Math 420 (Introduction to One-Variable Calculus)
Fall 2013


Instructor: Reza Pakzad Email: pakzad At-Sign pitt Dot edu

Lectures: MW 4:00PM-4:15PM at Thack 627

Office hours (subject to change): TTh 11:00-11:50AM, or by appointment, held at Thackeray Hall 610.

Recitation: W 6:30PM-7:20PM at Allen 106, Instructor: Nan Jiang

Textbook: Jiri Lebl: Basic Analysis. Custom Pitt edition.

Prerequisites: The course concerns the "theoretical" One-Variable Calculus. Prerequisite is Math 413: Introduction to Theoretical Mathematics. If you do not feel comfortable with the prerequisite material, please contact the instructor in the beginning of the course.

Syllabus:

  1. The Bolzano-Weierstrass Theorem; Cauchy sequences; Cauchy completeness of the real numbers.
  2. Real-valued functions on an interval: limits and continuity.
  3. Intermediate Value Theorem; Max-Min Theorem.
  4. Uniform continuity; continuous functions on a closed and bounded interval are uniformly continuous.
  5. Differentiable functions.
  6. Interior Extremum Theorem, Rolle's Theorem, Mean Value Theorem.
  7. Taylor's Theorem and Taylor Series.
  8. The Riemann Integral on a closed and bounded interval. Increasing functions are Riemann-integrable. Continuous functions are Riemann-integrable.
  9. The Fundamental Theorem of Calculus.
  10. Definition and examples of pointwise and uniformly convergent sequences of functions.
  11. Continuity of uniform limits of continuous functions.
  12. Interchange of uniform limits and integration.
  13. Interchange of limits with differentiation.
  14. The M-test for uniform convergence of series.
  15. Application to power series.
Grading: Exam grading is curved. Your final grade depends on your performance on the final exam as well as on your total grade calculated as follows:

Homework (30%), Class midterms (30%), final (40%).

Important notices about homeworks and exams:

Attending classes and recitations and working on the homework exercises are absolutely recommended for success in the exams. Clarity and tidiness of presentation, completeness and correctness are necessary to obtain full grade. In particular untidy presentations of correct proofs will be severely penalized.

You may work with other students or use library resources, but each student must write up his or her solutions independently. Copying solutions from other students will be considered cheating, and handled accordingly. The lowest homework score will be dropped.

There will be no make up midterm exams. If you miss the midterm exam for a *documented* medical reason, your grade on it will be the prorated grade of your final exam.

Homework: Weakly assignments will appear here. Homeworks are due every Wednesday at the beginning of class.

Midterm exams: The dates are: Monday Oct. 7 , 2011; Monday Nov. 11 , 2011; during class.

Final Exam: The final exam will be held on Saturday Dec. 14, 10:00-11:50 am at Thackeray Hall 627 . Here is a guideline.