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## Calculus 1

2018-2019
Dit vak wordt in het Engels aangeboden. Omschrijvingen kunnen daardoor mogelijk alleen in het Engels worden weergegeven.

### Doel vak

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

### Inhoud vak

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

### Onderwijsvorm

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

### Toetsvorm

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

### Literatuur

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

1 BA

### Overige informatie

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

### Algemene informatie

Vakcode X_400635 6 EC P1 100 Engels Faculteit der Bètawetenschappen dr. ir. R.F. Swarttouw dr. ir. R.F. Swarttouw dr. ir. R.F. Swarttouw dr. O. Fabert

### Praktische informatie

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Werkvormen Werkcollege, Deeltoets extra zaalcapaciteit, Hoorcollege
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