Calculus III, Fall 2017
Dr. Jo Nelson
Math V1201: Calculus III
Email:
nelson [at] math [dot] columbia [dot] edu
Lectures: MW 10.10-11.25am, 1.10-2.25pm
Location: 203 Math
Office Hours: MW 12pm -1pm
Office: 624 Math
Syllabus
Piazza
Homework
Homework will count for 19% of your final grade, and is due on Fridays by 5pm in the appropriate box outside of 410 Math. Clearly print your first and last name on your assignment. Staple together all of your homework that is due on a given day. Only homework that is turned into the correct location will be graded. You are encouraged to work together with your classmates on the assignments, but the write-up must be in your own words. Late homework will not be accepted. Your lowest homework score will be dropped. Syllabus Awareness will count for 1% of your grade. To earn Syllabus Awareness credit, please email me the with subject `Syllabus Awareness' and include the dates of the exams, the location and time that homework is due, and the permissible situations and documentation required for a make-up exams.Exams
There will be two in-class midterms, scheduled for Wednesday October 4, 2017 and Wednesday November 15, 2017. Each midterm will count for 20% of your final grade. The final exam will count for 40% of your final grade, and will be scheduled by the registrar. The final has been scheduled for the (AFTERNOON class) on Monday December 18, 2017 1.10-4pm in 203 Math and for the (MORNING class) on Wednesday December 20, 2017 9-11.50am in 203 Math. No calculators will be permitted for use on the exams. YOU MUST TAKE THE FINAL EXAM CORRESPONDING TO THE LECTURE TIME FOR WHICH YOU ARE ENROLLED.It is your responsibility to inform me in writing as soon as possible and no later than one month before each exam if you have a conflict with an exam. Per University policy no student is obliged to take three exams on any given calendar day. Students with three exams on the same day should visit the Student Service Center in 205 Kent Hall to fill out a form which can then be submitted to each instructor or department. An attempt will then be made to arrange for one of the instructors to schedule a make-up exam on a different day. Examinations are not rescheduled to accommodate travel plans. In the event of illness or family emergency I must be notified ideally at least 24 hours in advance and documentation from the dean and doctor must be provided to me.
Help
If you find yourself confused, please seek help sooner rather than later. I will be available to answer questions during my office hours. Additionally, the Barnard help room in 333 Milbank is open 10 am-10 pm Monday-Thursday and 10-4 pm on Friday. Information about tutoring services is available here.In order to receive disability-related academic accommodations, students must first be registered with the Disability Services (DS). More information on the DS registration process is available online at www.health.columbia.edu/ods. Registered students must present an accommodation letter to the professor before exam or other accommodations can be provided. Students who have, or think they may have, a disability are invited to contact DS for a confidential discussion.
Schedule & Assignments
Prerequisites: Math V1101 or the equivalentTextbook: Calculus: Early Transcendentals, 8th Edition, J. Stewart. WebAssign will not be required for this course, but may be a helpful supplement for you to have; more information here. The material that we will cover will come mostly from Chapters 12, 13 and 14. The homework assignments below all come from the 8th Edition of Stewart.
