Wednesday, 1/4 | Intro to the course, famous problems that Calc II can solve, discussion of syllabus, note card activity on kinds of functions. |
Friday, 1/6 | Review of functions and their derivatives: inverse functions, exponential and logarithmic functions, inverse trig functions, etc. To get ready for class, skim sections 1.5, 1.6, 3.8, 3.9. |
Monday, 1/9 | Continue function review, if necessary. Then review of basic integrals and the Fundamental Theorem of Calculus. Skim Sections 5.2 to 5.4. HW #1 due: (this should be mostly review) Section 1.5, #6, 16, 17, 29, 32. Section 1.6, #20, 26, 27, 31. Section 3.8, #27, 28, 33, 35, 40. Section 3.9, #6, 11, 12, 34, 45, 53, 59, 78, 79. |
Wednesday, 1/11 | Integration by Parts Read Section 7.1 |
Friday, 1/13 | Trigonometric Integrals Read: Section 7.2. HW #2 due: Section 5.4, #3, 15, 27, 34, 39. Section 5.7, #35, 42, 57. Section 7.1, #8, 11, 15, 18, 21, 24, 25, 26, 35, 42, 45, 49, 55. |
Monday, 1/16 | Trig substitution Read: Section 7.3 |
Wednesday, 1/18 | Partial fractions. A few words on improper integrals Read: Section 7.5 (but not the part about irreducible quadratic factors) HW #3 due: Section 7.2, #23, 24, 28, 29, 36, 39, 43, 45, 47, 50, 52. Section 7.3, #16, 21, 26, 30, 45, 51. |
Friday, 1/20 | Improper integrals Read: Section 7.7 |
Monday, 1/23 | More on improper integrals. HW due: Section 7.5, #11, 14, 16, 29, 49, 50. Section 7.6, #12, 13, 16, 17. Section 7.7, #1, 8, 10, 19, 23, 26, 30, 33, 38, 39. |
Wednesday, 1/25 | Arc Lengths and Surface Areas; Gabriel's Horn and philosophical implications. A bit on numerical integration. Read: Section 8.1. |
Friday, 1/27 | More on Numerical Integration and Simpson's Rule. Read: Section 7.9. HW due: Section 7.7, Preliminary questions #4, 5, then #62, 63, 65, 68, 71, 72. Section 8.1, #9, 32, 38. Section 7.9, #4, 11. |
Monday, 1/30 | A few final words on Simpson's rule. Review. |
Wednesday, 2/1 | Midterm 1 |
Friday, 2/3 | Separable Differential Equations (Section 9.1). |
Monday, 2/6 | No class -- Mid-term break |
Wednesday, 2/8 | More on Differential Equations. Read: Section 9.1. HW due: Section 7.9, #14, 15, 17, 27, 42, 43. Section 9.1, #8, 9, 15, 17, 24, 33, 37. |
Friday, 2/10 | More on Differential Equations. |
Monday, 2/13 | Taylor Polynomials. Read: Section 8.4. HW due: Section 9.1, #26, 27, 46, 57, 58, and the problems on this sheet. |
Wednesday, 2/15 | Error estimate for Taylor polynomials. Convergence of sequences. Read: Section 10.1 |
Friday, 2/17 | Introduction to series and their convegence; Divergence test and geometric series. Read: Section 10.2 HW due: Section 8.4, #7, 10, 11, 13, 14, 19, 38, 55. Section 10.1, #3, 6, 18, 19, 20, 22, 26, 38. |
Monday, 2/20 | More on geometric series. The integral test. Read: The part of section 10.3 on the integral test. |
Wednesday, 2/22 | The Integral and Comparison Tests. Read: re-read Section 10.3 HW due: Section 10.1, #40, 49, 50, 62. Section 10.2, preliminary exercises #3, 5, 6, 7, and regular exercises #2, 6, 27, 28, 29, 33, 34, 35, 43. |
Friday, 2/24 | Review |
Monday, 2/27 | Midterm 2 |
Wednesday, 3/1 | Comparison, Limit Comparison, Alternating Series. Read: Section 10.4 |
Friday, 3/3 | More on alternating series. The Ratio Test. Read: Section 10.5 HW due: Section 10.3, #2, 4, 7, 9, 10, 11, 12, 21, 45, 50, 53, 55, 56, 57, 59. Section 10.4, #3, 5, 7, 8. |
Monday, 3/6 | The Ratio Test. Power Series. Read: Section 10.6. |
Wednesday, 3/8 | Taylor Series. Read: Section 10.7. HW due: Section 10.4, #12, 13, 16, 17, 21, 22, 24, 29, 30. Section 10.5, #2, 6, 9, 10, 17, 20, 45, 51, 52, 58. Section 10.6, #10, 13, 16, 23. |
Friday, 3/10 | More on Taylor Series. Course wrap-up. Writing assignment due |
Monday, 3/13 | Final Exam, 3:30-6:00 pm, usual classroom |