Goals of the Course(JPN)
Goals of the Course
|Students taking Mathematical Physics I should also take this tutorial class. This course introduces first-order and second-order ordinary differential equations and their solution methods. Students will master exact and approximate analytical techniques for initial value problems that arise in physics, engineering and chemistry. Questions of existence, uniqueness and convergence will also be discussed. Fourier series follow naturally from the second-order theory and these are investigated, too.|
Objectives of the Course(JPN)
Objectives of the Course
|Students will master exact and approximate analytical techniques for initial value problems, Fourier series, and Laplace transform that arise in physics, engineering and chemistry.|
Course Content / Plan
|• First order ordinary differential equation (ODE) initial value problems. Integration factor; separable equations;|
systems of ODEs (Hamiltonian systems); phase plane, flow. Uniqueness and existence theorems. Some differences
between linear and nonlinear ODEs.
• Second order linear ODE initial value problems. Homogeneous solution. Proving linear independence (Wronskian).
Method of Undetermined Coefficients; Variation of Parameters. Series solutions: ordinary point, regular singular
point; convergence tests; Method of Frobenius. Examples from physics, engineering and chemistry.
• Fourier series. Dirichlet conditions. Role of symmetry. Gibbs phenomenon. Effect of jump discontinuity on speed of
convergence. Integration and differentiation of Fourier series.
• Fourier transform, convolution, Dirac delta function. Laplace transform.
Course Prerequisites and Related Courses
|Calculus I, Calculus II, Linear Algebra I, Linear Algebra II; or Consent of Instructor|
Course Evaluation Method and Criteria
|Tutorial performance: 30%, Homework score: 60%, Tutorial attendance: 10%.|
|1. Boas M.L., 2006, Mathematical Methods in the Physical Sciences, 3rd ed., John Wiley & Sons.|
2. Strang, G., Introduction to Linear Algebra, 4th Edition, Chapter 6.
3. Arfken G.B. & Weber H.J., 2005, Mathematical Methods for Physicists, 6th ed., Elsevier Academic Press. (Copies are available in the library.)
Study Load(Self-directed Learning Outside Course Hours)
|There are assignments for each tutorial.|
Language Used in the Course
Lecture format, etc.
|In person if possible. Online, remote class (using Microsoft Teams), otherwise.|
Additional measures for remote class (on-demand class)