Multivariable Analysis
Faculteit  Science and Engineering 
Jaar  2019/20 
Vakcode  WBMA19011 
Vaknaam  Multivariable Analysis 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester I b 
ECTS  5 
Rooster  https://rooster.rug.nl/#/en/current/course/WBMA19011 
Uitgebreide vaknaam  Multivariable Analysis  
Leerdoelen  1. The student can reproduce the basic theory of topological properties, such as open, closed, compact, and connected sets in R^n. The student is able to apply this theory to examples, and formally verify such properties in examples, rigorously prove simple corollaries of this theory, or produce counterexamples for nonvalid statements. 2. The student can formulate the Banach Contraction Principle and apply this theorem to prove the existence and uniqueness for solutions of differential equations. In addition, the student can explain the role of the Banach Contraction Principle in the proofs of the Implicit and Inverse Function Theorems. 3. The student can formulate the Implicit and Inverse Function Theorems and apply these theorems in concrete examples. 4. The student can reproduce the main theorems (e.g. concerning wedge product, exterior derivative, pullback) about differential forms on R^n and apply these in concrete problems. In addition, the student can apply Stokes' formula in concrete applications and use this formula to derive the classical integral theorems of multivariable calculus, such as Green's Theorem, Gauss' Theorem, and Stokes' Theorem. 

Omschrijving  This course provides a fundamental mathematical underpinning of many of the concepts and techniques as treated in the courses Calculus 2. The derivative of a multivariate function is introduced as a linear map; higher order derivatives then become multilinear maps. An important theorem is the Banach Contraction Principle, which can be used to prove the existence of solutions of nonlinear equations including differential and integral equations. In particular, the Banach Contraction Principle will be used to prove the Implicit and Inverse Function Theorems. Finally, the course provides a framework for multivariable calculus in terms of differential forms. This setup culminates in the elegant Stokes' formula, which can be interpreted as a farreaching generalization of the Fundamental Theorem of Calculus and which unifies all the classical integral theorems of calculus, such as Green's Theorem, Gauss' Theorem, and Stokes' Theorem.  
Uren per week  
Onderwijsvorm  Hoorcollege (LC), Werkcollege (T)  
Toetsvorm  Opdracht (AST), Schriftelijk tentamen (WE)  
Vaksoort  bachelor  
Coördinator  dr. R.I. van der Veen  
Docent(en)  dr. R.I. van der Veen  
Verplichte literatuur 


Entreevoorwaarden  
Opmerkingen  
Opgenomen in 
