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Accelerated Multivariable Calculus

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:

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

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