Math 20C: Calculus and Analytic Geometry for Science and Engineering

Fall 2019


Vector Calculus (Sixth Edition), Jerrold E. Marsden and Anthony Tromba,

H. Freeman and Company 2012, ISBN-10: 1-4292-1508-0, ISBN-13: 978-1-4292-1508-4.

Course Description

We will cover parts of Chapters 1-5 of the textbook. Topics covered in the course will include: vector geometry, vector functions and their derivatives, partial differentiation, maxima and minima, double integration.


Hang Xu


Office Location: AP&M 6305

Office Hours: MW 6:00-7:30 pm

Course Assistant

Chi Zhang


Office Location: AP&M 5412

Office Hours: Th 5:00-6:00 pm, F 2:00-4:00 pm


MWF 5:00-5:50 pm at HSS 1330

Discussion Sections

F01 F 9:00-9:50 pm at HSS 2154

F02 F 6:00-6:50 pm at HSS 2154

F03 F 7:00-7:50 pm at HSS 2154

F04 F 8:00-8:50 pm at HSS 2154


Your cumulative average will be the best of the following two weighted averages:

Your course grade will be determined by your cumulative average at the end of the quarter, and will be based on the following scale:



















The above scale is guaranteed: for example, if your cumulative average is 80, your final grade will be at least B-. However, your instructor may adjust the above scale to be more generous.

Course policies

Resources for assistance and tutoring


11:00-11:50 am

Center Hall 316


12:30-1:20 pm

TLC 1504


4:00-4:50 pm

TLC 1504


Students requesting accommodations for this course due to a disability must provide a current Authorization for Accommodation (AFA) letter issued by the Office for Students with Disabilities (OSD) which is located in University Center 202 behind Center Hall. The AFA letter may be issued by the OSD electronically or in hard-copy; in either case, please make arrangements to discuss your accommodations with me in advance (by the end of Week 2. We will make every effort to arrange for whatever accommodations are stipulated by the OSD. For more information, see here.

Academic Integrity

Academic dishonesty is considered a serious offense at UCSD. Students caught cheating will face an administrative sanction which may include suspension or expulsion from the university. It is in your best interest to take pride in your work maintain your academic integrity. (Click here for more information.)

Noise and common courtesy: When class/section begins, please stop your conversations. Wait until class/section is over before putting your materials away in your backpack, standing up, or talking to friends. Do not disturb others by engaging in disruptive behavior. Disruption interferes with the learning environment and impairs the ability of others to focus, participate, and engage.

Electronic devices: Please do not use devices (such as cell phones, laptops, tablets, iPods) for non-class-related matters while in class/section. No visual or audio recording is allowed in class/section without prior permission of the instructor (whether by camera, cell phone, or other means).

Tentative schedule (will be updated as the course progresses)

Homework will be posted on WebAssign by every Wednesday and due 11:00 pm on the next Friday.

Week 0 (9/27): Vectors

Read 1.1
No discussion sections.

Week 1 (9/30, 10/2, 10/4): Inner Product and Cross Product

Read 1.2, 1.3.
Lecture notes Sec 1.1 problems 2, 4; Sec 1.2 problems 3, 6.

Week 2 (10/7, 10/9, 10/11): Cross Product and Real-Valued Functions

Read 1.3, 2.1, 2.2
Lecture notes Sec 1.3 example 1, problem 4.

Week 3 (10/14, 10/16, 10/18): Differentiation

Read 2.3
Lecture notes Sec 2.1 example.

Week 4 (10/21, 10/23, 10/25): Midterm I, Paths and Curves

Read 2.4
Midterm I is on Monday in class. 10/25 is the last day to drop without ‘W’.
Week 5 (10/28, 10/30, 11/1): Paths and Curves, Properties of Derivatives
Read 2.5 and page 63-66 about the matrix multiplication.

Week 6 (11/4, 11/6, 11/8): Gradients and Directional Derivatives

Read 2.6
11/8 is the last day to drop without ‘F’.
Week 7 (11/13, 11/15): Iterated Partial Derivatives, Extrema
No class on Monday for Veteran’s Day.
Read 3.1 3.3
Week 8 (11/18, 11/20, 11/22): Lagrange Multiplier
Read 3.4
Midterm II is on Monday in class.

Week 9 (11/25, 11/27): Acceleration, Arc Length

Read 4.1, 4.2
No class on Friday for the Thanksgiving.

Week 10 (12/2, 12/4, 12/6): Double Integrals

Read 5.1, 5.2

Final Exam 7:00-10:00 pm on December 12