### 2016　Fourier and Laplace Transforms

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Computer Science
Instructor(s)
Nagahashi Hiroshi  Obi Takashi
Class Format
Lecture
Media-enhanced courses
Day/Period(Room No.)
Tue7-8(W631)  Fri7-8(W631)
Group
E
Course number
ZUS.C201
Credits
2
2016
Offered quarter
1-2Q
Syllabus updated
2017/1/11
Lecture notes updated
2016/7/27
Language used
Japanese
Access Index

### Course description and aims

The instructor will lecture on complex function theory and basic signal processing methods (Fourier analysis and Laplace transforms).

### Student learning outcomes

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.

### Keywords

- Complex function theory
- Linear system
- Fourier analysis
- Laplace transform

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills Critical thinking skills ✔ Practical and/or problem-solving skills

Lectures

### Course schedule/Required learning

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 6 Residue
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

### Assessment criteria and methods

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%).

### Related courses

• ZUS.F301 ： Foundations of Functional Analysis
• ZUS.C301 ： Signal Processing
• ZUS.M303 ： Digital Communications