Spring 2023 - MATH 242 D100
Introduction to Analysis I (3)
Class Number: 5277
Delivery Method: In Person
Course Times + Location:
Mo, We, Fr 1:30 PM – 2:20 PM
AQ 3154, Burnaby
Exam Times + Location:
Apr 19, 2023
12:00 PM – 3:00 PM
WMC 3260, Burnaby
Instructor:Nadish de Silva
1 778 782-7426
Prerequisites:MATH 152 with a minimum grade of C-; or MATH 155 or 158 with a grade of B.
Mathematical induction. Limits of real sequences and real functions. Continuity and its consequences. The mean value theorem. The fundamental theorem of calculus. Series. Quantitative.
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.
- Homework (11) (best 10 each worth 2%) 20%
- Midterm 1 20%
- Midterm 2 20%
- Final Exam 40%
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.
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).
Analysis with an Introduction to Proof
Steven R Lay
REQUIRED READING NOTES:
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