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MATH 1310 3.00MW (Winter 2016)
Integral Calculus with Applications
Topics and notes
I'll do many examples and proofs at the blackboard, but I will use the document
camera in class to summarize the topics we cover. I will post those
summaries below, as a guide for anyone who misses a particular class, or
who wants such a summary.
 Week 1

Jan 4: Review of Riemann sums (Section 5.2)

Jan 6: Antiderivatives, Fundamental Theorem of Calculus (Section 5.3)

Jan 8: Indefinite integrals and Change of variables (Sections 5.4 and 5.5)
Assignment 1 posted
 Week 2

Jan 11: Examples. Areas (Section 6.1)

Jan 13: Areas (Section 6.1).

Jan 15: Volumes (Section 6.2)
Assignment 2 posted
 Week 3

Jan 18: Volumes (Section 6.3)
Assignment 1 due

Jan 20: Work and Averages (Sections 6.4 and 6.5)

Jan 22: Integration by parts (Section 7.1)
Assignment 3 posted
 Week 4
 Jan 25 Integration by parts  examples (no new notes)
Assignment 2 due

Jan 27: Integration of powers of sine and cosine (Section 7.2)

Jan 29: Powers of sine and cosine (continued)
1st Quiz
 Week 5

Feb 1: Trig substitutions (Section 7.3)
Assignment 3 due
 Feb 3: Trig substitutions  examples (no new notes)
Quiz 1 returned

Feb 5: Rational functions (Section 7.4)
 Week 6

Feb 8: Rational functions, continued (Section 7.4)
Assignment 4 due

Feb 10: Rational functions, other methods (Sections 7.47.6)
 Feb 12: 1st Midterm
Assignment 5 posted
 Week 7
 No classes  Reading week
 Week 8

Feb 22: Numerical methods (Section 7.7)

Feb 24: Numerical methods (Section 7.7)
Assignment 5 due, Assignment 6 posted

Feb 26: Improper integrals (Section 7.8)
1st midterm returned
 Week 9

Feb 29: Improper integrals continued (Section 7.8)

Mar 2: Arc length and surface area (Sections 8.1 and 8.2)
Assignment 6 due, Assignment 7 posted

Mar 4: Infinite sequences (Section 11.1)
2nd Quiz, deadline to drop
 Week 10

Mar 7: Infinite sequences (Section 11.1)

Mar 9: Infinite series, geometric series (Section 11.2)
Assignment 8 posted

Mar 11: Integral test, Comparison test (Sections 11.3, 11.4).
You aren't responsible for the limit comparison test.
Assignment 7 due
 Week 11

Mar 14: Alternating series (Section 11.5)
Quiz 2 returned

Mar 16: Ratio test (Section 11.6). You aren't responsible for the
root test.
Assignment 8 due. Assignment 9 posted.
 Mar 18: 2nd Midterm
 Week 12

Mar 21: Power series (Section 11.8)

Mar 23: Exponential/sine/cosine series,
differentiation and integration of power series (Sections 11.9 and 11.10)
Assignment 10 posted.
 Mar 25: Statutory holiday  university closed
 Week 13
 Mar 28: More examples (Sections 11.9 and 11.10)
3rd Quiz, Assignment 9 due. Last lecture on exam material.

Mar 30: Taylor series and remainder (Section 11.10)

Apr 1: Taylor polynomials (Section 11.11)
 Week 14
 Apr 4: Review
Assignment 10 due, Quiz 3 returned, Midterm 2 returned