Math 4035
Advanced Calculus of n-variables
T-Th, 1:30-2:50, Lockett 0130
INSTRUCTOR Gestur Olafsson
Office 322 Lockett
Office Hours T-TH 10:30-11:30, and by request, best using email
Phone 578-1608 and 225-337-2206 (cell)
Text: Calculus on Manifolds, a modern approach to classical theorems of advanced calculus by Michael Spivak, Addison-Wesley Publishing Company. There are are several other very good books covering the same or similar material. The text by Spivak is very short. It is therefore a good idea to look at other books. We will also add more details in class. As an example, can recommend the book by L. Richardson Advanced Calculus: An Introduction to Linear Analysis. The author provides more details in the proofs.


This is one of three course on Advance Calculus. We expect that the students have basic knowledge of the material covered in 4031. We start with some elementary discussion about the structure and topology of finite dimensional vector spaces, limits and continuous functions. We then discuss differentiation of functions of several variables and approximation by linear maps. Inverse and implicit functions are covered at the end of Chapter 2. Chapter 3 covers integration and the basics rules like Fubini's theorem and change of variables. This is the minimum covered in class. If there is still time available then other advanced topics will be discussed.

I welcome any comments from students about topics to discuss in class, so please take a look at the book or any another book and let me know if there is something special that you would like to have covered or discussed in class.

Students are asked not to use their cell phone during the class. I do not want to see any cell phones during tests. Students are asked to arrive on time and not to leave before the class is over. Respect the other students!

Homework and Tests

I will regularly assign homework for students to work on. Those problems will be discussed in class and only three sets will be collected and graded. But students can only learn the material by working on problems to get familiar with the theorems. There will be three tests in class and a final. For dates see bellow.

  1. Each of the tests during the semester will count 100 points. Together that gives 300 points.
  2. The final counts 200 Points.
  3. Each set of collected homework counts 20 points.
  4. The total amount of points is 560.

Important dates

  1. Classes start Monday, August 24, 2015
  2. First Test, Thursday, Sept. 22, 2015
  3. Second Test, Thursday, Oct. 15, 2015
  4. Third Test, Thursday, Nov 19, 2105
  5. No class Thursday Nov. 26, Thanksgiving
  6. Final, Dec. 5, 10:00-Noon. Usual classroom or take home due, noon December 5. I will let you know!


  1. 100% to 97% A+
  2. 96.99-93%% A
  3. 92.99-90% A-
  4. 89.99% to 87% B+
  5. 86.99-83%% B
  6. 82.99-80% B-
  7. 79.99% to 77% C+
  8. 76.99-73%% C
  9. 72.99-70% C-
  10. 69.99% to 67% D+
  11. 66.99-63%% D
  12. 62.99-60% D-
  13. <60% F