Analysis II for Physics, Uni Leipzig, SS 2020

This is a direct follow up of the WS 2019/20 Analysis & Linear Algebra for Physics lecture.

General rules to be admitted to exam, you will need to have at least 50% of the HW points (points for problems marked with (*) are extra points). In this semester HWs will not affect the final exam grade. HW points available at: https://bit.ly/2YU5B0Q

Due to pandemia, we start our semester in e-learning mode.

General outline: there will be

  1. Lecture notes with some level of interactivity
  2. Homeworks (HWs) posted online, to be solved and submitted according to the guidelines https://bit.ly/3cbPZt2
  3. Tutorials by TA Mrs. Mahsa Sayyary Namin aimed at giving you opportunity to prepare for solving HWs and to understand better the material. More details at Mrs. Sayyary webpage: https://mahsasayyary.wixsite.com/mahsa/teaching

Main topics:

  1. linear algebra, part II (five weeks)

-basics on tensors, -orthonormal tensors, -relation between tensors and matrices -decompositions: polar, spectral, -eigenpairs, -characteristic polynomial, -applications of decompositions, -Cayley-Hamilton formula

2. analysis, part II (ten weeks)

-Riemann integral, -basics of differentiation of functions of several variables, -inverse function theorem, -implicit function theorem, -sequences and series of functions, -integration and differentiation of sequences and series of functions, -Fourier series, -introduction to ordinary differential equations

Literature

linear algebra references:

webpage of the 2019 course by Vitalii Konarovskyi: http://www.math.uni-leipzig.de/~konarovskyi/teaching/2019/Math2/Math2_2019.html

Lankam, Nachtergaele, Schilling Linear Algebra, available at https://bit.ly/2R5jIvC

Strang Introduction to Linear Algebra, http://math.mit.edu/~gs/linearalgebra/

for vector/tensor calculus: part I of Gurtin, Fried, Anand The Mechanics and Thermodynamics of Continua

analysis references:

Rudin Principles of Mathematical Analysis (available at the 2019 course website)

Schueler Calculus 1-4, https://bit.ly/2X68Am1

Remark for students repeating Analysis II, who passed Analysis I not to my lecture (in previous years): the initial part on Linear Algebra in this semester is not mandatory for you. You have two options: either you choose to take it, which means you will have the exam identical with the rest of the group, or you choose not to take it, which means you will sit an alternative exam, with purely analysis questions (number and difficulty of questions in both cases will be the same).

Detailed plan:

week 1 (6-10 April)

  • HW9 (deadline shifted by +1 week compared to the one on the pdf) related to the part of the Linear Algebra section lectured in the previous semester: http://bit.ly/31cfxSB (the subproblem with (*) is not mandatory, i.e. will produce extra points if solved) attention: due to lack of tutorials on 10.04, I have extended the deadline considerably (it may coincide with the deadline for HW10, please take it into account when managing your time)
  • lecture notes (relevant part from the previous semester): https://bit.ly/2R76e2q they are rather dirty and should serve only to fill in gaps in your own notes from the lecture
  • no virtual lecture (theory already covered in the previous semester)
  • no tutorials: Good Friday

week 2 (13-17 April)

  • no HW
  • lecture notes: https://bit.ly/2RvpJSw (we will have a Q&A session next week for your comments/questions)
  • tutorials Friday 17.04

week 3 (20-24 April)

week 4 (27 April-1 May)

week 5 (4 May- 8 May)

week 6 (11 May- 15 May)

  • no HW. current HW points available at: https://bit.ly/2YU5B0Q
  • lecture notes: https://bit.ly/2KWYehd The portion from week 5 covers also this week
  • no QA session: until Wednesday 13.05 morning it seems you have no questions: I received no emails.
  • tutorials Friday 15.05

week 7 (18 May- 22 May)

week 8 (25 May- 29 May)

week 9 (1 Jun- 5 Jun)