Kurse
Ãœber Sowiso
Kontakt
Freischalten 
English
Kurse
Ãœber Sowiso
Kontakt
Freischalten 
English
Calculus for Social Sciences
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Kursinhalt
Functions
Introduction to functions
THEORIE
T
1.
The notion of function
ÃœBUNG
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2.
The notion of function
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THEORIE
T
3.
Arithmetic operations for functions
ÃœBUNG
Ã
4.
Arithmetic operations for functions
6
THEORIE
T
5.
The range of a function
ÃœBUNG
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6.
The range of a function
6
THEORIE
T
7.
Functions and graphs
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8.
Functions and graphs
5
THEORIE
T
9.
The notion of limit
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10.
The notion of limit
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THEORIE
T
11.
Continuity
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12.
Continuity
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THEORIE
T
13.
Arithmetic operations for continuity
ÃœBUNG
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14.
Arithmetic operations for continuity
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Lines and linear functions
THEORIE
T
1.
Linear equations with a single unknown
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2.
Linear equations with a single unknown
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THEORIE
T
3.
The general solution of a linear equation
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ÃœBUNG
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4.
The general solution of a linear equation
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THEORIE
T
5.
Systems of equations
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6.
Systems of equations
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THEORIE
T
7.
The equation of a line
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8.
The equation of a line
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THEORIE
T
9.
Solving systems of equations by addition
ÃœBUNG
Ã
10.
Solving systems of equations by addition
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THEORIE
T
11.
Equations and lines
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ÃœBUNG
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12.
Equations and lines
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Quadratic functions
THEORIE
T
1.
Introduction
THEORIE
T
2.
Completing the square
ÃœBUNG
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3.
Completing the square
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THEORIE
T
4.
The quadratic formula
ÃœBUNG
Ã
5.
The quadratic formula
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THEORIE
T
6.
Factorization
ÃœBUNG
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7.
Factorization
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THEORIE
T
8.
Solving equations with factorization
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ÃœBUNG
Ã
9.
Solving equations with factorization
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Polynomials
THEORIE
T
1.
The notion of polynomial
ÃœBUNG
Ã
2.
The notion of polynomial
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THEORIE
T
3.
Calculating with polynomials
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4.
Caclulating with polynomials
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Rational functions
THEORIE
T
1.
The notion of rational function
ÃœBUNG
Ã
2.
The notion of rational function
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Power functions
THEORIE
T
1.
Power functions
ÃœBUNG
Ã
2.
Power functions
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THEORIE
T
3.
Equations of power functions
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ÃœBUNG
Ã
4.
Equations of power functions
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Conclusion of introduction to functions
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1.
Applications
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Operations for functions
Inverse functions
THEORIE
T
1.
The notion of inverse function
ÃœBUNG
Ã
2.
The notion of inverse function
2
THEORIE
T
3.
Injective functions
ÃœBUNG
Ã
4.
Injective functions
5
THEORIE
T
5.
Characterizing invertible functions
ÃœBUNG
Ã
6.
Characterizing invertible functions
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Exponential and logarithmic functions
THEORIE
T
1.
Exponential functions
ÃœBUNG
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2.
Exponential functions
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THEORIE
T
3.
Properties of the exponential functions
ÃœBUNG
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4.
Properties of the exponential functions
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THEORIE
T
5.
Growth of an exponential function
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ÃœBUNG
Ã
6.
Growth of an exponential function
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THEORIE
T
7.
Logarithmic functions
ÃœBUNG
Ã
8.
Logarithmic functions
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THEORIE
T
9.
Properties of logarithms
ÃœBUNG
Ã
10.
Properties of logarithms
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THEORIE
T
11.
Growth of a logarithmic function
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ÃœBUNG
Ã
12.
Growth of a logarithmic function
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New functions from old
THEORIE
T
1.
Translating functions
ÃœBUNG
Ã
2.
Translating functions
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THEORIE
T
3.
Scaling functions
ÃœBUNG
Ã
4.
Scaling functions
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THEORIE
T
5.
Symmetry of functions
ÃœBUNG
Ã
6.
Symmetry of functions
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THEORIE
T
7.
Composing functions
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ÃœBUNG
Ã
8.
Composing functions
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Conclusion of operations for functions
ÃœBUNG
Ã
1.
Applications
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Introduction to differentiation
Definition of differentiation
THEORIE
T
1.
Introduction
ÃœBUNG
Ã
2.
Introduction
2
THEORIE
T
3.
The notion of difference quotient
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Ã
4.
The notion of difference quotient
1
THEORIE
T
5.
The notion of derivative
ÃœBUNG
Ã
6.
