Course description: Vectors in 2 and 3dimensional Euclidean spaces. Parametric equations and polar coordinates. Partial derivatives. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes.
Instructor: Nikhil Srivastava, email: firstname at math.obvious.edu
Please come to office hours or consult with your GSI before sending me email about logistical concerns. As far as possible, please use Piazza for mathematical questions.Lectures: Tuesday and Thursday 5:106:30pm, 155 Dwinelle.
Office Hours: Tuesday 6:458:00pm and Wednesday 1:153:00pm in 1035 Evans.
Course Control Number: 31371
Piazza: Sign Up.
Enrollment Issues: Unfortunately, I have no control over enrollment issues. As far as possible, use CalCentral to handle enrollment issues. If you have any concerns about the waitlist, switching sections, and so on, please contact the registrar or one of the Mathematics undergraduate advisors: Thomas Brown, 965 Evans and Jennifer Sixt Pinney, 964 Evans.
Graduate Student Instructors, and office hours.
Student Learning Center The Student Learning Center offers a study group for Math 53: http://slc.berkeley.edu/math53
Textbook: Stewart, Multivariable Calculus: Early Transcendentals, UC Berkeley custom edition, 8th edition, Cengage Learning. (ISBN: 9781305756458)
Grading: 5% HW, 15% quizzes, 20% x 2 midterms, 40% final. The bottom two HW and Quiz grades will be dropped, and the lower midterm score will be replaced by the final, if it helps. All exams will be curved. The median grade will be at least a B. This is not an upperbound; if everyone does extremely well, I will be happy to give everyone an A+.
Exams: There will be two inclass midterm exams on Thursday, Feb 22, and Thursday, April 12. There will be no makeup exams, except for documented medical emergencies.
Quizzes will be held in section every Wednesday. They will cover material up to the preceding Thursday. The quizzes will be substantially easier than the exams, are and designed to regularly check basic understanding of the material, so that you know in case you are falling behind.
Homework will be assigned daily (problems from the textbook) on this webpage, and each week's homework will be collected the following Wednesday in section. Homework will be coarsely graded based on spot checks. You are free (and even encouraged) to talk to your classmates about the homework, but you must write up your own solutions. There is no point copying solutions from the internet since homework is mainly for your own benefit (and worth only 5%), and without working on problems you are likely to lose a lot more than that on the final.
Announcements
#  Date  Topics  Readings  Homework problems  Remarks 
1  T 1/16  intro, vectors, dot product  12.1, 12.2, 12.3  12.1: 3, 19, 21, 25, 29. 12.2: 2, 3, 8, 26, 12, 41, 43, 47. 12.3: 1bdf, 11, 23a, 27, 55, 63, 64. 

2  Th 1/18  cross product, determinant, lines and planes  12.4, 12.5  12.4: 10, 13, 20, 29, 44, 48, 53. 12.5: 4, 20, 26, 31, 35, 48, 61, 65. 

3  T 1/23  parameterized curves, vectorvalued functions  10.1, 10.2, 13.1  10.1: 10, 22, 24, 25, 26, 28, 43. 13.1: 4, 16, 2126, 28, 32, 42. 
skip areas in 10.2 
4  Th 1/25  calculus with vectorvalued functions  13.1, 13.2, 13.3  13.1: 41, 50, 53x. 13.2: 3, 19, 27, 28, 33, 44, 45x, 56. 13.3: 5, 11, 16. 
x means optional. skip curvature and normal/binormal vectors in 13.3. 
5  T 1/30  functions of many variables, limits and continuity  14.1, 14.2  14.1: 14, 30, 32, 36, 38, 46, 54, 6166, 71, 72. 14.2: 7, 9, 13, 28, 33, 45x, 46x. 

6  Th 2/1  partial derivatives, tangent planes, linear approximation  14.3, 14.4  14.3: 8, 18, 19, 41, 50, 56, 71, 74ad, 101. 14.4: 3, 13, 19, 31, 42, 46. 
skip partial diff eq. for now 
7  T 2/6  chain rule  14.5  14.5: 1, 5, 14, 16, 18, 23, 27, 33, 35, 39, 45, 52, 53. 

8  Th 2/8  directional derivative, gradient  14.6  14.6: 7, 9, 24, 27, 34, 39, 40x, 42, 50, 55, 56, 63, 65. 
Interactive Demo 
9  T 2/13  max/min  14.7  14.7: 3, 7, 14, 15, 31, 34, 41, 44, 51, 52.  
10  Th 2/15  Lagrange multipliers, partial differential equations  14.8  14.8: 1, 3, 11, 16, 23, 29, 30, 31, 37.  skip multiple constraints online demo 
11  T 2/20  review, more PDE  handout  
12  Th 2/22  Midterm 1 (in class)  
13  T 2/27  Double Integrals  15.1, 15.2  15.1: 11, 13, 24, 29, 32. 15.2: 3, 15, 19, 24, 25, 31. 

14  Th 3/1  Polar Coordinates  10.3, 10.4, 15.3  15.3: 1,2,4,7,10,12,17,21,22,26,28,32.  
15  T 3/6  Change of Variables in Double Integrals  15.4, 15.9  15.4: 4,8,12 15.9: 2,4,8,12,16,19. 
skip change of vars in triple integrals. 
16  Th 3/8  Triple Integrals  15.6  15.6: 6, 8, 10, 14, 22, 28, 30, 34.  
17  T 3/13  Cylindrical and Spherical Coordinates  15.7, 15.8  15.7: 4,8,12,20,28,30. 15.8: 4,8,12,20,26,28,36,42. 

18  Th 3/15  Vector Fields and Line Integrals  16.1, 16.2  16.1: 6,1114,1518,26,2932. 16.2: 17,18,19,20,32a,50,52x. 

19  T 3/20  The Fundamental theorem for line Integrals  16.3  16.3: 3,5,7,10,11,13,15,17,19,23,25,29.  guest lecture by Prof. Bamler 
20  Th 3/22  Conservative fields, Green's Theorem  16.4  16.3: 31, 33, 35, 36x. 16.4: 1, 4, 7, 12, 21x, 22. 

Spring Break  
21  T 4/3  Green's Theorem, Curl and Div  16.4, 16.5  Complete Step 4 of the proof of Green's Thm in lecture today (see lec21.pdf) 
due 4/11 
22  Th 4/5  Curl and Div, Parameterized Surfaces  16.5, 16.6  16.5: 2,7,911,12acegi,14,15,19,21,22,26. 16.6: 2,4,6,22,24,26,34,36,38. 
due 4/18 
23  T 4/10  review  up to 16.6  everything up to Lec 21  guest lecture by Prof. Lin 
24  Th 4/12  Midterm 2 (in class)  up to Lec 21  
25  T 4/17  Surface Area and Surface Integrals  16.6, 16.7  16.6: 41,45,50,61,62x,64x 16.7: 11,16,19,24,25(outward),30,38. 

26  Th 4/19  Divergence Theorem  16.9  16.9: 3,7,9,14,17,23,24,27,31x.  
27  T 4/24  Stokes' Theorem  16.8  16.8: 3,5,9,15,16,17,19.  
28  Th 4/26  Applications and review  
F 5/11  Final Exam (11:30am2:30pm, 155 Dwinelle) 