# Spring 2021 - MATH 242 D100

## Overview

• #### Course Times + Location:

Mo, We, Fr 1:30 PM – 2:20 PM
REMOTE LEARNING, Burnaby

• #### Exam Times + Location:

Apr 21, 2021
12:00 PM – 3:00 PM
REMOTE LEARNING, Burnaby

• #### Prerequisites:

MATH 152; or MATH 155 or 158 with a grade of B.

## Description

#### CALENDAR DESCRIPTION:

Mathematical induction. Limits of real sequences and real functions. Continuity and its consequences. The mean value theorem. The fundamental theorem of calculus. Series. Quantitative.

#### COURSE DETAILS:

This course will be delivered online. You are expected to have access to a reliable internet connection. You will need a computer from which you can download course materials and activities and watch live and/or recorded lectures and participate in live tutorials or workshops.

You will need a camera to take photographs of your work. A phone is acceptable.

Topics covered
Week 1: Techniques of Proof II §1.4, Basic Set Operations, §2.1
Week 2: Relations, Functions, Cardinality, Axioms for Set Theory §2.2– 2.5
Week 3: Ordered Fields [Absolute Value] §3.2, Completeness Axiom [Density]
Week 4: Topology of the Real Numbers §3.3–3.4, Convergence, Limit Theorems, Monotone and Cauchy sequences, §4.1–4.3, Quiz I
Week 5: Subsequences [limsup an liminf] §4.4, Compact Sets [Heine-Borel, Bolzano-Weierstrass] §3.5
Week 6: Limits of functions, Continuity and properties §5.1–5.3
Week 7:  Midterm, Uniform continuity §5.4
Week 8: Derivative, Mean Value Theorem, L'Hospital's Rule, Taylor's Theorem §6.1–6.4
Week 9: Riemann integral, Properties of the Riemann Integral, Fundamental Theorem of Calculus §7.1–7.3
Week 10: Convergence of series, Convergence tests, Power Series §8.1–8.3, Quiz II
Week 11: 11 Nov = Remembrance Day (tutorials cancelled), Uniform convergence §9.1
Week 12: Applications of Uniform Convergence, Uniform Convergence of Power series [Abel's Theorem, Fourier Series examples] §9.2–9.3
Week 13: [time allocation for quizzes]
Week 14: Review

#### COURSE DELIVERY

•  Lecture: synchronous- lectures will be held at fixed times, on-line
•  Midterm(s): synchronous; date: TBA
•  Final exam: synchronous; date: TBA

• Homework (11) (best 10 each worth 2%) 20%
• Midterm 1 20%
• Midterm 2 20%
• Final Exam 40%

#### NOTES:

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks.
Please pay careful attention to the options discussed in class at the beginning of the semester.

## Materials

Analysis with an Introduction to Proof
5/E
Steven R Lay
Pearson
ISBN: 978-0321747471