Tentative Schedule

Week 1

• Jan 4: Review of Sections 3.2-3.4 - Riemann sums and the fundamental theorem of calculus

Week 2

• Jan 7: Section 3.5 - indefinite integrals
• Jan 9: Sections 3.5 and 3.6 - algebraic manipulations and substitution
• Jan 11: Section 3.6 - trig substitutions

Week 3

• Jan 14: Section 3.7 - volumes
• Jan 16: Section 3.8 - volumes of revolution
  
  • Tutorial: Quiz 1 on 3.5 and 3.6 (not including trig substitutions)
• Jan 18: Section 3.8 - numerical methods

Week 4

• Jan 21: Section 3.9 - physics applications
• Jan 23: Section 4.2 - review of exponentials and logarithms
  • Tutorial: Quiz 2 on 3.7 (not including shells)
• Jan 25: Sections 4.2 and 4.3 - exponentials and logs

Week 5

• Jan 28: Sections 4.3 and 4.4 - logs, integration by parts formula
• Jan 30: Section 4.4 - integration by parts examples
  • Tutorial: Review session for midterm
• Feb 1: 4.5 - more trig substitutions

Week 6

• Feb 4: 4.6, 4.7 - reverse trig substitutions, rational functions
• Feb 6: 4.7 - rational functions
  • First midterm
• Feb 8: 4.7, 4.9 - rational functions, improper integrals

Week 7

Week 8

• Feb 18: Holiday - no classes.
• Feb 20: 4.9 - improper integrals
  • Tutorial: Quiz 3, on 4.4 (integration by parts)
• Feb 22: 4.9 - improper integrals

Week 9

• Feb 25: 4.11 - Differential equations
• Feb 27: 4.11, 5.2 - Differential equations, sequences
  • Tutorial: Quiz 4, on 4.7 (integration of rational functions)
• Feb 29: 5.2, 5.3 - sequences, limits

Week 10

• Mar 3: 5.4 - infinite numerical series (We'll return to the power series material from this section later in the course): convergence, divergence, geometric series
• Mar 5: 5.4 - telescoping series, nth term test, series of positive terms
  • Tutorial: Review session for midterm
• Mar 7: 5.4, 5.9 - comparison test, absolute and conditional convergence

Week 11

• Mar 10: 5.9 - integral test
• Mar 12: 5.9, 5.7 - limit comparison test, ratio test
  • Second midterm
• Mar 14: 5.9 - alternating series test

Week 12

• Mar 17: 5.4, 5.5 - simple power series, Taylor series
• Mar 19: 5.5 - Taylor polynomials (with error estimates)
  • Tutorial: Quiz 5 - numerical series (5.4, 5.9)
• Mar 21: Holiday - no classes

Week 13

• Mar 24: 5.5 - Applications of Taylor's theorem
• Mar 26: 5.5 - Taylor series, binomial series
  • Tutorial: Quiz 6: Taylor polynomials (5.5)
• Mar 28: 5.6 - General Taylor theorem and applications

Week 14

• Mar 31: 5.7 - Power series
• Apr 2: 5.7 - Power series
  • Tutorial: Review/problem session (given by Salisbury)
• Apr 3: Makeup class - course review
• Apr 4: Problem session (given by Ma Jianfu (TA))

Week 15