Spring 2019 - MATH 242 D100
Introduction to Analysis I (3)
Class Number: 4215
Delivery Method: In Person
Overview
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Course Times + Location:
Jan 3 – Apr 8, 2019: Mon, Wed, Fri, 1:30–2:20 p.m.
Burnaby -
Exam Times + Location:
Apr 17, 2019
Wed, 12:00–3:00 p.m.
Burnaby
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Instructor:
Nathan Ilten
nilten@sfu.ca
1 778 782-9887
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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:
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: 22 Sept = Last Day to Drop with no Notation on Transcript, 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: 13 Oct = Thanksgiving Day (classes cancelled), 15 Oct = 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
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
REQUIRED READING:
Analysis with an Introduction to Proof
5/E
Steven R Lay
Pearson
ISBN: 978-0321747471
Registrar Notes:
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
ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS