Math 409 Advanced Calculus I

Sections 200 and 501 Spring 2011

Course Schedule (subject to change)


January

Tuesday, January 18
Sections 1.1–1.6. The real numbers form a complete, ordered field.
Thursday, January 20
Sections 1.7–1.10. Properties of the natural numbers and the rational numbers: the Archimedean property, induction, density of the rationals. Distance on the real line.
Tuesday, January 25
Sections 2.1–2.4. Sequences, convergence of sequences. Section 2.3 on countable sets is optional for students in Section 501.
Thursday, January 27
Sections 2.5–2.7. Divergent sequences; boundedness of convergent sequences; algebraic properties of limits of sequences.

February

Tuesday, February 1
Sections 2.8–2.9. Order properties of limits, Squeeze Theorem, convergence of bounded monotonic sequences.
Thursday, February 3
Sections 2.10–2.13. Examples of limits; subsequences, Bolzano–Weierstrass theorem; Cauchy's criterion for convergence. Section 2.13 on upper and lower limits is optional for students in Section 501.
Tuesday, February 8
Sections 4.1–4.3. Open and closed sets, interior points, boundary points, accumulation points.
Thursday, February 10
Sections 4.4–4.5.1. Properties of open and closed sets; Bolzano–Weierstrass property.
Tuesday, February 15
Sections 4.5.2–4.6. Notions of compactness: Cantor's theorem on nested sets, Cousin's covering lemma, Heine–Borel property. Countable sets. Sections 4.5.2–4.5.4 are optional for students in Section 501.
Thursday, February 17
Catch-up and review.
Tuesday, February 22
First examination, covering Chapters 1, 2, and 4. Update: after the exam, solutions were posted.
Thursday, February 24
Section 5.1. Limits of functions.

March

Tuesday, March 1
Section 5.2. Properties of limits of functions.
Thursday, March 3
Sections 5.3–5.4. Continuity. Section 5.3 on limits superior and inferior is optional for students in Section 501, as is Section 5.4.4 about continuity on a set.
Tuesday, March 8
Sections 5.5–5.8. Properties of continuous functions, extreme-value property, intermediate-value property; uniform continuity.
Thursday, March 10
Section 5.9. Discontinuities; monotonic functions. Section 5.9.3 is optional for students in Section 501.
March 14–18
Spring Break
Tuesday, March 22
Sections 7.1–7.3.1. Definition of the derivative, algebraic rules. Section 7.2.3 is optional for students in Section 501.
Thursday, March 24
Sections 7.3.2–7.5. Chain rule, inverse functions, powers, discontinuous derivatives, local extrema.
Tuesday, March 29
Sections 7.6–7.7. Mean-value theorems, monotonicity.
Thursday, March 31
Sections 7.8–7.10. Dini derivates (Section 7.8 is optional for students in Section 501), intermediate-value property of derivatives, convexity.

April

Tuesday, April 5
Sections 7.11–7.12. L'Hôpital's rule, Taylor polynomials.
Thursday, April 7
Catch-up and review.
Tuesday, April 12
Second examination, covering Chapters 5 and 7. Update: after the exam, solutions were posted.
Thursday, April 14
Sections 8.1–8.2. The integral of a continuous function.
Tuesday, April 19
Sections 8.3–8.5. Properties of the integral, improper integrals.
Thursday, April 21
Section 8.6. Riemann's concept of the integral. Sections 8.6.2–8.6.4 are optional for students in Section 501.
Tuesday, April 26
Sections 8.7–8.9. Properties of the Riemann integral, improper integrals, fundamental theorem of calculus. Section 8.9 is optional for students in Section 501.
Thursday, April 28
Catch-up and review; last class day for this course.

May

Tuesday, May 3
This day is redefined as a Friday, so our class does not meet.
Wednesday, May 11
Comprehensive final examination, 8:00am–10:00am. Update: after the exam, solutions were posted.

Valid XHTML 1.0 Strict Valid CSS!