Welcome to this course on Differential Equations

In this course, we will study the ordinary differential equation and its application in our daily life

The main content are

1. understand that physical systems can be described by differential equations

2. understand the practical importance of solving differential equations

3. understand the differences between initial value and boundary value problems (IVPs and BVPs)

4. appreciate the importance of establishing the existence and uniqueness of solutions

5. recognize an appropriate solution method for a given problem

6. classify differential equations

7. analytically solve a wide range of ordinary differential equations (ODEs)

8. obtain approximate solutions of ODEs using graphical and numerical techniques

9. use Fourier analysis in differential equation solution methods

10. solve classical linear partial differential equations (PDEs)

11. solve differential equations using computer software

Learning & Teaching Modes

This course relies on course videos, online quizzes and workshops to guide students through the material, tutorial classes for peer and tutor support, and a sequence of written assignments that provide opportunities for students to practice techniques and develop their understanding of the course.

Learning Activities Summary

The course will explore and develop the following.

1. First-order ordinary differential equations

2. One-dimensional autonomous ODE models

3. Second- and higher-order ODEs

4. Partial differential equations

5. Representing periodic functions by Fourier series

6. Series solutions of ODEs

7. More partial differential equations

And most important fully solved exercises of each chapter.