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

### Mathematics II and Tutorial(4.0 credits)

Code:10210
Course Type:Basic Specialized Courses
Class Format:Lecture and Exercise
Course Name : Fundamental and Applied Physics Automotive Engineering Automotive Engineering
Starts 1 : 2 Autumn Semester 2 Autumn Semester 2 Autumn Semester
Elective/Compulsory : Compulsory Compulsory Compulsory
Lecturer : Takaaki　FUJITA Professor

 •Course Purpose This course introduces students to vector analysis and partial differential equations, expecting their applications to advanced engineering, such as those related to mechanics and electromagnetics, and those to materials and heat transfer phenomena. The purpose of the course is to acquire fundamental knowledge in vector analysis and partial differential equations and enable students to apply it to solve actual engineering issues through intensive exercises. Targets 1. Enable to solve basic problems on vector analysis. 2. Enable to solve basic problems on partial differential equations. •Prerequisite Subjects Calculus I, II Linear Algebra I, II •Course Topics 1. Vector algebra 2. Vector differential operations 3. Curved lines and curved surfaces 4. Gradient, divergence and rotation 5. Line integrals and surface integrals 6. Gauss theorem, Stokes theorem and Green's theorem 7. Irrotational (conservative) field and solenoidal field 8. Curvilinear coordinate systems (cylindrical coordinates and spherical coordinates) 9. Poisson's equation and Green function 10. Separation of variables: Laplace equation, diffusion equation and wave equation Students are expected to review the distributed notes after lectures. Students need to submit reports on the problems presented in the lecture. The solutions of the problems will be presented in the lecture where reports are returned, through which students are expected to deepen their understanding. •Textbook Not specified. Notes are distributed during the lecture. •Additional Reading Mathematical Methods for Physicists, sixth edition, by G. B. Arfken and H. J. Weber, Elesevier, 2005 (ISBN: 0-12-088584-0) Mathematical Methods in the Physical Sciences, by Mary L. Boas, Wiley, 2006 ((ISBN: 978-0471198260) •Grade Assessment Reports: (50%) Examinations: (50%) Students need to obtain at least 60% of the total marks to pass the course. •Notes •Contacting Faculty Office: Bld. No. 8 south, Room No. 407, Phone: 052-789-4593, E-mail : fujita@energy.nagoya-u.ac.jp

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