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# Analysis I

Math 3150, Section 001 - Analysis I, Spring 2019 [Course Syllabus]

Lectures: MWF 11:15 - 12:05 at MONT 314
Office hours: MW 1pm-2pm at MONT 304
Required Text Book: Elementary Analysis: The Theory of Calculus by Kenneth A. Ross. ISBN 978-1-4614-6270-5, Springer; 2nd ed. 2013 edition (April 17, 2013).
Exam Dates:
Exam 1: March 1, Friday.
Exam 2: April 5, Friday.
Final Exam: May 8, Wednesday.
Grading policy: Quiz: %20, Homework: %10, 1st Exam: %20, 2nd Exam: %20, Final Exam:%30.

• ### Homework

• HW1: Assigned problems for sections 1.1 to 1.5. Due date: Monday, February 4 before the class.
• HW2: Assigned problems for sections from 2.7 to 2.9. Due date: Friday, February 8 Monday, February 11 before the class.
• HW3: Assigned problems for 2.9 (if you did not sovle in HW2) and problems in this old exam. Due date: Monday, February 18 before the class.
• HW4: Assigned problems for 2.10, 2.11, and problems in this old exam. Due date: Monday, February 25 before the class.
• HW5: Assigned Problems for 2.11 and 2.12. Due date: Monday, March 11.
• HW6: Assigned Problems for 3.17, 3.18, 3.19. Due date: Wednesday, March 27.
• HW7: Assigned Problems for 3.20 and problems in these two old exams Old Exam 1 [You can skip problem 4] and Old Exam 2 [You can skip problem 5]. Due date: Monday, April 1.
• HW8: Assigned Problems for 5.28, 5.29, and 5.30. Due date: Monday, April 15.

• ### Lecture and Assignment Schedule

• Section Covered on Topics Assigned Problems
1.1 01/23 The Set $\mathbb{N}$ of Natural Numbers Page 5, Exercises 1.4, 1.7, 1.11.
1.2 01/23 and 01/25 The Set $\mathbb{Q}$ of Rational Numbers Page 13, Exercises 2.3, 2.8.
1.3 01/25 The Set $\mathbb{R}$ of Real Numbers Page 19, Exercises 3.6, 3.7.
1.4 01/30 The Completeness Axiom Pages 27-28, Exercises 4.1,4.3, 4.14.
1.5 02/01 The Symbols $+\infty$ and $-\infty$ Page 30, Exercise 5.6.
2.7 and 2.8 02/01 and 02/04 and 02/06 Limits of Sequences and A discussion about Proofs Page 44, Exercises 8.2 (b) (d) (e), 8.4, 8.6.
2.9 02/06 and 02/08 and 02/11 and 02/13 Limit theorems for sequences Page 54, Exercises 9.1 (a) (c), 9.2 (a) (b), 9.3, 9.4, 9.5.
2.10 02/15 and 02/18 and 02/20 Monotone sequences and Cauchy sequences Pages 64-65-66, Exercises 10.1 (a) (c) (e), 10.2, 10.4, 10.6 (a) (b), 10.7, 10.10, 10.12.
2.11 02/22 and 02/25 Subsequences Pages 76-77-78, Exercises 11.4, 11.10, 11.11
Exam 1 Review 02/27 We will talk about problems from the old exams
Exam 1 03/01 Exam 1 Covers 1.1-1.5 and 2.7-2.11.
2.11 and 2.12 03/06 Subsequences and lim sup's and lim inf's Page 82, Exercise 12.3
3.17 03/08 Continuous functions Pages 130-131-132, Exercises 17.2, 17.9, 17.12, 17.13.
3.18 03/11 Properties of continuous functions Page 139, Exercises 18.4, 18.5, 18.6, 18.8, 18,9, 18.10.
3.19 03/13 and 03/15 Uniform continuity Pages 151-152, Exercises 19.2 (b), 19.5 (d) (e) (f), 19.8, 19.9
3.20 03/27 and 03/29 and 04/01 Limits of Functions Pages 162-163, Exercises 20.1, 20.2, 20.5, 20.6, 20.11, 20.12
Exam 2 Review 04/03 We will talk about problems from the old exams
Exam 2 04/05 Exam 2 Covers 2.11-2.12 and 3.17, 3.18. 3.19, and 3.20
5.28 04/08 Basic Properties of the Derivative Pages 230-231-232, Exercises 28.1 (a), 28.2 (a), 28.3(a), 28.7(a)(b)(c)(d), 28.14(a)(b), 28.16.
5.29 04/10 The Mean Value Theorem Pages 239-240, Exercises 29.1 (a)(c), 29.3, 29.4, 29.5, 29.7, 29.9.
5.30 04/12 L'Hospital's Rule Pages 248, Exercises 30.1, 30.3, 30.5.
6.32 04/15 and 04/17 and 04/19 The Riemann Integral Page 279, Exercises 32,1, 32.2, 32.3
6.33 04/22 and 04/24 Properties of the Riemann Integral Page 289, Exercises 33.4, 33.7, 33.8
6.34 04/26 and 04/29 Fundamental Theorem of Calculus Page 296, Exercises 34.2, 34.3
Final Exam Review 05/01 and 05/03 We will talk about problems from the old final exams