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Functions
Introduction to functions
THEORY
T
1.
The notion of function
PRACTICE
P
2.
The notion of function
6
THEORY
T
3.
Arithmetic operations for functions
PRACTICE
P
4.
Arithmetic operations for functions
6
THEORY
T
5.
The range of a function
PRACTICE
P
6.
The range of a function
6
THEORY
T
7.
Functions and graphs
PRACTICE
P
8.
Functions and graphs
5
THEORY
T
9.
The notion of limit
PRACTICE
P
10.
The notion of limit
11
THEORY
T
11.
Continuity
PRACTICE
P
12.
Continuity
7
THEORY
T
13.
Arithmetic operations for continuity
PRACTICE
P
14.
Arithmetic operations for continuity
8
Lines and linear functions
THEORY
T
1.
Linear equations with a single unknown
PRACTICE
P
2.
Linear equations with a single unknown
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THEORY
T
3.
The general solution of a linear equation
PRACTICE
P
4.
The general solution of a linear equation
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THEORY
T
5.
Systems of equations
PRACTICE
P
6.
Systems of equations
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THEORY
T
7.
The equation of a line
PRACTICE
P
8.
The equation of a line
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THEORY
T
9.
Solving systems of equations by addition
PRACTICE
P
10.
Solving systems of equations by addition
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THEORY
T
11.
Equations and lines
PRACTICE
P
12.
Equations and lines
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Quadratic functions
THEORY
T
1.
Introduction
THEORY
T
2.
Completing the square
PRACTICE
P
3.
Completing the square
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THEORY
T
4.
The quadratic formula
PRACTICE
P
5.
The quadratic formula
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THEORY
T
6.
Factorization
PRACTICE
P
7.
Factorization
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THEORY
T
8.
Solving equations with factorization
PRACTICE
P
9.
Solving equations with factorization
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Polynomials
THEORY
T
1.
The notion of polynomial
PRACTICE
P
2.
The notion of polynomial
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THEORY
T
3.
Calculating with polynomials
PRACTICE
P
4.
Caclulating with polynomials
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Rational functions
THEORY
T
1.
The notion of rational function
PRACTICE
P
2.
The notion of rational function
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Power functions
THEORY
T
1.
Power functions
PRACTICE
P
2.
Power functions
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THEORY
T
3.
Equations of power functions
PRACTICE
P
4.
Equations of power functions
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Conclusion of introduction to functions
PRACTICE
P
1.
Applications
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Operations for functions
Inverse functions
THEORY
T
1.
The notion of inverse function
PRACTICE
P
2.
The notion of inverse function
2
THEORY
T
3.
Injective functions
PRACTICE
P
4.
Injective functions
5
THEORY
T
5.
Characterizing invertible functions
PRACTICE
P
6.
Characterizing invertible functions
4
Exponential and logarithmic functions
THEORY
T
1.
Exponential functions
PRACTICE
P
2.
Exponential functions
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THEORY
T
3.
Properties of the exponential functions
PRACTICE
P
4.
Properties of the exponential functions
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THEORY
T
5.
Growth of an exponential function
PRACTICE
P
6.
Growth of an exponential function
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THEORY
T
7.
Logarithmic functions
PRACTICE
P
8.
Logarithmic functions
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THEORY
T
9.
Properties of logarithms
PRACTICE
P
10.
Properties of logarithms
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THEORY
T
11.
Growth of a logarithmic function
PRACTICE
P
12.
Growth of a logarithmic function
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New functions from old
THEORY
T
1.
Translating functions
PRACTICE
P
2.
Translating functions
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THEORY
T
3.
Scaling functions
PRACTICE
P
4.
Scaling functions
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THEORY
T
5.
Symmetry of functions
PRACTICE
P
6.
Symmetry of functions
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THEORY
T
7.
Composing functions
PRACTICE
P
8.
Composing functions
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Conclusion of operations for functions
PRACTICE
P
1.
Applications
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Introduction to differentiation
Definition of differentiation
THEORY
T
1.
Introduction
PRACTICE
P
2.
Introduction
2
THEORY
T
3.
The notion of difference quotient
PRACTICE
P
4.
The notion of difference quotient
1
THEORY
T
5.
The notion of derivative
PRACTICE
P
6.
