MTH 311: ADVANCED CALCULUS - Fall 2015
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Assignments
Assignments
Written assignments: Solutions to the problems in graded assignments, such as Homework, Quizzes, and Exams must be written neatly (Illegible or sloppy work will not be graded.) The core of your work should be your insight how to solve a problem. Present this main idea in careful and correct English. Use generally known mathematical notation; stay as close as possible to the conventions used in the textbook and in class. Your grade will depend both on the correctness of the solution and on the quality of its presentation.

Policy on group work vs individual work: It is all right for students to talk about problems that they are solving. However, no exchange of written materials is allowed unless explicitely stated. In particular, it is not OK if one person takes detailed notes on the board, and another person copies all or part of these notes. Following an outline of a solution that several people worked on together is fine, but please be sure and state explicitly who worked in your group, and change study groups: this will make you a stronger mathematician as you learn to communicate your ideas broadly. Any violation of these rules will be treated seriously , see links to OSU policies on academic dishonesty.

Homework is due in class at the beginning of class period.

Please contact our grader, Mr. Reed, with questions on graded HW (AFTER IT WAS GRADED). Follow up with me if necessary.

Solutions to HW and other assignments will be occasionally available on CANVAS. Please note that these are subject to the class policy on not sharing written materials. In particular, it would be againts class policy and OSU's plagiarism laws to post these solutions online.
  1. 9/25: Introduction and syllabus. Set notation and inequalities. [Read Chapter 1 and preliminaries]
  2. 9/28: [Warm-up: inequalities with absolute value.] Archimedean principle and Completeness Axiom.
  3. 9/30: [Warm-up: geometric series and proofs by induction.] Density of Q in R.
    HW discussion, worksheet on induction.
    HW 1 due Friday 10/2: 1.1/3, 15, 17; 1.2/5; 1.3/4, 14
    [notice a typo in 1.1/17c, Should be: Show that if b^2< c etc.];
  4. 10/2: [Warm-up: injective (1-1) and surjective (onto) functions. Bijections.] Start sequences [Chapter 2]. Tools: the "floor" and "ceiling" functions. Convergence of a sequence. Examples of convergent sequences and those that do not converge.
  5. 10/5: [Warm-up: floor and ceiling functions]. Continue sequences. Linearity of limits.
  6. 10/7: Further properties of limits. Closed sets.
    HW 2 due Friday 10/9: 1.3/12; 2.1/2,3,8,15. 2.2/2.
  7. 10/9: Quiz 1 (Chapter 1 and preliminaries).
  8. 10/12: Warm-up: 2.1/10. Monotone sequences and Monotone Convergence Theorem. Examples.
  9. 10/14: Sequential Compactness Theorem.
    Problem solving.
  10. 10/16: Quiz 2 (Chapter 2).
    Start Chapter 3: sequential definition of continuity. 3.1.
    HW 3 due Friday 10/16: 2.3/3,7,8; 2.4/4,8
  11. 10/19 Warm-up: show that 1/n does not converge to 1. Examples of continuity and of lack of continuity.
  12. 10/21 Further properties of continuous functions. [cd 3.1]. Review and problem solving
    Extra office hours on Thursday, 10/22, time 10:00-11:30am and 3:00-4:00pm..
  13. 10/23: Midterm. Scope: Chapters 1,2, and 3.1.
  14. 10/26: Properties of continuous functions on [a,b]: Extreme Value Thm and Intermediate Value theorem. Warm-up: why sqrt(x) is continuous on [0,\inf) [Read 3.2, 3.3]
  15. 10/28: Uniform continuity [Read 3.4]. Problem solving.
  16. 10/30: Epsilon-delta property. Limits of functions. [Sections 3.5, 3.7]
    HW 4 due Friday October 30: 3.1/7,13, 3.2/7; 3.3/4; 3.4/6,7;
  17. 11/2: Finish 3.7. Monotonicity, images, and inverse functions [Section 3.6]
  18. 11/4: Quiz 3 [Please review 3.1-3.5], problems solving from 3.6-7.
  19. 11/6: Warm-up: quiz solutions. Start 4.1: Differentiation
    HW 5 due Friday November 6: 3.5/4,5,7; 3.6/5,13; 3.7/8,9.
  20. 11/9: 4.2 (Chain Rule)
  21. 11/11: NO CLASS (Veteran's Day)
    Extra office hours on Friday, 11/13, time 11:00-12:00
    HW 6 due Friday November 13: 4.1/9,11,12,17; 4.2/4,6.
  22. 11/13: 4.3 (Mean Value Theorem) and 4.4 (Cauchy Mean Value Theorem)
    HW 8 due Friday 11/20: 4.3/3,5, 15; 4.4/1,5.
  23. 11/16: Identifity Criterion. [4.4] Cauchy Mean Value Theorem). Problem solving.
  24. 11/18: Warm-up: evaluating derivatives from the definition. Quiz 4. [Chapter 4]. Problem solving on differentiation and limits.
  25. 11/20: Integration: lower and upper Darboux sums [Sections 6.1-2].
  26. 11/23: Integrable functions: Riemann-Archimedes theorem.
  27. 11/25: Chapter 5 presentations. (Second hour cancelled)
  28. 11/30: [Sections 6.3 and 6.4, read lightly] Which bounded functions are integrable ? (monotone, continuous, step functions).
    HW 9 due Wed 12/2: 6.1/4; 6.2/12; 6.3/1,2,6;
  29. 12/2: Proof of Archimedes-Riemann theorem. Problem solving.
    Big picture going forward: how to evaluate the integrals; Fundamental Theorem of Calculus.
  30. 12/4: Review for the final.
    Monday-Wednesday 12/7-12/9. Office hours with Mr Reed, Kidd 360, 9:00-12:00.
    Wednesday 12/9 office hours with M. Peszynska, Kidd 292a, 4:00-6:00pm.
    Thursday 12/10 9:30-11:30. Final Exam in Rogers 230.
    Final exam scope: mostly Chapters 3,4,and 6.1-3, but you must know all the basic material from Chapters 1-2. The Final will be similar to the Midterm in structure: there will be a definitions/theorems part, True/False part, and a problem solving part. Please use Practice problems, HW problems, and class examples to prepare.
    There will also be extra credit problems from Chapters 1-2 for those who want to improve their grade.

Additional practice problems:
  1. 1.1/1,4,5,13,18-19
  2. 1.2/1,3,4,7
  3. 1.3/3,5,6,7,9,11,15,16,20-22,24,25
  4. 2.1/1,12,14,16
  5. 2.2/1,3; 2.3/1,2,6; 2.4/1,2,3,9
  6. 3.1/1,2,3,5,6,11,12; This section will be part of Midterm .
  7. 3.2/1,2;3.3/1,2,3.
  8. 3.5/1,2,3.
  9. 3.4/1,2,4,5,8,11.
  10. 3.6/1-4,6,8,14,15.
  11. 3.7/1-7,10,12.
  12. 4.1/1-8,14.
  13. 4.2/1-3, 7, 9.
  14. 4.3/1,2,7,8,9.
  15. 4.4/2,3,4.
  16. 6.1/1,2,5,7; 6.2/1,4,5,6,10; 6.3/3,4;