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Course Information

Description: Introduction-Real Analysis 1.

Instructor: Casian Pantea. email me

Class schedule: TR 11:30AM-12:45PM in Armstrong 117

Office hours: Tuesday 10-11AM, Thursdays 1-2PM, in Armstrong Hall 305B

Info sheet containing more or less the stuff on this webpage.

Textbooks and resources


[http://link.springer.com/book/10.1007%2F978-1-4614-6271-2 Ross, Elementary Analysis; The Theory of Calculus]

Alternative Textbook:

Rudin, Principles of Mathematical Analysis

Useful free resources:

Web goodies

Khan Academy


Grading scheme

  • 30% Final exam on Tuesday Dec 15 2015, 8-10AM in Armstrong Hall room 117
  • 40% Two midterm exams (2x20%)
  • 20% Quizzes
  • 10% Homework assignments
  • Letter grades will be assigned according to the scheme
A 90-100% | B 80-90% | C 70-80% | D 60-70% | F 0-60%


  • There will be six 10-minute quizzes (one every two weeks); best five will count towards your grade.
  • Quizzes will test the material covered during the previous two weeks.
  • No make-up quizzes will be given.


  • Homework will be assigned once every two weeks, and due two weeks later (please see the course schedule below for exact dates).
  • Your best five homework papers will count towards the final grade.
  • Late turn-ins will not be accepted.


  • There will be two 75-minutes in-class midterm exams, on September 22 and November 3.
  • Midterm exams will test material covered after the previous midterm (they are not cumulative).
  • Calculators will not be allowed.

Final Exam

  • Wednesday Dec 16 2015, 11AM-1PM in Armstrong 117.
  • Final is cumulative.

Course Schedule (updated as we go along)

Date Topic Resources HW/Quiz
Tuesday, Aug 18 Introduction. Natural numbers 1 Evaluation Test
Thursday, Aug 20 Rational Numbers 2
Tuesday, Aug 25 Real numbers 3
Thursday, Aug 27 Completeness 4
Tuesday, Sep 1 Infinity 5
Thursday, Sep 3 Sequences. Limits 7, 8 HW1 due
Tuesday, Sep 8 More on limits 8
Thursday, Sep 10 Limit theorems 9 Quiz1
Tuesday, Sep 15 Monotone sequences. liminf, limsup 10
Thursday, Sep 17 Review HW2 due
Tuesday, Sep 22 Midterm Exam Solutions
Thursday, Sep 24 Cauchy sequences 10 Quiz2
Tuesday, Sep 29 Subsequences 11
Thursday, Oct 1 Subsequences 11 HW3 due
Tuesday, Oct 6 liminf, limsup 12
Thursday, Oct 8 liminf, limsup 12 Quiz3
Thursday, Oct 15 Series 14
Tuesday, Oct 20 Alternating series; Integral test 15
Thursday, Oct 22 Continuous functions 17 Quiz4
Tuesday, Oct 27 Continuous functions 18
Thursday, Oct 29 Review HW4 due
Tuesday, Nov 3 Midterm Exam
Thursday, Nov 5 Uniform continuity 19 Quiz5
Tuesday, Nov 10 Uniform continuity 19
Thursday, Nov 12 Limits of functions 20 HW5 due
Tuesday, Nov 17 Review
Thursday, Nov 19 Derivative 28 Quiz6
Tuesday, Dec 1 Mean value theorem 29
Thursday, Dec 3 L'Hospital rule 30 HW6 due
Tuesday, Dec 8 Taylor's theorem 31
Wednesday, Dec 16 Final Exam - 11AM-1PM, ARM 117

Where does your score stand?

Inclusivity statement

The West Virginia University community is committed to creating and fostering a positive learning and working environment based on open communication, mutual respect, and inclusion. If you are a person with a disability and anticipate needing any type of accommodation in order to participate in this class, please advise me and make appropriate arrangements with the Office of Accessibility Services (293-6700). For more information on West Virginia University's Diversity, Equity, and Inclusion initiatives, please see http://diversity.wvu.edu.