Nagoya University, School of Engineering Lecture information system (SYLLABUS)

### Mathematical Physics Tutorial I(1.0 credits)

Code:10518
Course Type:Basic Specialized Courses
Class Format:Exercise
Course Name : Chemistry
Starts 1 : 2 Autumn Semester
Elective/Compulsory : Elective
Lecturer : Tadakatsu SAKAI Associate Professor

 •Course Purpose 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. Students will master exact and approximate analytical techniques for initial value problems, Fourier series, and Laplace transform that arise in physics, engineering and chemistry. •Prerequisite Subjects Calculus I, Calculus II, Linear Algebra I, Linear Algebra II;or Consent of Instructor •Course Topics • 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. •Textbook None. •Additional Reading 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.) •Grade Assessment Tutorial performance: 30%, Homework score: 60%, Tutorial attendance: 10%. The “Absent/W” grade is reserved for students who withdraw by November 30. After that day, grade (A+ to F) will be awarded based on marks earned from all assessments during the semester. •Notes In person if possible. Online, remote class (using Microsoft Teams), otherwise. •Contacting Faculty Instructor: SAKAI Tadakatsu Office: ES Building, ES711 Email: tsakai@eken.phys.nagoya-u.ac.jp

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