Syllabus
1. Convergent versus asymptotic expansions, Landau notation
2. Asymptotic expansion of functions, Stirling expansion of the Gamma function
3. Asymptotic series, Padé approximants, continued fractions
4. Asymptotic expansion of Laplace integrals, Watson's lemma
5. Laplace's method
6. Method of steepest descents for one-dimensional integrals: Example of asymptotic expansion of Bessel functions
7. Stationary phase method (in optics), eikonal, diffraction
8. Method of steepest descents for multidimensional integrals, Feynman diagrams, demonstration of one and two-loops calculations
9. WKB method in quantum mechanics, the anharmonic oscillator.
10. Solution of nonlinear differential equations by WKB method; application to fluid mechanics
11. Theory of a scalar quantum field, one and two loop calculation of effective potential
12. Introduction to renormalization theory
Annotation
Convergent versus asymptotic expansions. Asymptotic relations and expansions - properties, algebraic and analytical operations with them.
Various methods for asymptotic evaluation of parametric integrals. Applications in problems of mathematical physics.