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## Multivariable Calculus

2019-2020

### 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)

### Method 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.

### Entry Requirements

Single Variable Calculus (XB_41007)

### Literature

Calculus: A Complete Course, by Adams and Essex, 9th edition, Pearson,
2016. ISBN 978-0134154367

### Target Audience

Bachelor Mathematics Year one

### General Information

Course Code XB_41008 6 EC P4+5 100 English Faculty of Science prof. dr. R.C.A.M. van der Vorst prof. dr. R.C.A.M. van der Vorst prof. dr. R.C.A.M. van der Vorst

### Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods Seminar, Lecture
Target audiences

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