Calculus 1

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

FORM OF TUITION
Lectures (3x per week) and tutorials (2x per week)

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

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