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:

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
  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:

Main topics:

  1. linear algebra, part II (six 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 (nine weeks)

-Riemann integral, -basics of differentiation of functions of several variables, -inverse function theorem, -implicit function theorem, -introduction to ordinary differential equations


linear algebra references:

webpage of the 2019 course by Vitalii Konarovskyi:

Lankam, Nachtergaele, Schilling Linear Algebra, available at

Strang Introduction to Linear Algebra,

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,

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: (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): 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: (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:
  • lecture notes: 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)

week 10 (8 Jun- 12 Jun)

week 11 (15 Jun- 19 Jun)

few additional matters:

partially due to my fault (inconsistent date for QA session in week 10 on webpage, sorry for that, no such problem in the email via Almaweb) the QA session of week 10 on Thursday 11.06 was not very crowded

there were some requests for more details on marked HWs. I suggest the following solution. You can find here: and here: more detailed distribution of points. Compare the solutions you have sent with the benchmark solutions on TA’s webpage. In case you absolutely disagree with your mark after making this comparison, please write to asking for feedback. (remark: links are newly created on 15.06, in case you had difficulties accessing the content before, try now again)

Exam details: 3.08.2020, 9:30-12. There will be five problems to be solved, ca 2 from linear algebra, 2 from Riemann integration, 1 from the remaining material. Every problem will be similar to either HW assignments or simpler proofs in the lecture notes. To be admitted to the exam you need at least 50% of your HW points. HW points do not influence exam grade. In case you have passed math1 not as my course, you are eligible for an alternative exam: 2 questions from linear algebra will be replaced by another 2 problems of analysis. To sit this alternative version, a student needs to send me until 17.07 his decision and proof of having math1 passed not to my course.

week 12 (22 Jun- 26 Jun)

week 13 (29 Jun- 3 Jul)

week 14 (6 Jun- 10 Jul)

  • HW15 (last one): A request from the marking person (repeated): use plane paper sheets for HWs! Take good quality scans! The marking person is entitled to reduce points if these conditions are not met, and in extreme cases give null points
  • lecture notes for week 14&15:
  • Figures to the lecture notes:
  • no QA session
  • tutorials Friday 10.07
  • detailed results of HW13

there are two ways to earn extra points for the exam admission: (i) each point from HW15 is doubled (details in the HW file), (ii) you can write a short lecture note (details in the lecture notes)

in week 15 a mock exam will appear, there will be QA session on Wednesday 15.07, and last tutorials. between 15.07 and 27.07 I am not available. on 28.07 the final point count will be made and thus the admission decision. in the time-frame 28.07-31.07 there will be an additional QA session.

exam presence: unfortunately, the faculty insists on the presence exam as the only option. those who cannot come will be given opportunity to take the resit exam as the first exam. the resit is (very roughly) expected in early October