## Semester 2, 2019-20

Course Lecturer

#### Dr. Judith Packer, Dept. of Mathematics

Tel: (303) 492-6979
Office: Math 227

Course Syllabus: For course syllabus, complete with list of university policies, click here!

Course Information:
This course is meant to familiarize the student with the rigorous theory behind the study of functions of a single real variable, and goes over the proofs of some of the major results used in calculus. Topics to be covered include: the topology and order structure of the real line; sequences of real numbers and limits of sequences; functions of a real variable: limits of functions at a point, continuous functions and their properties -- Intermediate Value Theorem , uniform continuity; the derivative of a function at a point and differentiability, the Mean Value Theorem, and Taylor's Theorem; the Riemann integral and its properties, and the Fundamental Theorem of Calculus; and if time permits, a brief overview of series of real numbers and power series expansions.

Prerequisite:
Math 2001 or the equivalent.

Course Text:
We will use the text "Analysis, With an Introduction to Proof", S.R. Lay, Pearson - Prentice Hall, 2014, 5th edition. After a quick review of Chapters 1 and 2, we will cover most of Chapters 3--7, and part of Chapter 8.

Assessment:
Lecture Hours and Venue:
MWF 10 a.m.-10:50 a.m. ECCR 110.

Office Hours:
MWF 11 a.m. - 12 noon, and by appointment.

Extra slides:

Homework:
• Assignment 1: Due Wednesday, January 22: read Sections 3.1 and 3.2; do problems 3.1.3, 3.1.4, 3.1.7, 3.1.16, 3.1.20, 3.2.3 (a) (e) (j), 3.2.4, 3.2.6 all parts, 3.2.7, 3.2.8, 3.2.9.
• Some solutions to HW 1.
• Assignment 2: Due Friday, January 31: read sections 3.3 and 3.4, do problems 3.3.3 (a), (d), (f), (h), (i), (k), (n), 3.3.7 (a), 3.3.8, 3.3.12 (a), (b), 3.4.3 (a), (c), (e), 3.4.4 (a), (c), (e). For extra credit do 3.3.7 (b).
• Some solutions to HW 2.
• Assignment 3, due Friday, February 7: Problem 3.4.5, 3.4.8, 3.4.14, 3.4.15, 3.4.16, 3.4.17, 3.4.24, 3.5.1, 3.5.3, 3.5.4, 3.5.5, 3.5.6.
• Some solutions to HW 3.
• Assignment 4, due Friday, February 14: finish reading 3.5, begin reading 4.1, do problems 3.5.8, 3.5.11, 3.5.12, 4.1.2, 4.1.3, 4.1.6 (a), (c), (d), (e), 4.1.7 (a), (c), (d), 4.1.9 (a), (b).
• Some solutions to HW 4.
• Assignment 5, due Friday, February 28: continue reading 4.2, begin reading Section 4.3; do problems 4.1.11, 4.1.12, .2.1, 4.2.5 (a),(b),(e),(g),(j),(k), 4.2.15 (b),(c), 4.2.16, 4.3.1, 4.3.3 (a),(d), 4.3.7, 4.3.10(a).
• Some solutions to HW 5.
• Assignment 6, due Friday, March 6: finish reading 4.3; read Sections 4.4 and 5.1, do problems 4.4.3 (all), 4.4.4 (all), 4.4.7 (all), 4.4.11, 4.4.13; 5.1.3 (a), (c), (d), (e), (h), 5.1.4, 5.1.7, 5.1.9, 5.1.11, 5.1.13.
• Some solutions to HW 6.
• Assignment 7, due Friday March 13: read sections 5.1 and 5.2, do problems 5.1.4, 5.1.7, 5.1.9, 5.1.11, 5.1.13, 5.1.14, 5.1.16, 5.1.18, 5.2.4, 5.2.8, 5.2.10(a), 5.2.12.
• Some solutions to HW 7.
• Assignment 8, due Monday, March 30: read section 5.3, do problems 5.2.13, 5.2.14, 5.2.17, 5.2.18, 5.3.4, 5.3.6, 5.3.7, 5.3.8, 5.3.9, 5.3.12, 5.3.16. Please submit the solutions through Canvas system on March 30, 2020.
• Some solutions to HW 8.
• Assignment 9, due Friday April 10: read sections 6.1 and first half of section 6.2, do problems 5.4.4(a),(c), 5.4.12, 6.1.3(a),(b), 6.1.4, 6.1.5, 6.1.8, 6.1.12, 6.1.13, 6.1.15, 6.2.1, 6.2.3, 6.2.5 (a),(b),(f). Please submit the solutions through the Canvas system on April 10, 2020.
• Some solutions to HW 9.
• Assignment 10, due day April 17: Read second half of section 6.2 and section 7.1, do problems 6.2.11, 6.2.15, 6.2.17, 6.2.18, 7.1.4, 7.1.5, 7.1.8. 7.1.11, 7.1.12, 7.1.13, 7.1.15, 7.1.16, 7.1.17. Please submit the solutions through the Canvas system on April 17, 2020.
• Some solutions to HW 10.
• Assignment 11, due day April 24: Please review second half of Section 7.2 and read Section 7.3, do problems 7.2.3, 7.2.5, 7.2.6, 7.2.8, 7.2.9, 7.2.11, 7.2.15(a); 7.3.5 (c), (d), 7.3.8, 7.3.11. Please submit the solutions through the Canvas system on April 24, 2020.
• Some solutions to HW 11.
• Assignment 12, due day, Thursday April 30: do problems 7.3.12, 7.3.14, 7.3.15, 7.3.16. Please submit the solutions through the Canvas system by Thursday, April 30, 2020.
• Solutions to the Spring 2016 sample final exam.
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