**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**:

- Homework will be assigned regularly (see the syllabus) and due at 11pm on Gradescope. I grant extensions in reasonable circumstances, but you must talk to me
**as early as possible**. The longer you wait, the less flexible I will be. - You may work together to figure out homework problems, but you must write up your solutions in your own words in order to receive credit. In particular, please do not copy answers from the internet or solution manuals. Since a major purpose of the homework is to prepare you for the exams, I encourage you to give each problem an honest shot by yourself (say, at least thirty minutes) before discussing it with others. Another useful practice is if you're stuck on a problem, come to office hours and ask for a hint. The more you figure out on your own, the better your understanding of the material, and the better you'll do both on the exams and in your future endeavours that might require abstract algebra.
- You may cite any results from the notes, unless otherwise stated.
- The usual expectations and procedures for academic integrity at UC Berkeley apply. Cheating on an exam will result in a failing grade and will be reported to the University Office of Student Conduction. Please don't put me through this.
- Please let me know sooner rather than later if you need any accommodations related to the Disabled Student Program (DSP). I am more than happy to make arrangements, but it really helps if you tell me earlier rather than later.
- Per university guidelines, it is your responsibility to notify the instructor in writing by the end of the second week of classes (January 31) of any scheduling conflicts due to religious observance or extracurricular activities, and to propose a resolution for those conflicts.

**Additional resources (will be on Bcourses when needed)**:

*Calculus: Early Transcendentals*by James Stewart, denoted [S]*Calculus Volume II*by Tom Apostol, denoted [A]*div grad curl and all that*by H. M. Schey, denoted [dgcaat]*Line Integrals and Green's Theorem*by Jeremy Orloff, denoted [O]

**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.

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**:

- Please fill out the preliminary survey by January 26 (earlier preferred).
- Homework 1, due Thursday, January 28 at 11pm (on Gradescope).
- Homework 2, due Thursday, February 4 at 11pm (on Gradescope).
- Homework 3, due Thursday, February 11 at 11pm (on Gradescope).
- Homework 4, due Thursday, February 18 at 11pm (on Gradescope).
- Midterm 1, released Sunday, February 21, due Tuesday, February 23 at 12pm (on Gradescope).
- Homework 5, due Tuesday, March 2 at 11pm (on Gradescope).
- Homework 6, due Tuesday, March 9 at 11pm (on Gradescope).
- Homework 7, due Thursday, March 18 at 11pm (on Gradescope).
- Homework 8, due Thursday, April 1 at 11pm (on Gradescope) - extended to Sunday, April 4.
- Homework 9, due Thursday, April 8 at 11pm (on Gradescope).
- Homework 10, due Tuesday, April 20 at 11pm (on Gradescope).
- Homework 11, due Thursday, April 29 at 11pm (on Gradescope).
- Homework 12, due Thursday, May 6 at 11pm (on Gradescope).