Course Name: Mathematical Physics Methods (1)
Course type: undergraduate students in physics department are only optional.
Class credits: 108 class hours, 6 credits.
Prerequisites: advanced mathematics, general physics.
Basic purpose:
1. Give priority to the methods commonly used in classical mathematics and physics, and introduce the new development in recent years appropriately.
2. Prepare for the related math and physics problems in the following courses.
3. Master the basic theory of analytic function and skillfully apply it to solving ordinary differential equations and calculating definite integrals.
4. Master the basic solutions of mathematical and physical equations.
5. Master the main properties and applications of basic special functions.
Executive summary:
1. Analytic function theory: calculus, infinite series, analytic continuation, multivalued function.
2. Application of analytic function theory: series solution of ordinary differential equation and residue theorem to calculate definite integral.
3. Main solutions of mathematical and physical equations: separation of variables, integral transformation and Green's function.
4. Special functions (γ function, spherical function, cylindrical function) and their applications.
5. Preliminary variational method.
Teaching methods: classroom teaching, including an appropriate number of practice (discussion) classes.
Textbooks and reference books:
1. edited by Wu chong, Methods of Mathematical Physics, Peking University Publishing House 1999.
2. Wu Ren, Problem Set of Mathematical Physics Methods, Peking University Publishing House, 2nd Edition, 1995.
3. Guo Dunren, Mathematical Physics Methods, Higher Education Press, 2nd Edition, 199 1.
4. Liang, Mathematical Physics Methods, Third Edition, Higher Education Press, 1998.
5. Edited by Hu Sizhu. Guide to solving problems in mathematical physics methods, higher education press 1998.
6. Advanced Applied Calculus, F.B.Hildebrand, Prentice-Hall (Englewood Cliffs, New Jersey, USA), 1976.