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## Calculus 1

2018-2019

### Course Objective

At the end of this course the student is able to
a) calculate limits, using several methods like l'Hopitals rule or the
squeeze theorem
b) calculate derivatives and to find local extreme values
c) calculate integrals, using several methods like the substitution
method, integration by parts, partial fraction expansion
d) verify if a function is continuous, differentiable,
Riemann-integrable
e) calulate and apply a Taylor polynomial
f) formulate and apply several important theorems for continuous and/or
differentiable functions, like the Intermediate Value Theorem, the Mean
Value Theorem and the Fundamental Theorem of Calculus

### Course Content

Real functions of one variable. Topics that will be treated are:
1) Preliminaries, Real functions, Trigonometric functions
2) Limits, Continuity, Intermediate Value Theorem
3) Transcendental Functions, Inverse Functions
4) Differentiation, Chain Rule, Mean Value Theorem
5) Applications of Differentiation, Extreme Values, l'Hôpital's Rule,
Taylor Polynomial
6) Integration, Fundamental Theorem of Calculus, Improper Integrals

### Teaching Methods

Lectures (3x per week) and tutorials (2x per week)

### Method of Assessment

Midterm exam and Final exam. More details can be found in the manual on
Canvas.

### Literature

Adams en Essex, Calculus: A Complete Course, 9th edition, Pearson 2018,
ISBN-10: 0134154363 • ISBN-13: 9780134154367.

### Target Audience

1 BA

Participation in the working classes is compulsory! Detailed rules will
be announced in the manual on Canvas.

### General Information

Course Code X_400635 6 EC P1 100 English Faculty of Science dr. ir. R.F. Swarttouw dr. ir. R.F. Swarttouw dr. ir. R.F. Swarttouw dr. O. Fabert

### 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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