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Last update: RNDr. Vojtěch Kapsa, CSc. (14.01.2020)
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Last update: RNDr. Vojtěch Kapsa, CSc. (17.01.2020)
The aim of this course is to deepen and broaden knowledge of approximate methods with applications in physics.
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Last update: RNDr. Vojtěch Kapsa, CSc. (17.01.2020)
The course credit is awarded for participation and activity in exercises. Insufficient participation cannot be compensated in any other way. Course credit is a condition of admission to the exam. The exam is oral and the requirements correspond to the syllabus of the subject in the range that was presented at the lecture.
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Last update: RNDr. Vojtěch Kapsa, CSc. (14.01.2020)
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Last update: RNDr. Vojtěch Kapsa, CSc. (20.01.2020)
Lectures and exercises.
Exercises contain examples of asymptotic expansions and their properties, basic properties of asymptotic expansions and algebraic operations with them, asymptotics of Laplace-type integrals, applications of Watson's lemma, application of Laplace's method in symbolic programming etc.
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Last update: RNDr. Vojtěch Kapsa, CSc. (17.01.2020)
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
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