## Contents

4 ECTS credits
56 contact lessons

#### 4

Sets
2
Set, element, empty set, subset, intersection, union, complement
Numbers
2
Number sets N, Z, Q, R
Intervals
Absolute value
Algebra (review/self study)
0

#### 28

Function
2
Domain, codomain, range
Arrow diagram, table of values, formula, graph

Linear function and equations
6
Linear function
Linear equations
Equivalence operations
Relation between a linear function and a linear equation
Linear systems of equations
Financial mathematics: Simple interest, costs, revenue, profit, break-even
8

General form, vertex form
Completing the square
Financial mathematics: Supply, demand, market equilibrium

Exponential function and equations
12
Exponential function
Exponential equations
Logarithm
Financial mathematics: Compound interest, annuity

#### 12

Derivative
4
Rate of change
Derivative
Derivative of constant/power/exponential functions
Financial mathematics: Profit - marginal profit

Differentiation rules
4
Coefficient/sum/product rule
Chain rule
Higher-order derivatives
Applications
4
Increasing/decreasing, concavity
Relative/absolute maxima/minima, points of inflection
Financial mathematics: Marginal/average cost/revenue/profit
Financial mathematics: Point of diminishing returns

#### 8

Indefinite integral
4
Antiderivative
Indefinite integral of constant/power/exponential functions
Coefficient/sum rule
Financial mathematics: Marginal cost/revenue/profit - total cost/revenue/profit

Definite integral
4
Area under a curve
Fundamental theorem of calculus
Financial mathematics: Consumer's/producer's surplus

19.8.2015 tb