Mathematics Department
13.340 Advanced Calculus, 2000-2001
Course Outline
Instructor: Sasho Kalajdzievski
Office: 357 Machray Hall
Phone: 474-6929
e-mail: sasho@cc.umanitoba.ca
web: server.maths.umanitoba.ca/homepages/sasho
Text: Mathematical Analysis (2nd ed.) by T. M. Apostol, Addison-Wesley
Time permitting, tbe following areas will be studied. Not all sections of the chapters referred to will necessarily be covered.
1. Review: cardinal numbers, properties of real numbers, open and closed sets, limits and continuity,deriatives. Relevant text: parts of Chapters 1 - 5.
2. Functions of bounded variations, curves, rectifiable curves. Text: Chapter 6.
3. Riemann-Stieltjes integral. Text: Chapter7.
4. Sequences and series of functions; uniform convergence. Text: Chapter 9.
5. Fourier series. Text: Chapter 11.
6. Difterential calculus of several variables; total derivative, Jacobian matrix. Text:Chapter 12.
7. Implicit functions. inverse and implicit function theorems, extrema. Text: Chapter13.
8. Multipk Riemann integrals. Text: Chapter 14
Evaluation
(Assignments may include presenting material in class. )
Two tests, 10% each, total 20%
Final examination 50%
Bonus 5%
(unannounced short in-class quizzes, questions)
Plagiarism and Cheating: Students are advised to familiarize themselves with the University's policies on Plagiarism and Cheating and Examination Impersonation found on pages 31 and 32 of the General Calendar.