Multivariable Calculus

Vrije Universiteit Amsterdam

Course Description

  • Course Name

    Multivariable Calculus

  • Host University

    Vrije Universiteit Amsterdam

  • Location

    Amsterdam, The Netherlands

  • Area of Study

    Calculus

  • Language Level

    Taught In English

  • Prerequisites

    SIngle Variable Calculus (XB_41007)

  • Course Level Recommendations

    Lower

    ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

    Hours & Credits

  • Recommended U.S. Semester Credits
    3
  • Recommended U.S. Quarter Units
    4
  • Overview

    COURSE OBJECTIVE
    At the end of this course students will be able to ...
    1. ... differentiate functions of several variables (partial derivatives), find local extreme values and use these to graph functions;
    2. ... parametrize curves and surfaces;
    3. ... apply the implicit and inverse function theorem;
    4. ... calculate and investigate multivariable Taylor polynomials of functions of several variables;
    5. ... calculate multivariable integrals (2D and 3D integrals) using appropriately chosen methods, such as the substitution method, integration by parts and changing the order of integration;
    6. ... investigate vector fields and line integrals;
    7. ... work with differential k-forms;
    8. ... formulate (the general) Stokes theorem and derive the classical integral theorems of Gauss, Green and Stokes;
    9. ... write down the arguments involved in solving a calculus problem in a logically correct manner.

    COURSE CONTENT

    This course deals with the calculus of functions of several variables. In particular, we cover
    * parametrized curves and arc length
    * planes and lines
    * functions of several variables and level sets
    * partial derivatives, gradients and directional derivatives
    * tangent planes and multivariable Taylor polynomials
    * the multivariable chain rule
    * the implicit and inverse function theorem
    * optimization and optimization under constraints
    * 2D integrals, order of integration
    * 3D integrals, cylindrical and spherical coordinates
    * changes of variables
    * vector fields
    * line integrals and surface integrals
    * parametrized hyper-sufaces and manifolds
    * differential k-forms
    * (the general) Stokes theorem and the classical integral theorems of Gauss, Green and Stokes

    TEACHING METHODS
    Class meetings (twice per week) and office hours (twice per week)

    TYPE OF ASSESSMENT
    Weekly MyMathLab exercises (10%), one Midterm exams (35%) and a Final exam (55%). The resit exam counts for 90%, with the 10% of
    the MyMathLab exercises still counting for the resit grade. There is no resit opportunity for the MyMathLab exercises.

     

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