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

### Mathematical Physics I(2.0 credits)

Code:10156
Course Type:Basic Specialized Courses
Class Format:Lecture
Course Name : Chemistry
Starts 1 : 2 Autumn Semester
Elective/Compulsory : Elective
Lecturer : John A. WOJDYLO Designated Professor

 •Course Purpose This course is a companion course to Mathematical Physics II. Students master analytical techniques for problems that arise in physics, engineering and chemistry. This course introduces first order and second order ordinary differential equations and their solution methods. Questions of uniqueness of solutions and convergence are also discussed. Students are also introduced to Fourier series, the Fourier transform, convolution, Laplace transform, and the Dirac delta function. Students will find this mathematical methods course helpful in other units such as Quantum Mechanics, Analytical Mechanics, Electricity and Magnetism, as well as in Automotive Engineering and other engineering courses. This course has dual aims: 1) to convey mathematical principles; 2) to improve students’ technical ability ‒ i.e. ability to express intuition in mathematical terms and ability to solve problems. •Prerequisite Subjects Calculus I; Calculus II; Linear Algebra I; Linear Algebra II, or Consent of Instructor Mathematical Physics Tutorial I, Mathematical Physics II •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 and engineering. • 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 Boyce W., DiPrima R, Elementary Differential Equations, 7th ‒10th Ed., Wiley. •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 Attendance: 5%; Weekly Quizzes and Assignments: 25%; Mid-term exam: 35%; Final Exam: 35% The “Absent” grade is reserved for students who withdraw by November 16. After that day, a letter grade will be awarded based on marks earned from all assessment during the semester. •Notes •Contacting Faculty Office: Science Hall 5F 517 Phone: 052-789-2307 Email: john.wojdylo@s.phys.nagoya-u.ac.jp

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