## Mathematical Physics

 Faculteit Science and Engineering Jaar 2021/22 Vakcode WBPH049-05 Vaknaam Mathematical Physics Niveau(s) propedeuse Voertaal Engels Periode semester II b ECTS 5 Rooster rooster.rug.nl

Uitgebreide vaknaam Mathematical Physics
Leerdoelen At the end of the course, the student is able to:

1.
reproduce and apply the basic concepts of sequences of real numbers, limits of a sequence, series, convergence of series, power series, sequences/series of functions, uniform convergence, Taylor expansions, Fourier series, Fourier integral, Second order ordinary differential equations , Partial Differential equations

2.
determine when a series is convergent, determine Taylor expansions, Fourier and integral expansion, and solve elementary second order differential equations, including those with applications to physical systems

3.
interpret the properties of series, sequences, and differential equations and is able to use these properties to investigate the behavior of physical systems.

4.
apply the definitions of the various types of series convergence and is able to classify and Interpret the various of types of convergence (absolute, uniform, conditional) and determine the radius of convergence.

5.
solve differential equations using series expansions and Fourier transformations.
Omschrijving The course Mathematical Physics deals with more advanced topics from calculus for Physics and Applied Physics and Astronomy students.

The course is about sequences and series (limits of sequences, (uniform) convergence of series), second order differential equations (techniques to solve second order differential equations and application to atomic force microscopy), basic introduction to Fourier analysis, and a basic introduction to partial differential equations with an emphasis on applications in Physics (heat conduction, vibrations, Laplace and Poisson equation).

Below is a list of topics to be treated:
• sequences of real numbers
• limits of a sequence
• series
• convergence of series
• power series
• sequences/series of functions,
• Taylor expansions,
• Fourier series
• Fourier integral
• Second order ordinary differential equations
• Partial Differential equation
• Applications: heat conduction, vibrations, Laplace and Poisson equation
Uren per week
Onderwijsvorm Hoorcollege (LC), Opdracht (ASM), Werkcollege (T)
(LC 32, T 32, ASM 48 self study 28 hrs)
Toetsvorm Opdracht (AST), Schriftelijk tentamen (WE)
(WE 100%, AST 0% home work)
Vaksoort propedeuse
Coördinator Prof. Dr. G. Palasantzas
Docent(en) Prof. Dr. G. Palasantzas
Verplichte literatuur
Titel Auteur ISBN Prijs
Calculus. Early transcendentals. newest edition (International Student Edition), London: Thomson Learning James Stewart 978-0538-49887-6
Entreevoorwaarden The course unit assumes basic prior knowledge acquired from Calculus 1.
Opmerkingen If final exam grade <4.5 then: