# Multivariable Calculus

Vrije Universiteit Amsterdam

## Course Description

• ### Course Name

Multivariable Calculus

• ### Host University

Vrije Universiteit Amsterdam

• ### Location

Amsterdam, The Netherlands

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.

### Course Disclaimer

Courses and course hours of instruction are subject to change.

Some courses may require additional fees.