Course: 2018/2019

Foundations of Calculus

(12876)

To identify functions, their dependence on variables and their basic properties
To understand the concept of limit and compute easy limits.
To understand the definition of derivative and use its interpretation as tangent line. TO compute derivatives
To understand the difference between indefinite and definite integral and compute easy integrals

Description of contents: programme

Funcitions and their graphs (4 lessons)
¿ Lines and quadratic functions
¿ Functions
¿ Combinations of functions
Inverse functions
Polinomial and rational functions (4 Lessons)
Polynomial functions of Higher Degree
Polynomial division
Rational functions
Ineqaulities and absolute values
Limits and their properties. Continuous functions (4 lessons)
¿ Evaluating limits analytically
¿ Infinite limits
¿ Limits at infinity
¿ Continuity and one-side limits
Definition and basic differentiation rule (4 lessons)
¿ The derivative and tangent line
¿ Basic differentiation rules
¿ Product and quotient rules and higher-order derivatives
¿ The Chain rule
L'Hôpitals rule
Primitives (4 lessons)
¿ Antiderivatives and indefinite integration
¿ Area and definite integrals
¿ Integration by substitution
¿ Integration by parts

Assessment System

Basic Bibliography

- Larson, R., Edwars, B. H.. Calculus of a single variable. Cengage.
- Larson R; Hostetler, R.P. Precalculus. Cengage. 2014