| Date | Section | Homework from Calculus: Early Transcendentals 8th Edition, J. Stewart. |
| 9/6 | 10:5 Conic sections OPTIONAL |
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| 9/11 | 10.1 & 10.2: Parametric equations OPTIONAL 10.1: 5-28, 37-38 , 10:2 1-8, 9-10 (no graph, 11-20, 25, 28-30 |
10.1: 8, 12, 15, 24, 28 10.2: 2, 3, 7, 13, 20, 25 10.5: 4, 7, 15, 24, 30, 33, 40, 45, 52, 55 Due 9/15 (HW 1) |
| 9/13 | Coordinate systems (rectangular, polar, cylindrical, spherical), Read 10.3, 12.1, 15.7, 15.8, but IGNORE INTEGRALS OPTIONAL 15.7: 1-12 15.8: 1-16 |
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| 9/18 | 12.2: Vectors |
10.3: 4, 5 12.1: 3, 6, 15, 20, 38 12.2: 1, 3, 4, 7, 16, 21, 25, 26, 27, 43, 46, 48 15.7: 1, 3, 8, 9 15.8: 1, 3, 7, 8 Due 9/22 (HW 2) |
| 9/20 | 12.3: The dot product OPTIONAL 12.3: 1-32 odd, 44-48. NO direction angles, NO direction cosines |
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| 9/25 | 12.4: The cross product OPTIONAL 12.4: 1-37 odd |
12.3: 1, 4, 9, 13, 19, 24, 28, 44, 48, 54, 64 12.4: 6, 13, 15, 23, 26, 33, 38, 43, 45, 53 12.5: 1, 5, 12, 15, 20, 24, 32, 37, 55, 64, 79 Due 9/29 (HW 3) |
| 9/27 | 12.5: Equations of lines and planes OPTIONAL 12.5: 1-59 odd, 61-68, 71-74 |
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| 10/2 | Review extra dr jo office hours today (609 Math): 2.30-4pm |
Suggested Practice Problems (do NOT hand-in) Chapter 12 Concept Check (p 841) 1-19 Chapter 12 T/F Quiz (p 842) 1-22 Chapter 12 review exercise (p 842-843) 1-11, 15-36, 38 10.1: 11, 37 10.2: 5, 11, 17 10.3: 3, 11, 13, 17, 22, 65 10.5: 5, 13, 17, 21, 12.1: 17, 40, 41 15.7: 4, 5, 6, 7 15.8: 4, 5, 6 12.2: 8, 23, 29, 45 12.3: 27, 47, 53 12.4:7, 29, 35 12.5: 16, 21, 31, 38, 39, 67, 68, 75, 76 12.6: 6, 20, 34, 45 (use wolfram alpha to check) |
| 10/4 | Midterm Exam I (through 12.5) no dr. jo office hours today |
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| 10/9 [last day to drop class is 10/10] | 12.6: Cylinders and quadric surfaces OPTIONAL 12.6: 1-20 odd, 21-30, 31-38 odd no dr. jo office hours today |
12.6: 1, 3, 5, 9, 14, 15, 19, 21-28, 33, 46 Due 10/13 (HW 4) |
| 10/11 | 13.1: Vector functions OPTIONAL 13.1: 1, 3, 4, 6, 10, 11, 13, 31 office hours 12-1pm and 2.30-4pm |
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| 10/16 | 13.2: Derivatives and integrals of vector functions OPTIONAL 13.2: 1, 2, 3, 7, 10, 11,12, 13, 14, 19, 20, 23 , 25, 26, 42 |
13.1: 2, 5, 7, 14, 15, 21-26, 29 13.2: 5, 9, 15, 17, 21, 24, 28, 33, 35, 41, 49, 54 Due 10/20 (HW 5) |
| 10/18 | 13.3: Arc length and curvature (no oscillating things) OPTIONAL 13.3: 1, 4, 5, 18, 20, 23, 25, 47 |
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| 10/23 | 13.4: Motion in space (no Kepler's laws) OPTIONAL 13.4: 3, 5, 7, 9, 13, 15, 25, 37 |
13.3: 2, 3, 13, 15, 17, 19, 21, 33a, 48 13.4: 4, 8, 11, 16, 19, 22, 27, 36, 39, 40 (ok to use calculator) Due 10/27 (HW 6) |
| 10/25 | 14.1 & 14.2: Functions of several variables, limits, continuity OPTIONAL 14.1: 9, 10, 15, 19, 21, 27, 29, 47, 49, 68 14.2: Show the limit does not exist for 9, 11, 12, 20 (harder). Separately: 29, 33, 36, 38, 40. |
