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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 7.4-7.6)
• 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