MAT 21C: Calculus: Partial Derivatives and Series

This is course webpage of MAT 21C.

Important Announcement: The Final will be on Sep 8th, not Sep 9th.

Important Announcement: We will have the last lecture on Sep 6th, have the last discussion on Sep 7th.

Final Week Office Hours: 10:00am-12:00pm on Sep 6th and 7th.

Announcement: If you have any doubts on grading of your midterms, please submit your argument in class on Thursday, 25th of August. We will make a short review of Midterm on that day, too. Arguments submitted later than that lecture or via email will not be accepted.

Announcement: If someone found a textbook after midterm, please contact with me. Thank you a lot.

Syllabus: syllabus

Office Hours: M 10am-12pm MSB3229
No mathematics related problem answered via email. Please talk with me on your problems in mathematics during my office hours.

Homework Presentation: Schedule
You can only choose problems out of homework problems from the week before you present.
You are welcome to present previous open-spot problems on Monday, August 29th.

Homework: Problems with star sign '*' are presentation problems.
08/01: Sec 10.1: 16, 23, 28, 31, 46, 54*, 58*, 87*, 101a*, 125*.
08/02: Sec 10.2: 18, 28, 36*, 56*, 60*;
Sec 10.3: 6*, 33*, 43a*, 57ab*.
08/03: Sec 10.4: 1, 5*, 10, 15*, 17, 20, 64.
08/04: Sec 10.5: 1, 6, 12*, 15*, 18, 29, 31, 45*;
Sec 10.6 4, 20, 28, 30*, 49*, 62*.
08/09: Sec 10.7: 2, 5*, 12*, 15*, 27*, 37*, 56*, 57*.
08/10: Sec 10.8: 1, 7, 14*, 19*, 26*, 33*;
Sec 10.9: 11*, 12*, 29*, 37*, 41*, 43*, 44*, 47*.
08/11: Sec 10.10: 3, 11, 15, 23*, 26*, 29*, 30, 58*, 61*.
08/16: Sec 12.1: 2, 9, 15, 17a, 25a;
Sec 12.2: 3, 10, 41, 46;
Sec 12.3: 1abcd*, 15a*, 24*, 28*.
08/17: Sec 12.4: 1, 15ab, 23, 28bfgh*, 31abcd*, 33*, 35.
08/18: Sec 12.5: 1, 2, 6, 9, 21, 23, 33, 39, 47, 53, 67*.
08/24: Sec 13.1: 5, 7, 9, 15*, 19*, 21*, 23a*, 25, 27*, 28*, 32*, 34*.
08/25: Sec 13.2: 1, 6, 13, 20ab, 23ab*, 29*, 37*, 40*, 42*.
The last two weeks:
Sec 14.1: 5, 6, 7, 18*, 26, 42.
Sec 14.2: 1, 9, 12, 13*, 17*, 20*, 33, 38a*, 41, 48, 49*, 52*, 56*, 58*, 62*, 70.
Sec 14.3: 1, 5, 17, 43, 51, 57*, 60*, 61a, 65, 72ab*, 88*, 92*.
Sec 14.4: 1, 25, 30, 33, 39*, 43*, 51*.
Sec 14.5: 1*, 3, 7, 11, 23, 26*, 29ab, 31, 36ab*.
Sec 14.6: 1, 3, 9, 13, 19*, 27a, 33, 53*, 57*, 58*.
Sec 14.7: 1, 23, 31, 33, 39*, 43a, 44a*, 45*, 50*, 54*, 60*, 61*.

Lecture Notes:
Disclaimer: There may be some typos or errors in my lecure notes. Please refer to your textbooks. You are welcome to point out typos or errors if any. Thank you a lot!
08/01: 10.1 Sequences
08/02: 10.2-3 Infinite Series and Integral Test
08/03: 10.4-5 Comparision Tests and Absolute Convergence
08/04: 10.5-6 The Ratio/Root Tests, Alternating Series and Conditional Converenges
08/09: 10.7 The Power Series
08/10: 10.8-9 The Taylor and Maclaurin Series errata: (Right below Thm 23, $R_n(b)=\frac{f^{(n+1)}(c)}{(n+1)!}(b-a)^{n+1}$). Thanks Joel Tinseth if I remember correctly.
08/11: 10.10 The Binomial Series and Applications of Taylor Series
08/16: 12 The Vectors in the space and The Dot Product
08/17: 12.4 The Cross Product
08/18: 12.5 The lines and planes in the space
The correct formula for the distance between point and plane is $d=\frac{|\vec{PS}\cdot\mathbf{n}|}{|\mathbf{n}|}$.
08/24: 13 Vector-Valued Functions and Motion in Space Part 1
08/25: 13 Vector-Valued Functions and Motion in Space Part 2
08/30: 14.1-2 Multi-Variable Functions and Limits
08/31: 14.2-3 Continuity and Partial Derivatives of Multi-Variable Functions
09/01: 14.4-5 Chain Rule, Directional Derivatives and Gradient
09/06: 14.6-7 Tangent Plane, Normal lines and Extreme Values

Solution Keys:
Homework Solution 1
Homework Solution 2 errata: (10.8#7, use $(x-\frac{\pi}{4})$ to replace $(x-\frac{\sqrt{2}}{2})$, Thanks Natalie Hernandez and Serena Tan for pointing this out.)
Homework Solution 3
Homework Solution 4
Homework Solution 5

Exams: No Practice Exams will be provided; No notes, books or calculators allowed in exams.
Mids: Date: August 23rd. 100 minutes.
The Midterm will cover section 10.1--10.10, 12.1--12.5. Examples in textbooks, examples and proofs in the lecture notes, and homework.
10 multiple-choices and true-or-false questions. 4 problems including partial questions.
The summaries of the basci results provided by Professor John Hunter may be helpful.
Part 1
Part 2 (except partial derivatives part)
Midterm_Solution
Suggestions for future study after midterm:
1.Read textbooks carefully, I mean you should read it word-by-word. Try your best to understand rather than to memorize theorems and formulas. Where does that theorem come from? Why do people need this theorem? What is the basic idea and intuition behind the theorem?
2.Do more practices. There are Practice Exercises, Additional and Advanced Exercises by the end of each chapter on the textbook.
3.Come to my office hours for your questions. Discuss on your concerns.
Final: Date: September 8th. 100 minutes.
The Final should cover 13.1-13.2, 14.1-14.7 and something before midterms. (This will be determined and updated after the last lecture.)
The summaries of the basci results provided by Professor John Hunter may be helpful.
Final_Part

Bonus:
1. Make a presentation on quizzes problems;
2. Or make some special-topic presentation, like introducing some useful tools in Mathematics.

Available Speical Topics for bonus: (Meet with me before you make this presentation)
1. Introduction to Latex;
2. Applications of Matlab/Maple/Mathematica in MAT21C;