Advanced Calculus I

- Lectures : Monday-Wednesday-Friday 1:00-1:50pm, Math building room 0305

- Instructor : Pierre-Emmanuel Jabin
- Contact information, Phone : 301 405 5122, Office : 2307 in Math. Bldg and 4117 in Cscamm, e-mail : pjabin@cscamm.umd.edu
- Office hours: Monday-Friday 10:30-12:00

- Textbook: Advanced Calculus, by M. Fitzpatrick, 2nd edition, ISSBN 9780821847916.

- Material: A more complete description of the material covered week by week and assignmnents can be found at the address http://www2.cscamm.umd.edu/~jabin/Schedule_410_14.html
- Homework: There will be several homework assignments, and tests...
- Examination: 1 midterm and a final exam.
- If you cannot be present for a test, please
inform me at least one week in advance and one month in the case of the
midterm. Partial credit will be given for homeworks submitted late.

- Grades: 20% for the homework, 20% for the tests, 30% for the midterm and 30% for the final exam. Letter grades will be based on the accumulated points at the end of the semester, according to the following scheme: 90%-A; 80%-B; 70%-C; 50%-D; less than 50%-F.
- Disabilities : Please inform me as soon as possible if you need accommodations because of a disability.
- Communication : Informations about the course will be given during class and through this web page. In specific cases (unexpected class cancellations), students will be contacted by e-mail.
- Academic integrity : The University of Maryland, College Park has a nationally recognized Code of Academic Integrity, administered by the Student Honor Council. This Code sets standards for academic integrity at Maryland for all undergraduate and graduate students. As a student you are responsible for upholding these standards for this course. It is very important for you to be aware of the consequences of cheating, fabrication, facilitation, and plagiarism. For more information on the Code of Academic Integrity or the Student Honor Council, please visit www.shc.umd.edu. To further exhibit your commitment to academic integrity, remember to sign the Honor Pledge on all examinations and assignments: "I pledge on my honor that I have not given or received any unauthorized assistance on this examination (assignment)."
- Some examples about academic integrity : It is all right for students to discuss between them about the homework assignments. It is similarly permitted to look for tips on the internet, from other students or other resources. It is wrong to simply copy the solution to a homework exercise from any student, a book, a web page or any other source.

Course Description (Preliminary)

This class will construct the main tools and results of Calculus for real numbers

- Quantifiers in mathematics, induction argument, argument by contradiction...

- Construction of the real numbers. Sequences: Precise notion of limit, Cauchy sequence...

- Continuity/derivation of functions: Precise definition, main results

- Integration: Rigorous construction of the Riemann integral, main properties... Some notions of the L^1 space.

- Series of number and functions: Simple, absolute, uniform and normal convergences.