Math 126 CA, CB

Calculus with Analytic Geometry III

Winter Quarter 2011

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This is the third and the most difficult course in the 124/5/6 three quarter sequence.
It covers analytic geometry, differential geometry, partial derivatives, double integrals, and Taylor polynomials and series. The detailed syllabus is here.
Prerequisites: Math 124, Math 125. You should be familiar with differential and integral calculus of functions of one variable.
This course is often chosen by future science, engeneering, chemistry or biology majors.
(For math majors, we have another sequence: the Honors Calculus Sequence Math 134/5/6.)
We use Stewart's book Multivariable Calculus , chapters 10, 12 - 15, and Taylor Notes.
These are the lecture notes on Taylor polynomials and series, which are used instead of the Chapter 11 of Multivariable Calculus


You will receive your grades after Friday, 03/18/2011.

Thank you for your collaboration. Good luck!

Time Schedule Useful Links Syllabus Grades Homework Mini-Lectures Quizzes and Solutions Challenge Problems with Solutions Exams Miscellaneous

Time Schedule

The course instructor is Professor James Zhang
Office hours: Wednesday and Friday 4:00-4:45pm at Padelford Hall C420
E-mail: zhang[a_t]

The teaching assistant is Andrey Sarantsev
Office hours: Wednesday, 1-2 and 4-5pm, Math Study Center, Communications Building B014, cubicle 4
E-mail: ansa1989[a_t]

Useful links to departmental resources


We use the textbook: Stewart, Multivariable Calculus and Taylor Notes

By default, the sections in the syllabus below relate to the Stewart's book

  1. Analytic Geometry

    • Three-dimensional Cartesian coordinates and vectors (12.1-2)
    • Polar coordinates (10.3)
    • Dot and cross product (12.3-4)
    • Lines and planes (12.5)
    • Quadric surfaces (12.6)

  2. Differential Geometry

    • Derivatives and integrals of vector functions (10.2, 13.2)
    • Curvature (13.3)
    • Motion in the space: velocity and acceleration (13.4)

  3. Multivariable Differential Calculus

    • Partial derivatives of first and higher orders (14.3)
    • Tangent planes and linear approximation (14.4)
    • Local maxima and minima of functions of two variables (14.7)

  4. Multivariable Integral Calculus

    • Definition of double integrals (15.1, 15.3)
    • Double and iterated integrals (15.2)
    • Double integrals in polar coordinates (15.4)
    • Applications of double integrals (15.5)

  5. Taylor Polynomials and Taylor Series (Taylor Notes)

    • Linear and quadratic approximation (sections 1-2)
    • Taylor approximation in the general case (section 3)
    • Taylor series (sections 4-5)


Your grade is determined by how you do relative to the class as a whole. Grades will be based on the following:


Homework will be assigned weekly and be collected in Quiz Section on Thursday every week (except for week 1, 4 and 8).
We have a grader to grade your homework, but the amount of homework that can be graded is limited. No late homework will be accepted. Click here for Homework

Mini-Lectures on Quiz Sections

Quizzes and Solutions

Quizzes will be given on Tuesday in week 2, 6, and 10.

If you have sufficient reasons, you can take a make-up quiz during my office hours. This will be the same quiz, but with slightly altered problems.

Challenge Problems with Solutions

Thursday Quiz Sections are devoted to questions and answers; you are also given a set of Challenge Problems taken from old exams, this is a practice for midterms and the final exam. They are totally non-mandatory; if you solve some of them and submit them at the end of Thursday quiz section, I will grade them. It will not affect your grade in any way whether you solve or not solve them.


  1. Midterm 1

  2. Midterm 2

  3. Final Exam

Rules for taking exams


It is a good idea to conduct a mid-quarter evaluation of your teaching. This helps to get a constructive feedback and improve your quality of teaching. Here are the two Anonymous Surveys used this quarter.

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