Math H53: Honors Multivariable Calculus

Instructor: David Corwin (dcorwin at berkeley dot edu). In all e-mail correspondence, please include "[MathH53]" in the subject line.

GSI: Michael Smith (find his e-mail on math.berkeley.edu)

All Zoom IDs under "Syllabus" on Bcourses

Lecture: TTh 11-12:29 Pacific Time

GSI Office hours: TTh 2-3:30 Pacific Time

Instructor Office hours: Regular office hours: 4:30-5:30 on Tuesday and 2-3:30 on Thursday. Check Bcourses "Syllabus" for Zoom ID. Always feel free to send me questions or ask for alternative office hours.

Final exam: Check UC Berkeley final exam schedule

Prerequisites: Math 1B or equivalent.

Text: The primary texts for this course are Vector Calculus by Michael Corral ([Co]) and Notes on Multivariable Calculus by Cain and Herod ([CH]). Students should feel free to consult other books for additional exercises and/or alternative presentations of the material. Wikipedia also has lots of great articles on the topics at hand. Students are expected to read the relevant sections of the notes, as the lectures are meant to complement the notes, not replace it, and we have a lot of material to cover.

Grading: Your homework grade (hw) will be the average of all homeworks, with the lowest dropped. Your exam grade (exams) will be computed based on the maximum of the following three schemes: (0.2)MT1 + (0.2)MT2 + (0.4)F; (0.2)MT1 + (0.6)F; (0.2)MT2 + (0.6)F. Finally, your total grade will be calculated as the maximum of: (0.2)hw + (0.8)exams, (0.3)hw + (0.7)exams.

Website: For now, the only website is this page, http://math.berkeley.edu/~dcorwin/mathh53s21.html. I will use bcourses for solutions and other non-public information, such as book excerpts, exams, and my phone number.

Course policies:

Additional resources (will be on Bcourses when needed):

Course Overview: Outlined below is the rough course schedule. Depending on how the class progresses it may be subject to minor changes over the course of the semester.

Course calendar; "[Co], [CH], [A], [S] mentioned above. [W] is Wikipedia.
Date Topics References Alternative References
1/19 Introduction/Overview, vectors 1.1-1.2 of [Co] 1.1-1.3, 2.1 of [CH]
1/21 Dot and Cross Products 1.3-1.4 of [Co] 2.2-2.3 of [CH]
1/26 Products continued, Lines and Planes 1.4-1.5 of [Co]
1/28 Surfaces and Curvilinear Coordinates 1.6-1.7 of [Co] 1.4 of [CH]
2/2 Vector-Valued Functions 1.8 of [Co] 3.1-4.1 of [CH]
2/4 Arc Length, Curvature, etc 1.8 of [Co], 4.2-4.4 of [CH]
2/9 Functions of several variables, graphs and level curves, limits and continuity 2.1 of [Co]
2/11 Partial Derivatives and Tangent Planes 2.2-2.3 of [Co]
2/16 Directional Derivatives and Gradients 2.4 of [Co] 8.1-8.2 of [CH]
2/18 Multidimensional Linear Functions Chapters 5-6 of [CH]
2/23 Multidimensional Derivatives Chapter 7 of [CH] 8.11, 8.13 of [A]
2/25 Multidimensional Derivatives (cont.), Chain Rule Chapter 7 of [CH] 8.11, 8.13 of [A]
3/2 Chain Rule (cont.) Critical Points Chapter 7 of [CH], 2.5 of [Co] 8.4, 8.6 of [CH]
3/4 Lagrange Multipliers, Begin Double Integrals 2.7 of [Co], 3.1 of [Co], begin 3.2 8.7 of [CH], 12.1-12.2 of [CH]
3/9 Double Integrals cont., Center of Mass 3.2 of [Co], 13.1 of [CH] 12.2 of [CH], 3.6 of [Co]
3/11 Change of Variables for Double Integrals 13.2 of [CH], 3.5 of [Co] (double integrals part)
3/16 Triple Integrals 3.3 of [Co] 13.3 of [CH]
3/18 Integrals cont. (TBD) 3.5 or 3.6 of [Co]
Schedule below is more tentative
3/30 Line Integrals 4.1 of [Co] 14.2 of [CH]
4/1 Fundamental Theorem, Conservative Vector Fields 4.2 of [Co], please read 14.3 of [CH] 14.3 of [CH], these notes
4/6 Green's Theorem 4.3 of [Co] 17.2-17.3 of [CH], these notes
4/8 More Green's Theorem 4.3 of [Co], these notes [O] 11.19-20 of [A], Calculus to Cohomology Intro p.1-3
4/13 More Green's Theorem and Simple Connectedness these notes [O] 11.21, 11.24 of [A], Calculus to Cohomology Intro p.1-3
4/15 Surface Integrals 4.4 of [Co] 15.1, 16.1 of [CH]
4/20 Surface Integrals (cont.), Divergence Theorem 4.4 of [Co] 16.2 of [CH], 17.1 of [CH]
4/22 Stokes Theorem 4.5 of [Co] 18.1-18.2 of [CH]
4/27 More on Stokes 4.5, 4.6 of [Co] Div, Grad, Curl, and all That (dgcaat), Ch. 19 of [CH]
4/29 Div, Grad, Curl, and Other Topics 4.6 of [Co] dgcaat, Calculus to Cohomology p.4-5, Many articles on [W] - see announcement on Bcourses for some useful articles

Homework and Exams: