Course Introduction

• Prerequisite：Advanced Calculus and Linear Algebra
• Recommended for： Graduate
• Introduction：

Understand the basic ideas and tools used in the formulations and solutions of problems.

The object of this course is the construction, analysis, and interpretation of the mathematical models to help us understand the world we live in. We shall introduce key ideas in mathematical methods and modeling, with an emphasis on the connections between mathematics and applied natural sciences. The course covers both standard and modern topics, including scaling and dimensional analysis, regular and irregular perturbation; calculus of variations and continuum mechanics, etc.

• Syllabus：

1. Dimensional Analysis and Scaling
2. Green's Functions
3. Method of Eigenfunction Expansions
4. Perturbation Methods
5. Calculus of Variations
6. Mathematical Models of Continua

• Reference：

1. J. David Logan, Applied Mathematics 3rd Ed., Wiley-interscience, 2006