Math 10C Fall 2017

Meeting TimeMWF, 12:00 PM - 12:50 PM
Location PETER 110
Instructor Dragos Oprea
Sittipong Thamrongpairoj (Sections A01-A04) Xiaochen Liu (Sections A05-A08)
Announcements and Dates
  • Friday, September 29: First lecture
  • Monday, October 23: Midterm I
  • Friday, November 10: Veteran's Day, no class
  • Monday, November 20: Midterm II
  • Thursday-Friday, November 23-24: Thanksgiving Break, no class
  • Friday, December 8: Last Lecture
  • Thursday, December 14: FINAL EXAM, 11:30-2:30pm in MANDEVILLE.

Calculus, sixth edition, by Deborah Hughes-Hallett; published by John Wiley & Sons, Inc. We will cover parts of Chapters 12-16 of the text.

  • You must buy a copy of the book that has the WileyPLUS Online Homework code. Otherwise you will have to buy the code separately! (If you were in Math 10B last quarter, then you can use the same WileyPlus code as last quarter.)
  • If you want ELECTRONIC ACCESS ONLY, you can buy the WileyPLUS code separately. Then you do not need to buy a physical copy of the book. (This is the cheapest option.)
  • The publisher also has a Wiley companion site for the textbook.
  • Important: Register for WileyPlus using your UCSD email address and Student ID. Failure to do so may result in loss of your homework grade!
  • Click here to access the Wiley Plus webpage for the course.

The grade is computed as the best of the following weighed averages:

  • Homework 20%, Midterm I 20%, Midterm II 20%, Final Exam 40%.
  • Homework 20%, Best midterm 20%, Final Exam 60%.
Introduction to functions of more than one variable. Vector geometry, partial derivatives, velocity and acceleration vectors, optimization problems.
Prerequisites AP Calculus BC score of 3, 4, or 5, or Math 10B, or Math 20B.

Reading the sections of the textbook corresponding to the assigned homework exercises is considered part of the homework assignment. You are responsible for material in the assigned reading whether or not it is discussed in the lecture. It will be expected that you read the assigned material in advance of each lecture.


Graphing calculators and computer programs (or online computing websites such as Wolfram|Alpha) can be very helpful when working through your homework. However, a calculator/computer should be used as an aid in learning concepts, not just as a means of computation. You should not hesitate use these devices when working on math problems at home. However, always keep in mind that:

  • The use of electronic devices will not be permitted during exams. You will not be asked to solve problems on the exams that require any electronic computing devices.

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. We will have two different kinds of homework assignments in this class: online homework (which will be graded) and "paper-and-pen" homework (which will not be graded).

  • The "paper-and-pen" homework assignments will be announced on the course homework page . These assignments will not be turned in and will not be graded; however, if you seek help from the instructor or TAs, they will usually do these problems, not the online homework problems.
  • Online homework will be done through WileyPlus, a service hosted by the the publisher of our textbook.
  • In order to use WileyPLUS, you must have a WileyPLUS Online Homework code.
  • No homework assignment scores will be dropped at the end of the quarter.
You can get help with the homework assignments in the Calculus Tutoring Lab. A Student Solutions Manual (available in the Bookstore) has complete solutions for odd-numbered problems in the text.

There will be two midterm exams given in class. The dates are October 23 and November 20.

  • There will be no makeup exams for any reason. We do not allow alternate times for taking exams. (If you have a documented disability or must miss the exam for a university sponsored activity, then arrangements can be made using the standard procedures.)
  • One 8.5 x 11 page of notes is allowed (front only, no photocopies).
  • No calculators or electronic computing devices will be allowed during the examinations.

The final examination will be held on Thursday, December 14, 11:30-2:30PM in Mandeville Auditorium. There is no make up final examination for any reason. It is your responsability to ensure that you do not have a schedule conflict during the final examination; you should not enroll in this class if you cannot sit for the final examination at its scheduled time. For the final, you are allowed one page of notes, back and front (no photocopies). Again, no calculators or other electronic computing devices are allowed.


Discussion Sections are held on Tuesdays.

  • Course Assistant: Sittipong Thamrongpairoj
    • Section A01, Tuesday 2-2:50PM, YORK 4080A
    • Section A02, Tuesday 3-3:50AM, YORK 4080A
    • Section A03, Tuesday 4-4:50AM, YORK 4080A
    • Section A04, Tuesday 5-5:50AM, YORK 4080A
  • Course Assistant: Xiaochen Liu
    • Section A05, Tuesday 6-6:50PM, YORK 4080A
    • Section A06, Tuesday 7-7:50PM, YORK 4080A
    • Section A07, Tuesday 8-8:50PM, YORK 4080A
    • Section A08, Tuesday 9-9:50PM, YORK 4080A

If you are having trouble with the homework or have questions about the material, the best way to get help is to attend the office hours offered by me and the teaching assistants. If you can't make the scheduled times, then email us and we'll set up an appointment.

Additional help is given by


It is your responsibility to check your homework and exam scores on Gradescope and contact your TA before the end of the 10th week of the quarter to resolve recording errors. Questions regarding missing or incorrectly recorded exam scores will not be considered after the last day of instruction.


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 maintain your academic integrity. (Click here for more information.)

Lecture Summaries
  • Lecture 1: Introduction. Functions of two variables. Drawing simple shapes in 3 dimensions: points, planes, spheres.
  • Lecture 2: Graphs and surfaces. Paraboloids, cylinders and planes.
  • Lecture 3: Level curves and contour diagrams. More graphs: paraboloids, cones, saddles.
  • Lecture 4: Planes and linear functions. Contour diagrams consist of parallel lines. Cross sections are parallel lines. Equations of planes. Tables of linear functions.
  • Lecture 5: Vectors. Magnitude. Components. Operations with vectors. Unit vectors.
  • Lecture 6: Applications of vectors. Properties of vector operations.
  • Lecture 7: Dot product. Algebraic definition. Geometric interpretation. Perpendicular vectors. Normal to planes. Angle between vectors.
  • Lecture 8: Using dot product to resolve vectors into components. Cross product. Algebraic expression and properties.
  • Lecture 9: More on cross product. Magnitude of the cross product. Area of parallelograms. Planes through 3 points.
  • Lecture 10: Derivatives in several variables. Interpretation of derivatives as rate of change. Derivatives and level diagrams. Derivatives and graphs.
  • Lecture 11: Tangent planes to graphs. Linear approximation. Differential.
  • Lecture 12: Directional derivative. Motivation and definition. Gradient and directional derivatives.
  • Lecture 13: More on gradient. Gradient is normal to level curves. Gradient as the direction of steepest increase.
  • Lecture 14: Chain rule in several variables and some examples.
  • Lecture 15: Second order derivatives. Mixed partial derivatives are equal. Quadratic approximation.
  • Lecture 16: Critical points and second derivative test. Examples.
  • Lecture 17: Global minima and global maxima. Functions on compact sets. Optimization.
  • Lecture 18: Lagrange multipliers and constrained optimization.
  • Lecture 19: Inequality constraints and Lagrange multipliers. Examples.
  • Lecture 20: Integration. Riemann sums. Applications of the integral: volume under the graph, area of regions, average values of functions.
  • Lecture 21: Integration. First examples using symmetry. Integration over rectangular regions. Iterated integrals.
  • Lecture 22: Integration over arbitrary regions. Examples.
  • Lecture 23: Changing the order of integration. Examples.