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| 10/30 | 14.3: Partial derivatives OPTIONAL 14.3: 15-37 odd, 41, 47, 49, 51, 57, 59, 65, 67 |
14.1: 8, 11, 17, 25, 28, 32, 36, 38, 45, 46, 61-66, 69, 70 14.2: 1, 2, 7, 10, 15, 18, 25, 31, 39 14.3: 5-8 (minimal work), 9, 19, 25, 29, 34 Due 11/3 (HW 7) |
| 11/1 | 14.4: Tangent planes and linear approximations OPTIONAL 14.4: 2, 6, 11, 15, 17, 21, 26, 29, 30, 32 |
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| 11/6 | University Holiday | |
| 11/8 | 14.5: The chain rule Extra office hours in 624 Math: 12-1pm and 2.30-3.30pm OPTIONAL 14.5: 1, 3, 7, 11, 19, 21, 23, 29, 31, 45 |
14.3: 43, 50, 52, 54, 61, 67, 71, 75, 77, 86, 90, 95 14.4: 3, 5, 13, 19, 25, 31 14.5: 5, 9, 13, 20, 23, 27, 33, 42, 50 Due 11/10 (HW 8) |
| 11/13 | Review Extra office hours in 624 Math: 12-1pm and 2.30-3.30pm |
Chapter 13 pg 881-883 13 Concept Check: 1-6, 7a, 8 13 T/F quiz: 1-12, 14 13 Exercises: 1-3, 6, 8, 10-13, 17-22 Chapter 14 pg 981-984 14 Concept Check: 1-5, 7-12 14 T/F quiz: 1-3, 5,6, 8 14 Exercises: 1-10, 13-17, 19-22, 23-26, 32-33, 35-37, 39, 41, 42 |
| 11/15 | Midterm II (12.6 and through 14.5) No Dr. Jo Office hours today |
Practice Midterm (do these problems in 75 minutes) Chapter 13 review exercises (pg 882-883?): 4 (no graphing), 8, 11(a) and (b), 19 AND chapter 14 review exercises pg 982-984: 2, show the limit in 10 does not exist, 23, 29(a), 36. |
| 11/20 | 14.6: Directional derivatives and complex numbers (Appendix H) OPTIONAL 14.6: 1-46 odd, 49-63 odd |
14.6: 5, 7, 10, 12, 15, 17, 21, 24, 28, 35, 42, 45, 54, 59, 63 H: 3, 7, 15, 23, 29, 35, 39, 45 Due 11/29 WEDNESDAY 5pm (HW 9) (formerly due on Monday) |
| 11/22 | University Holiday for Thanksgiving (videos if you skipped 11/20 lecture)
Intro to Directional Derivs (11min) Properties of the gradient (10 min) Tangent planes via gradient (8 min) |
Complex number videos polar form (11 min) multiplication and division (7 min) |
| 11/27 | 14.7: Maxima and minima OPTIONAL 14.7 : 1-21 odd, 31-38 odd, 41-53 odd. |
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| 11/29 | 14.8: Lagrange Multipliers OPTIONAL 14.8: 1-23 odd, 31-39 odd |
14.7: 1, 5, 9, 12, 13, 31, 34, 36, 41, 43, 46, 56
14.8: 3, 4, 7, 11, 21, 31, 33, 34 Due 12/6 WEDNESDAY 5pm (HW 10) |
| 12/4 | Catch-up |
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| 12/6 | Chapter 14 Review |
Do the remaining Chapter 14 concept check (13-19), t/f (9-12), and review exercises (43-56, 59-65) |
| 12/11 | Cumulative Review Office hours: 12-1pm and 2.30-4pm 624 Math Practice for 1/2 of Final, Midterm 1 Material (do in 90 minutes) solutions: 1a) 10 Review #4 2) 12.3 #27 3) 12.3 #47 4) 12.5 #48 5) 12.5 #38 6) to appear 7a) 15.7 #9a 7b) 15.8 #9b 8) 12.6 #18 |
Practice for Final (do in 90 minutes) 13 Review: 20, express answers in terms of g. I would tell you r(t) = -1/2 g t^2 j + t v_0, v_0=< v_0 cos(alpha), v_0 sin(alpha) >. 14 Review: 7, 8, 37, 44, 48, 54, 56, 63. also a couple of complex number multiplication/division/exponentiation/roots/polar form problems |