**Math 20C**

**Calculus andanalytic geometry**

**Fall 2019**

**Announcements: The final exam is Friday, December 13th from 3pm-6pm. Here is the practice final. Here are some old finals from previous incarnations of 20C (Final1, Final2, Final3).
During finals week David will have office hours from 1pm-3pm on Monday and Wednesday.
Gary will hold office hours from 6pm-8pm on Tuesday, Wednesday, and Thursday in AP&M 5402
Patrick will hold a review session from 5pm-7pm on Tuesday in AP&M B402A and will hold office hours from 1pm-3pm on Thursday in AP&M 5412.
There is walk-in tutoring available through the Teaching+Learning Commons. Information is in this flyer.**

Monday | Wednesday | Friday |
---|---|---|

9/23. No class. |
9/25. No class. |
9/27. §1.1 Vectors in 2D and 3D |

9/30. §1.2 The Inner Product, Length, and Distance.HW1 due. |
10/2. §1.2 The Inner Product, Length, and Distance. |
10/4. §1.3 Matrices, Determinants, and the Cross Product. |

10/7. §1.3 Matrices, Determinants, and the Cross Product.HW2 due. |
10/9. §1.3 Matrices, Determinants, and the Cross Product. |
10/11. §2.1 The Geometry of Real-Valued Functions. |

10/14. §2.2 Limits and Continuity.HW3 due. |
10/16. §2.3 Differentiation. |
10/18. §2.3 Differentiation. |

10/21. §2.4 Intro to Paths and Curves.HW4 due (solutions). |
10/23. Midterm 1 (solutions). Practice Midterm (solutions). |
10/25. §2.5 Properties of the Derivative. |

10/28. §2.6 Gradients and Directional Derivatives.HW5 due (solutions). |
10/30. §2.6 Gradients and Directional Derivatives. |
11/1. §3.1 Iterated Partial Derivatives. |

11/4. §3.3 Extrema of Real-Valued Functions.HW6 due (solutions). |
11/6. §3.3 Extrema of Real-Valued Functions. |
11/8. §3.4 Constrained Extrema and Lagrange Multipliers. |

11/11. No class. Veterans Day. |
11/13. §3.4 Constrained Extrema and Lagrange Multipliers.HW7 due (solutions). |
11/15. §4.1 Acceleration and Newton's Second Law. |

11/18. §4.2 Arc Length.HW8 due (solutions). |
11/20. Midterm 2 (solutions). Practice Midterm (solutions). |
11/22. §5.1 Intro to Double and Triple Integrals. |

11/25. §5.2 The Double Integral over a Rectangle.HW9 due (solutions). |
11/27. §5.3 The Double Integral over More General Regions. |
11/29. No class. Thanksgiving. |

12/2. §5.4 Changing the Order of Integration. |
12/4. §5.5 The Triple Integral. |
12/6. Final review.HW10 due. Practice Final (solutions). |

**Course Description:** Math 20C is the third quarter course in calculus for students majoring in Mathematics, Engineering and the sciences. Math 20C introduces vectors and three-dimensional geometry and covers multivariable differential calculus with an introduction to multiple integrals.

**Prerequisites:** Math 20B, an AP Calculus BC score of 4 or above, or the consent of instructor.
**Textbook:** *Vector Calculus*, sixth edition, by Jerrold E. Marsden and Anthony J. Tromba, published by W. H. Freeman and Company (2012).

(This is the same book as the one used in Math 20E.
We will use Chapters 1-5 of the text. Math 20E covers almost everything else in this text.)
**Homework:** Homework is a very important part of the course, and in order to fully master the topics, it is essential that you work carefully on every assignment and try your best to complete every problem. Homework will be due on Mondays at 10pm and will be handed in on Gradescope. You can find the homework assignments on the calendar and on gradescope.

**Reading:** Reading the sections of the textbook corresponding to the assigned homework exercises is considered part of the homework. Lecture time is very limited and not every subject can be fully discussed in the time allotted for lecture. Thus, you must read the assigned sections of your textbook (and work through the examples) to fully understand the subject. You should expect questions on the exams that will test your understanding of concepts addressed in the reading and assigned homework exercises, whether or not they are discussed in the lecture.

**Grades:** There are three methods to compute your grade. Your grade will be determined using each method, and then the best grade will be used.

**• Method 1.** (20% HW)+(20% Midterm 1)+(20% Midterm 2)+(40% Final Exam).

**• Method 2.** (20% HW)+(20% Best Midterm)+(60% Final Exam).

**• Method 3.** (25% Midterm 1)+(25% Midterm 2)+(50% Final Exam).

After your grade is calculated, your letter grade will be calculated, based on a scale. The following are grades are guaranteed:

A ≥ 93%, B ≥ 83%, C ≥ 73%, D ≥ 63%.

However, it is possible that I will change the grading scale to be more lenient.

**Exams:** There will be 3 exams. Two midterms and one final.

**First Midterm:** The first midterm will be held on October 23rd.
**Second Midterm:** The second midterm will be held on November 20th.
**Final Exam:** The final will be held on Friday, December 13th from 3pm-6pm.
**Homework Policy:** Late homework will not be accepted. At the top of each assignment should appear:

(1) Your name,

(2) Either a list of sources consulted (other than the textbook, lectures, and things posted on this site), or the sentence "Sources consulted: none."

You are not expected to solve every single problem on your own, and you are encouraged to work in groups. However, your homework write-ups should be done independently. Office hours are a great time to ask questions about the homework assignments.

**Course Policies:**

No make up exams will be given. A missed midterm will be scored a 0.

Accomodations for students with disabilities must be requested in accordance with the Mathematical Departmental Policies. In particular, any such request must be made sufficiently in advance.

Violations of UCSD's academic integrity policies will be addressed using internal measures (e.g., asking students to defend their work orally, zeroing out affected homework or exam scores) and/or UCSD administrative measures at the professor's discretion. If you suspect a violation of academic integrity, please bring it to the attention of the professor and/or TA immediately.