The instructor will lecture on complex function theory and basic signal processing methods (Fourier analysis and Laplace transforms).
The aim of this course is for students to derive solutions of definite integrals with residue theorem and solutions of partial differential equations by using Laplace transforms.
- Complex function theory
- Linear system
- Fourier analysis
- Laplace transform
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||✔ Practical and/or problem-solving skills|
|Course schedule||Required learning|
|Class 1||Complex numbers: Four arithmetic operations, Euler's formula|
|Class 2||Complex functions: continuity, differentiability, holomorphic functions|
|Class 3||Holomorphic function and complex integral|
|Class 4||Cauchy's integral theorem/formula|
|Class 5||Taylor expansion and Laurent expansion|
|Class 7||Residue theorem|
|Class 8||Applications to definite integral|
|Class 9||Fourier series and its properties 1|
|Class 10||Fourier series and its properties 2|
|Class 11||Fourier series and its properties 3|
|Class 12||Fourier transform and its properties 1|
|Class 13||Fourier transform and its properties 2|
|Class 14||Laplace transform and its properties|
|Class 15||Applying the Laplace transform to solve linear differential equations|
Students will be assessed on their understanding of Fourier series, Fourier transform and Laplace transform.
Students' course scores are based on exercise problems (20%) and midterm and final exams (80%).