| Time | Tue/Thu 11:40am–12:55pm (section 6) or 2:40pm–3:55pm (section 7) |
| Place | Room 312, Math building |
| Instructor | Anand Deopurkar (anandrd at math) |
| TAs | Corrin Clarkson (clarkson at math), Tanvi Gupta (tg2362), Chang Yup Kim (ck2513), Aditi Nair (asn2115), Fan Zhou (zhou35 at gmail) |
| Office hours | Tue/Thu 1pm–2:30pm |
| Textbook | Stewart, Calculus, Early Transcendentals, 7E (No WebAssign) |
Announcements
The finals have been graded. The mean was 79 with a standard deviation of 13.
Your letter grade will be based on the Cumulative score that you can see on Courseworks. It is a weighted sum of the final, the midterms, and the homework scores as described in the syllabus. The only change is that I have added 5 points to all Midterm 2 scores to compensate for the big difference in difficulty of the two midterms.
Homework/Syllabus (PDF)
Homework is due before class in the mailbox on the 4th floor of the Math building on the indicated date (usually Tuesday). The graded homework will be returned the following Tuesday in class. Thereafter, it will be in the North corridor on the 5th floor of the Math building for you to pick up.
The problem numbers below are from the textbook. If you are using the 6th edition, make sure you do the right problems using this conversion table.
| Date | Topic | Reading | Homework |
| Jan 22 | Introduction, coordinate systems | 12.1 | 12.1 (3,6,10,14,30,31,38), 12.2(5,8,13,17,21,26,31,32) Solutions |
| Jan 24 | Vectors | 12.2 | |
| Jan 29 | Dot product | 12.3 | 12.3 (8, 11, 15, 24, 27, 50, 55), 12.4 (4, 6, 12, 15, 33, 39, 44) Solutions |
| Jan 31 | Cross product | 12.4 | |
| Feb 5 | Equations of lines and planes | 12.5 | 12.5 (9, 10, 14, 22, 24, 31, 61, 67), 12.6 (21–28: no reasons) Solutions |
| Feb 7 | Equations of quadric surfaces | 12.6 | |
| Feb 12 | Complex numbers | Appendix H | Appendix H (3, 4, 5, 8, 12, 20, 21, 26, 33, 37, 40, 44, 46) Solutions |
| Feb 14 | Complex numbers (contd) | Appendix H | |
| Feb 19 | Review | ||
| Feb 21 | Midterm I | ||
| Feb 26 | Vector valued functions | 13.1 | 13.1 (5, 7, 8, 14, 21–26 (no reasons), 28, 48), 13.2 (9, 20, 21, 24, 27, 34)
Solutions |
| Feb 28 | Derivatives, tangent vectors | 13.1 | |
| Mar 5 | Arc length | 13.2 | 13.3 (1,4,13,15,17,24,32,49,55)
Solutions |
| Last day to drop the course for most schools. | |||
| Mar 7 | Curvature | 13.3 | |
| Mar 12 | Motion in space | 13.4 | 13.4 (5, 8, 15, 27), 13 (True-False: 1-8 (no reasons), Exercises: 12,
20), 14.1 (5,13, 16, 32 (no reasons))
Solutions |
| Mar 14 | Functions of several variables | 14.1 | |
| Mar 18–22 | Spring break | ||
| Mar 26 | Review | ||
| Mar 28 | Midterm II | ||
| Apr 2 | Contour plots | 14.1 | 14.1 (34, 43, 44, 45, 53, 54, 59–64 (no reasons), 65, 67)
Solutions |
| Apr 4 | Limits and continuity | 14.2 | |
| Apr 9 | Limits and continuity | 14.3 | 14.2 (6, 8, 14, 20), 14.3 (4, 5, 10, 20, 21, 28, 30, 39, 44, 74 (a,b))
Solutions |
| Apr 11 | Partial derivatives | 14.3 | |
| Apr 16 | Tangent planes and linear approximations | 14.4 | 14.4 (3, 4, 18, 19, 21, 22, 33, 38), 14.5 (1, 6, 12, 15, 23, 36)
Solutions |
| Apr 18 | The chain rule | 14.5 | |
| Apr 23 | Directional derivatives and the gradient | 14.6 | 14.6 (2, 4, 7, 20, 22, 25, 33, 44, 55), 14.7 (2, 3, 44, 51)
Solutions |
| Apr 25 | Maxima and minima, Optimization | 14.7 | |
| Apr 30 | Constrained optimization - Lagrange multipliers | 14.8 | Suggested: 14.8 (1, 3, 7, 11, 27, 42), 14.7 (39, 41, 45, 50, 52) |
| May 2 | Review |
Grading
The final grade will be assigned based on the following:
- Homework (20%)
- Better midterm (25%)
- Worse midterm (15%)
- Final (40%).
Collaboration
You are allowed to work in groups on the homework problems, but you should write-up the solutions by yourself. Also, you must write the names of your collaborators at the top of your write-up.
Old announcements
Here is a practice final. Here are the solutions.
I will be in my office from 4 to 5 on Monday and Wednesday of the finals week. You are welcome to stop by and ask questions. You can also email me and we can arrange to meet at some other time.
I have compiled a list of many practice problems covering everything we have learned.
Here are the review slides from class. Note that the final is comprehensive wheras the review only covers the last third of the course.
Here are some old final exams:
- Summer 2011 (Ignore 2(b), 3, 4). Solutions.
- Fall 2012 (Ignore 9(b), 12) Solutions
- Fall 2011(Ignore 3, 5(a,b), 10, 12, 13)
You may also benefit from a study guide for a similar course at UArizona with answers. Not all problems are in our syllabus. In particular, ignore #1, 7, 9, 18 (b,c,e), 26–47.
You will get the same formula sheet on the final.
Here is the grade distribution for the second midterm. The mean was 32.5 (with standard deviation 8.5) and the median was 35.
The solutions to midterm 2 are here: Section 6 (morning), Section 7 (afternoon).
Have fun with the applet for plotting functions of two variables and the applet for sketching parametric 3D curves.
Here is the list of topics from the review done in class.
Here is a practice exam for the second midterm. Here are the solutions.
The second midterm is on Thursday, March 28. It will cover the material up to March 14, namely vector functions, space curves, and graphs of functions of several variables. This corresponds to the sections 13.1, 13.2, 13.3, 13.4 and 14.1 (without the contour plots) in the book. The exam will have this formula sheet for you to use.
The solutions to midterm 1 are here: Section 6 (morning), Section 7 (afternoon).
Midterm 1 scores have been posted on Courseworks; you will get the exams back on Tuesday. The mean was 40 (standard deviation 9) and the median was 43. Since the letter grade is based on a weighted cumulative score of all the exams and the homeworks, it does not make sense to assign a letter grade now. If you want to know where you stand in the class, look at the score distribution.
You can use the list of topics for your preparation.
I will have extra office hours on Wednesday (Feb 20) from 5pm–7pm (or later).
The first midterm is on Thursady, Feb 21 during class time. Here is a practice midterm with solutions. For more practice, here are some old midterms: Fall 2011, Fall 2012 (Solutions), Fall 2012 (practice) (Solutions). Since the syllabus varies from instructor to instructor, the old midterms may have some problems on unfamiliar material; ignore them.
Check out the delightful BBC documentary The Story of One about the history of numbers.
You can view the demonstration about quadric surfaces using Wolfram's CDF player or Mathematica.
Those who have WebAssign can use the code columbia 9347 1843 to access the e-book.