Simon Fraser University
Engaging the World

Course Outlines

Spring 2022 - MATH 242 D100

Introduction to Analysis I (3)

Class Number: 6534

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 10 – Apr 11, 2022: Mon, Wed, Fri, 1:30–2:20 p.m.
    Burnaby

  • Exam Times + Location:

    Apr 21, 2022
    Thu, 3:30–6:30 p.m.
    Burnaby

  • Prerequisites:

    MATH 152 with a minimum grade of C-; 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:

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, 

Week 5: Subsequences [limsup and 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: 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

Week 11: 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

  •  Midterm(s): synchronous; date: TBA
  •  Final exam: synchronous; date: TBA

Grading

  • 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

MATERIALS + SUPPLIES:

The class will run in-person. However, given the ongoing unpredictability induced by the pandemic, it is prudent to plan for various eventualities. Ensure that you have:

  • Access to strong and reliable internet.
  • Ability to scan documents for homework/ exams (phone app acceptable)
  • Access to webcam and microphone (embedded in computer sufficient)

REQUIRED READING:

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

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating.  Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the University community.  Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html

TEACHING AT SFU IN SPRING 2022

Teaching at SFU in spring 2022 will involve primarily in-person instruction, with safety plans in place.  Some courses will still be offered through remote methods, and if so, this will be clearly identified in the schedule of classes.  You will also know at enrollment whether remote course components will be “live” (synchronous) or at your own pace (asynchronous).

Enrolling in a course acknowledges that you are able to attend in whatever format is required.  You should not enroll in a course that is in-person if you are not able to return to campus, and should be aware that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes.

Students with hidden or visible disabilities who may need class or exam accommodations, including in the context of remote learning, are advised to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112) as early as possible in order to prepare for the spring 2022 term.