Overview

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:

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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.

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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

Grading

Materials

REQUIRED READING: