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401-1262-07L 10 Credits BSC D-CHAB , D-MATH , D-PHYS

Analysis II: Several Variables

Analysis II: mehrere Variablen

Lecturers: Prof. Dr. Joaquim Serra
Examiners: Prof. Dr. Alessio Figalli, Prof. Dr. Joaquim Serra
VVZ CR n/a

Last Updated: 2026-06-03 00:41:00

Abstract

Introduction to differential and integral calculus in several real variables, vector calculus: differential, partial derivative, implicit functions, inverse function theorem, minima with constraints; Riemann integral, vector fields, differential forms, path integrals, surface integrals, divergence theorem, Stokes' theorem.

Objective

The ability to work with the basics of calculus/analysis in several variables in a mathematically rigorous way.

Content

Calculus in several variables; curves and surfaces in R^n; extrema with constraints; integration in n dimensions; vector calculus.

Resources

Literature

H. Amann, J. Escher: Analysis II https://link.springer.com/book/10.1007/3-7643-7402-0 J. Appell: Analysis in Beispielen und Gegenbeispielen https://link.springer.com/book/10.1007/978-3-540-88903-8 R. Courant: Vorlesungen über Differential- und Integralrechnung https://link.springer.com/book/10.1007/978-3-642-61973-1 O. Forster: Analysis 2 https://link.springer.com/book/10.1007/978-3-658-02357-7 H. Heuser: Lehrbuch der Analysis https://link.springer.com/book/10.1007/978-3-322-96826-5 K. Königsberger: Analysis 2 https://link.springer.com/book/10.1007/3-540-35077-2 W. Walter: Analysis 2 https://link.springer.com/book/10.1007/978-3-642-97614-8 V. Zorich: Mathematical Analysis II (englisch) https://link.springer.com/book/10.1007/978-3-662-48993-2

Learning Materials (Links)

General Information

Language
English (lecture), German (exercise)
Levels
BSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
written 150 minutes and 180 minutes
Aids
Gemäss Angaben zu den Leistungskontrollen als Semesterkurse:in der Sommerprüfungssession 2025: vom HS 2024 und FS 2025;in der Winterprüfungssession 2025/26: vom FS 2025 und HS 2025.
Die Lernelemente (BYOD) der beiden Semesterkurse gelten auch für den Jahreskurs.

Course Components

Type Title Time & Place Hours
lecture Analysis II: mehrere Variablen
Mittwoch 8-10 im HG F 7 mit Videoübertragung im HG F 5.
  • Mon 08:15-10:00 (ETA F 5)
  • Wed 08:15-10:00 (HG F 5)
  • Wed 08:15-10:00 (HG F 7)
  • Thu 16:15-18:00 (ETA F 5)
6 h weekly
exercise Analysis II: mehrere Variablen
Groups are selected in myStudies. Mo 10-12 oder Mo 16-18 (oder Mo 12-14). Dritte Übungsstunde gemäss Gruppeneinteilung (verschiedene Termine). Zusätzlich wird das StudyCenter angeboten:
  • Mon 10:15-12:00 (CAB G 56)
  • Mon 10:15-12:00 (CHN C 14)
  • Mon 10:15-12:00 (CHN D 42)
  • Mon 10:15-12:00 (CHN D 46)
  • Mon 10:15-12:00 (ETZ E 8)
  • Mon 10:15-12:00 (ETZ E 9)
  • Mon 10:15-12:00 (HG E 33.3)
  • Mon 10:15-12:00 (HG E 33.5)
  • Mon 10:15-12:00 (HG G 26.3)
  • Mon 10:15-12:00 (LFW C 4)
  • Mon 10:15-12:00 (LFW E 13)
  • Mon 10:15-12:00 (ML F 38)
  • Mon 10:15-12:00 (ML H 43)
  • Mon 10:15-12:00 (ML J 34.1)
  • Mon 10:15-12:00 (ML J 34.3)
  • Mon 10:15-12:00 (ML J 37.1)
  • Mon 12:15-14:00 (CHN F 46)
  • Mon 16:15-18:00 (CAB G 52)
  • Mon 16:15-18:00 (CAB G 59)
  • Mon 16:15-18:00 (CHN E 42)
  • Mon 16:15-18:00 (HG F 26.3)
  • Mon 16:15-18:00 (LEE C 104)
  • Mon 16:15-18:00 (LFW C 11)
  • Mon 16:15-18:00 (ML J 37.1)
  • Mon 16:15-18:00 (NO D 11)
  • Tue 13:15-14:00 (CHN D 48)
  • Tue 13:15-14:00 (HG G 26.5)
  • Tue 13:15-14:00 (NO C 6)
  • Wed 12:15-13:00 (ML J 34.1)
  • Wed 16:15-17:00 (HG E 33.3)
  • Wed 16:15-17:00 (LEE C 114)
  • Thu 15:15-16:00 (CAB G 52)
  • Thu 15:15-16:00 (CAB G 56)
  • Thu 15:15-16:00 (CAB G 59)
  • Thu 15:15-16:00 (CHN D 48)
  • Thu 15:15-16:00 (HG G 26.3)
  • Thu 15:15-16:00 (IFW A 32.1)
  • Thu 15:15-16:00 (LEE D 105)
  • Thu 15:15-16:00 (LFW B 2)
  • Thu 15:15-16:00 (LFW C 4)
  • Thu 15:15-16:00 (NO D 11)
  • Fri 12:15-13:00 (CAB G 56)
  • Fri 12:15-13:00 (CLA E 4)
  • Fri 12:15-13:00 (HG G 26.5)
  • Fri 12:15-13:00 (ML J 34.1)
  • Fri 13:15-14:00 (ETZ E 7)
  • Fri 13:15-14:00 (HG G 26.5)
  • Fri 13:15-14:00 (ML J 34.1)
3 h weekly

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