Teaching of Maxim Braverman for the  

Course Information
Instructor: Maxim Braverman   457 LA, ext. 8769 
Class hours: MW 5:50-7:20  PM   Location:   511 LA
Textbook: I will use different books for different parts of the course and will distribute printouts after each class. A big part of the course will follow the book "Mathematical Analysis" by Andrew Browder
Prerequisites: Analysis 1, Linear Algebra. 
Grading: Weekly homework problems may be done collaboratively. The take-home final exam must be entirely your own work.
Course Description:  
  In the first part of the course I will discuss some elements of multivariable integration theory on Rn and on manifolds. In particular I will introduce differential forms and prove the general Stockes' theorem. Then I will discuss elements of vector analysis and show that classical Green’s, Gauss-Ostrogradski’s, and Stockes’ Theorems a particular cases of the general Stockes' theorem for differential forms.

In the second part of the course I will present the basic theory of functions of one complex variable. In particular, the methods of computing integrals using complex analysis will be presented.

Main topics to be covered:
 
  1. Introduction to Manifolds.
  2. Tensor Algebra, Exterior Algebra. Tensor and Vector Fields on Manifolds.
  3. Stockes’ Theorem for Differential Forms and its consequences (classical Green’s, Gauss-Ostrogradski’s, and Stockes’ Theorems)
  4. Calculus of Vector Fields on Manifolds. Harmonic functions.
  5. Functions of one complex variables. Holomorphic functions.
  6. Cauchy integral formula. First properties of holomorphic functions.
  7. Classification of singular points of complex analytic functions.
  8. The residue formula. Computing of integrals using complex analysis.
  9. Analytic continuation. Computing integrals using multivalued analytic functions.
Homework:
 
  1. Due February 4
    2.
  2. Due February 20
 

 

 

 

 

 

Instructor: Maxim Braverman   457 LA, ext. 8769   
Class hours: MW 5:50-7:20  PM   Location:   4 SH  
Textbook: I will use different books for different parts of the course and will distribute printouts after each class. A big part of the course will follow the book "Mathematical Analysis" by Andrew Browder      
Prerequisites: Analysis 1, Linear Algebra.       
Grading: Weekly homework problems may be done collaboratively. The take-home final exam must be entirely your own work.      
Course Description:        
  In the first part of the course I will discuss some elements of multivariable integration theory on Rn and on manifolds. In particular I will introduce differential forms and prove the general Stockes' theorem. Then I will discuss elements of vector analysis and show that classical Green’s, Gauss-Ostrogradski’s, and Stockes’ Theorems a particular cases of the general Stockes' theorem for differential forms.

In the second part of the course I will present the basic theory of functions of one complex variable. In particular, the methods of computing integrals using complex analysis will be presented.

     
Main topics to be covered:      
 
  1. Introduction to Manifolds.
  2. Tensor Algebra, Exterior Algebra. Tensor and Vector Fields on Manifolds.
  3. Stockes’ Theorem for Differential Forms and its consequences (classical Green’s, Gauss-Ostrogradski’s, and Stockes’ Theorems)
  4. Calculus of Vector Fields on Manifolds. Harmonic functions.
  5. Functions of one complex variables. Holomorphic functions.
  6. Cauchy integral formula. First properties of holomorphic functions.
  7. Classification of singular points of complex analytic functions.
  8. The residue formula. Computing of integrals using complex analysis.
  9. Analytic continuation. Computing integrals using multivalued analytic functions.
Homework:
 Homework

Previously taught courses

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Created: August 17, 2000.  Last modified: 

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