The notion of derivative
13
Calculating derivatives
THEORIE
T
1.
Derivatives of polynomials and power functions
ÃœBUNG
Ã
2.
Derivatives of polynomials and power functions
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Derivatives of exponential functions and logarithms
THEORIE
T
1.
The natural exponential function and logarithm
ÃœBUNG
Ã
2.
The natural exponential function and logarithm
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THEORIE
T
3.
Rules of calculation for exponential functions and logarithm
ÃœBUNG
Ã
4.
Rules of calculation for exponential functions and logarithm
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THEORIE
T
5.
Derivatives of exponential functions and logarithms
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ÃœBUNG
Ã
6.
Derivatives of exponential functions and logarithms
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Conclusion introduction to differentiation
THEORIE
T
1.
Summary
ÃœBUNG
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2.
Applications
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Rules of differentiation
Rules of computation for the derivative
THEORIE
T
1.
The sum rule for differentiation
ÃœBUNG
Ã
2.
The sum rule for differentiation
7
THEORIE
T
3.
The product rule for differentiation
ÃœBUNG
Ã
4.
The product rule for differentiation
10
THEORIE
T
5.
The quotient rule for differentiation
ÃœBUNG
Ã
6.
The quotient rule for differentiation
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THEORIE
T
7.
The chain rule for differentiation
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ÃœBUNG
Ã
8.
The chain rule for differentiation
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THEORIE
T
9.
Exponential functions and logarithm derivatives revisited
ÃœBUNG
Ã
10.
Exponential functions and logarithm derivatives revisited
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THEORIE
T
11.
The derivative of an inverse function
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ÃœBUNG
Ã
12.
The derivative of an inverse function
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Applications of derivatives
THEORIE
T
1.
Tangent lines revisited
ÃœBUNG
Ã
2.
Tangent lines revisited
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THEORIE
T
3.
Approximation
ÃœBUNG
Ã
4.
Approximation
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THEORIE
T
5.
Elasticity
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ÃœBUNG
Ã
6.
Elasticity
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Conclusion of rules of differentiation
THEORIE
T
1.
Summary
ÃœBUNG
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2.
Summary
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ÃœBUNG
Ã
3.
Applications
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Applications of differentiation
Analysis of functions
THEORIE
T
1.
Monotonicity
ÃœBUNG
Ã
2.
Monotonicity
8
THEORIE
T
3.
Local minima and maxima
ÃœBUNG
Ã
4.
Local minima and maxima
11
THEORIE
T
5.
Analysis of functions
ÃœBUNG
Ã
6.
Analysis of functions
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Higher derivatives
THEORIE
T
1.
Higher derivatives
ÃœBUNG
Ã
2.
Higher derivatives
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Conclusion of applications of differentiation
ÃœBUNG
Ã
1.
Applications
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Multivariate functions
Basic notions
THEORIE
T
1.
Functions of two variables
ÃœBUNG
Ã
2.
Functions of two variables
12
THEORIE
T
3.
Functions and relations
ÃœBUNG
Ã
4.
Functions and relations
6
THEORIE
T
5.
Visualizing bivariate functions
ÃœBUNG
Ã
6.
Visualizing bivariate functions
6
THEORIE
T
7.
Multivariate functions
ÃœBUNG
Ã
8.
Multivariate functions
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Partial derivatives
THEORIE
T
1.
Partial derivatives of the first order
ÃœBUNG
Ã
2.
Partial derivatives of the first order
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THEORIE
T
3.
Chain rules for partial differentiation
ÃœBUNG
Ã
4.
Chain rules for partial differentiation
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THEORIE
T
5.
Higher partial derivatives
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ÃœBUNG
Ã
6.
Higher partial derivatives
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THEORIE
T
7.
Elasticity in two variables
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ÃœBUNG
Ã
8.
Elasticity in two variables
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Conclusion of Multivariate functions
THEORIE
T
1.
Conclusion
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2.
Applications
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Optimization
Extreme points
THEORIE
T
1.
Stationary points
ÃœBUNG
Ã
2.
Stationary points
11
THEORIE
T
3.
Minimum, maximum, and saddle point
ÃœBUNG
Ã
4.
Minimum, maximum, and saddle point
11
THEORIE
T
5.
Criteria for extrema and saddle points
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ÃœBUNG
Ã
6.
Criteria for extrema and saddle points
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THEORIE
T
7.
Convexity and concavity
ÃœBUNG
Ã
8.
Convexity and concavity
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THEORIE
T
9.
Criterion for a global extremum
THEORIE
T
10.
Hessian convexity criterion
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Conclusion of optimization
THEORIE
T
1.
Conclusion
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2.
Applications
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