The notion of derivative
13
Calculating derivatives
THEORY
T
1.
Derivatives of polynomials and power functions
PRACTICE
P
2.
Derivatives of polynomials and power functions
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Derivatives of exponential functions and logarithms
THEORY
T
1.
The natural exponential function and logarithm
PRACTICE
P
2.
The natural exponential function and logarithm
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THEORY
T
3.
Rules of calculation for exponential functions and logarithm
PRACTICE
P
4.
Rules of calculation for exponential functions and logarithm
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THEORY
T
5.
Derivatives of exponential functions and logarithms
PRACTICE
P
6.
Derivatives of exponential functions and logarithms
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Conclusion introduction to differentiation
THEORY
T
1.
Summary
PRACTICE
P
2.
Applications
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Rules of differentiation
Rules of computation for the derivative
THEORY
T
1.
The sum rule for differentiation
PRACTICE
P
2.
The sum rule for differentiation
7
THEORY
T
3.
The product rule for differentiation
PRACTICE
P
4.
The product rule for differentiation
10
THEORY
T
5.
The quotient rule for differentiation
PRACTICE
P
6.
The quotient rule for differentiation
13
THEORY
T
7.
The chain rule for differentiation
PRACTICE
P
8.
The chain rule for differentiation
12
THEORY
T
9.
Exponential functions and logarithm derivatives revisited
PRACTICE
P
10.
Exponential functions and logarithm derivatives revisited
8
THEORY
T
11.
The derivative of an inverse function
PRACTICE
P
12.
The derivative of an inverse function
3
Applications of derivatives
THEORY
T
1.
Tangent lines revisited
PRACTICE
P
2.
Tangent lines revisited
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THEORY
T
3.
Approximation
PRACTICE
P
4.
Approximation
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THEORY
T
5.
Elasticity
PRACTICE
P
6.
Elasticity
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Conclusion of rules of differentiation
THEORY
T
1.
Summary
PRACTICE
P
2.
Summary
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PRACTICE
P
3.
Applications
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Applications of differentiation
Analysis of functions
THEORY
T
1.
Monotonicity
PRACTICE
P
2.
Monotonicity
8
THEORY
T
3.
Local minima and maxima
PRACTICE
P
4.
Local minima and maxima
11
THEORY
T
5.
Analysis of functions
PRACTICE
P
6.
Analysis of functions
38
Higher derivatives
THEORY
T
1.
Higher derivatives
PRACTICE
P
2.
Higher derivatives
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Conclusion of applications of differentiation
PRACTICE
P
1.
Applications
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Multivariate functions
Basic notions
THEORY
T
1.
Functions of two variables
PRACTICE
P
2.
Functions of two variables
12
THEORY
T
3.
Functions and relations
PRACTICE
P
4.
Functions and relations
6
THEORY
T
5.
Visualizing bivariate functions
PRACTICE
P
6.
Visualizing bivariate functions
6
THEORY
T
7.
Multivariate functions
PRACTICE
P
8.
Multivariate functions
5
Partial derivatives
THEORY
T
1.
Partial derivatives of the first order
PRACTICE
P
2.
Partial derivatives of the first order
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THEORY
T
3.
Chain rules for partial differentiation
PRACTICE
P
4.
Chain rules for partial differentiation
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THEORY
T
5.
Higher partial derivatives
PRACTICE
P
6.
Higher partial derivatives
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THEORY
T
7.
Elasticity in two variables
PRACTICE
P
8.
Elasticity in two variables
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Conclusion of Multivariate functions
THEORY
T
1.
Conclusion
PRACTICE
P
2.
Applications
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Optimization
Extreme points
THEORY
T
1.
Stationary points
PRACTICE
P
2.
Stationary points
11
THEORY
T
3.
Minimum, maximum, and saddle point
PRACTICE
P
4.
Minimum, maximum, and saddle point
11
THEORY
T
5.
Criteria for extrema and saddle points
PRACTICE
P
6.
Criteria for extrema and saddle points
11
THEORY
T
7.
Convexity and concavity
PRACTICE
P
8.
Convexity and concavity
4
THEORY
T
9.
Criterion for a global extremum
THEORY
T
10.
Hessian convexity criterion
Conclusion of optimization
THEORY
T
1.
Conclusion
PRACTICE
P
2.
Applications
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