### Applied Mathematics University of Tsukuba

#### Course Overview

Applied mathematics will focus on the applications of mathematics in the field of engineering and physics. Students in this course will acquire problem-solving skills using applied knowledge in mathematics in vector analysis, complex variables, group theory, partial differential equation, Fourier series, Fourie and Laplace transforms.

#### Learning Achievement

Applied mathematics will focus on the applications of mathematics in the field of engineering and physics. Students in this course will acquire problem-solving skills using applied knowledge in mathematics in the field of partial differential equation, Fourier series, Fourie and Laplace transforms, special functions in combination with prior knowledge in calculus and complex variables.

#### Competence

Related to 1. Mathematical logic and calculation skills.

#### Course prerequisites

Students should have completed at least Calculus I, Calculus II, and prior knowledge about complex variables.

#### Grading Philosophy

？ 20% Attendance:

？ Be in class on time! If you are more than 15 minutes late then no class credit on that day.

？ If you are absent more than 3 times (classes) then you fail the course.

？ 20% Participation, HomeWorks.

？ 30% Midterm exam, class quizzes.

？ 30% Final Exam.

#### Course schedule

1. Review (Series, Complex variables, vectors etc.)

2. The Dirac-delta Function

3. Fourier Series (The Sine-Cosine Series, Exponential Form

4. Fourier Series (Convergence of Fourier Series, The Discrete Fourier Series)

5. Integral Transform (Fourier Transform)

6. Integral Transform (Laplace Transforms)

7. Mid Term Examination

8. Partial Differential Equations ( Wave Equations)

9. Partial Differential Equations ( Diffusion Equations)

10. Partial Differential Equations ( Laplace Equations)

11. Ordinary Differential Equations (solving by Transforms )

12. Ordinary Differential Equations (Operator and Inverse Operator, series solution)

13. Gamma function, Beta function

14. Sturm？Liouville Theory-Orthogonal Functions

15. Bessel Functions

16. Legendre Functions

17. Integral Equation

18. Review and Exercises.

#### Course type

Lectures

#### Online Course Requirement

#### Instructor

Islam Monirul Muhammad

#### Other information

？ Students are expected to be in class on time! Late more than 15 minutes will be counted as absent.

- Absent more than 3 times (classes) without prior notification will be considered fail in the course.

？ No computers or mobile phones during class except necessary for class purposes.

- Students are expected to bring note book and pencil.

* All exams are closed book.

* Rules and regulations regarding examination as set forth by University of Tsukuba will be strictly observed.

#### Site for Inquiry

Link to the syllabus provided by the university