Mathematical Physics Tutorial I(1.0 credits)
|Course Type||:||Basic Specialized Courses|
|Starts 1||:||2 Autumn Semester|
|Lecturer||:||KITAHARA Teppei Designated Assistant Professor|
|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 master exact and approximate
analytical techniques for initial value problems that arise in physics, engineering and chemistry. Questions of
existence, uniqueness and convergence are also discussed. Fourier series follow naturally from the 2nd-order theory
and these are investigated, too.
|Calculus I, Calculus II, Linear Algebra I, Linear Algebra II;or Consent of Instructor|
|• 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.
|There is no designated textbook, but lecture materials will be handed out at every class.|
|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.)
|tutorial Attendance: 50%; Class performance: 50%
The “Absent” grade is reserved for students who withdraw by November 14.
After that day, a letter grade will be awarded based on marks earned from
all assessments during the semester.
|Instructor: KITAHARA Teppei
Office: ES Building, ES714