Course description: Vectors in 2- and 3-dimensional 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 5:10-6:30pm, 155 Dwinelle.
Office Hours: Tuesday 6:45-8:00pm and Wednesday 1:15-3:00pm 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/math-53
Textbook: Stewart, Multivariable Calculus: Early Transcendentals, UC Berkeley custom edition, 8th edition, Cengage Learning. (ISBN: 978-1-305-75645-8)
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 in-class 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. |
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| 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. |
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| 3 | T 1/23 | parameterized curves, vector-valued functions | 10.1, 10.2, 13.1 | 10.1: 10, 22, 24, 25, 26, 28, 43. 13.1: 4, 16, 21-26, 28, 32, 42. |
skip areas in 10.2 |
| 4 | Th 1/25 | calculus with vector-valued 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, 61-66, 71, 72. 14.2: 7, 9, 13, 28, 33, 45x, 46x. |
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| 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. |
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| 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. |
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| 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. |
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| 18 | Th 3/15 | Vector Fields and Line Integrals | 16.1, 16.2 | 16.1: 6,11-14,15-18,26,29-32. 16.2: 17,18,19,20,32a,50,52x. |
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| 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. |
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| 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: 2,7,9-11,12acegi,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. |
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| 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 (11:30am-2:30pm, 155 Dwinelle) |
