**Prerequisites:** MATH UN1101 (Calculus I) and MATH UN1102 (Calculus II), or equivalents.

** Instructor:** Robert Friedman, 605 Mathematics, 212-854-4355, ` rf@math.columbia.edu `

** Office Hours:** tba, 605 Mathematics

**Course Description:** Vectors in dimensions 2 and 3, vector-valued functions of one variable, scalar-valued functions of several variables, partial derivatives, gradients, optimization, Lagrange multipliers, double and triple integrals, line and surface integrals, vector calculus.

**Overview and Goals:** during this semester you will learn:

- Multidimensional spaces: coordinate systems, vectors, dot product, cross product,

lines and planes. - Vector functions: limits, derivatives, and integrals of vector functions; velocity and acceleration.
- Multivariable differentiation: partial derivatives, directional derivatives, gradients, critical points and the second derivative test, maximum and minimum values, method of Lagrange multipliers.
- Multivariable integration: double and triple integrals, line and surface integrals,

Green’s theorem, Stokes’ theorem, and the divergence theorem.

** Typical Syllabus**: A sample syllabus is available.

**Textbook:** James Stewart, *Calculus, Early Transcendentals*, 8th edition.

** Help Room ** for this course (Mathematics UN1205) is located in 333 Milbank Hall, Barnard Campus. In addition to office hours and the Help Room, tutoring services are available.

**Grading:** Homework 20%, 1st Midterm 20%, 2nd Midterm 20%, Final Exam 40%

** Exam Policies:** No calculators, books, notes, formula sheets etc. are allowed on exams. Cell phones must be turned off during exams.

If you have a conflict with any of the exams, please contact the instructor as soon as possible and at least one week before the exam. You may miss an exam only in a medical and family emergency, documented by a note from your doctor or dean.

**Information on Calculus Classes:**

- Calculus Placement
- WebAssign
- options to buy the course textbook
- answers to frequently asked questions

For questions not covered here or on the links, contact Michael Thaddeus, the Math Department Calculus Director.

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