Simon Fraser University
Engaging the World

Course Outlines

Spring 2023 - MATH 242 D100

Introduction to Analysis I (3)

Class Number: 5277

Delivery Method: In Person

Overview

  • Course Times + Location:

    Jan 4 – Apr 11, 2023: Mon, Wed, Fri, 1:30–2:20 p.m.
    Burnaby

  • Exam Times + Location:

    Apr 19, 2023
    Wed, 12:00–3:00 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.

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.

REQUIREMENTS:

This course is delivered in person, on campus. Should public health guidelines recommend limits on in person gatherings, this course may include virtual meetings. As such, all students are recommended to have access to strong and reliable internet, the ability to scan documents (a phone app is acceptable) and access to a webcam and microphone (embedded in a computer is sufficient). 

Materials

REQUIRED READING:

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

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website 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