Math 420 (Introduction to One-Variable Calculus)
Fall 2011


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

Lectures: MWF 1:00PM-1:50PM at Thack 627

Office hours: MW 3:00PM-3:50PM, or by appointment, held at Thackeray Hall 610.

Recitation: Tu 1:00PM-1:50PM at Thack 627, Instructor: Nicholas Hurl

Textbook: Bartle and Sherbert, Introduction to Real Analysis, Third Edition, Wiley. The course covers chapters 4 through 10.

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:

Quizes (10%), Homework (20%), Class midterms (30%), final (40%).

Important notices about homeworks, quizzes and 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.

Quizzes will be given in class, usually on Wednesdays, but without previous warning. They can cover the topics covered during the same day class. The lowest quiz score will be dropped. There will be no makeup quizzes. If you miss a quiz, that will be the one that's 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 during your recitation.

Midterm exams: The dates are: Wednesday Oct. 5 , 2011; Wednesday Nov. 16 , 2011; during class.

Final Exam: The time, date and place of the final exam will be posted here soon.