistant: Hao-Yu Lin 林顥羽
Course Meetings: Wednesdays 14:20–17:20 @ room B101, Gongguan Campus Library B1 Room 002
Office Hours: Tuesday and Thursday 2–4pm @ room 511, Applied Science Building, Gongguan Campus (by appointment)

配合教育部雙語政策，此課程為 EMI 英文授課。

Contents

Course Syllabus

Engineering mathematics is a core subjectin many engineering disciplines. Essentially, it is a “language” by which we may describe, analyze, and predict behaviors of some dynamical systems. Such dynamical systems include, but not limit to, mechanical systems, electrical systems, multimedia systems (audio and graphical), and robotic systems. And because this “language” is all together general, precise, and beautiful, it informs and inspires people who seek for good ways to study and to control the mentioned dynamical systems. And, more importantly but perhaps often unfortunately buried in details in equation-solving, in my own opinion, studying engineering mathematics might give us a glimpse of common structures shared by seemingly unrelated systems. As Shakespeare rightly put it, “What’s in a name? That which we call a rose by any other name would smell as sweet.” It is this sweetness that we might taste when we finally “get it” and see that math helps express the essense of many things.

This course is designed for undergraduate students who have taken calculus and linear algebra, have had some programming experience, am willing to use modern AI, and are not afraid of building some simple hardware circuits using micro-controller units (MCUs) — we try to balance theoretical investigation with practical applications. To this end, we will also make ample use of GNU Octave, the language for scientific computing and visualization. We do not teach GNU Octave for you, and we believe students can use modern AI to learn how to use it.

Starting this semester, we will offer an AI-assisted system for students to self-generate exercise questions and answers to enhance learning.

Grading:

  • 50% Homework assignments (5-minute video recording per hands-on homework assignment.)
  • 10% Class discussion involvement (In-class and online/offline discussion and feedback, and how you will use our AI-assisted online learning service.)
  • 40% Other (In-class written/oral quizzes and demonstrations; the topic and coverage will be announced one week ahead.)

Course Schedule

The 16-week course schedule:

  1. Introduction to linear time-invariant systems; continuous and discrete signals
  2. Convolution, impulse responses, and applications
  3. Orthogonal basis and Fourier series
  4. Continuous Fourier transform
  5. Discrete Fourier transform and FFT
  6. Sampling theorem and applications
  7. Z-transform and digital filter
  8. Singular value decomposition (SVD) and applications
  9. Laplace transform
  10. Ordinary differential equations (ODE) and system modeling
  11. Transfer function and stability
  12. State-space representation
  13. State-space analysis
  14. Controllability and observability
  15. Feedback control and PID controller
  16. Introduction to physics-informed neural networks (PINN) and Hamiltonian neural networks (HNNs)

Textbook and References

There is no single book that covers all aspects that we hope to study. We encourage students to consult the following books for in-depth study of each specific topic. For each book, any edition will do:

  1. Engineering Mathematics, by O’Neil
  2. Signals and Systems, by Oppenheim, Willsky, and Nawab
  3. Differential Equations, Dynamical Systems, and an Introduction to Chaos, by Hirsch, Smale, and Devaney

Some more references will be posted on Moodle.

Accessibility

Students in need are encouraged to bring their considerations to the instructor.

Academic Integrity

All homework assignments and exams must be completed individually and independently, except as specifically allowed by the instructor.

Academic integrity is a key component of your education, which is for your benefit. Anyone found to be cheating or helping someone else cheat will receive zero score for that homework/exam. Please reflect on the university’s motto: Sincerity 誠, Integrity 正, Diligence 勤, Simplicity 樸.

Homework Assignment

All homework assignments will be announced on Moodle.