Chapter 1: Functions

- Introduction to functions
- - The notion of function
- - Arithmetic perations for functions
- - The range of a function
- - Functions and graphs
- - The notion of limit
- - Continuity
- - Arithmetic operations for continuity
- Lines and linear functions
- - Linear functions with a single unknown
- - The general solution of a linear equation
- - Systems of equations
- - The equation of a line
- - Solving systems of equations by addition
- - Equations and lines
- Quadratic functions
- - Completing the square
- - The quadratic formula
- - Factorization
- - Solving equations with factorization
- Polynomials
- - The notion of polynomial
- - Calculating with polynomials
- Rational functions
- - The notion of a rational function
- Power functions
- - Power functions
- - Equations of power functions
- Applications
- - Applications of functions

Chapter 2: Operations for functions

- Inverse functions
- - The notion of inverse function
- - Injective functions
- - Characterizing invertible functions
- Exponential and logarithmic functions
- - Exponential functions
- - Properties of exponential functions
- - Growth of an exponential function
- - Logarithmic functions
- - Properties of logarithms
- - Growth of a logarithmic function
- New functions from old
- - Translating functions
- - Scaling functions
- - Symmetry of functions
- - Composing functions
- Applications
- - Applications of operations for functions

Chapter 3: Introduction to differentiation

- Definition of differentiation
- - The notion of difference quotient
- - The notion of derivative
- Calculating derivatives
- - Derivatives of polynomials and power functions
- Derivatives of exponential functions and logarithms
- - The natural exponential function and logarithm
- - Rules of calculation for exponential functions and logarithms
- - Derivatives of exponential functions and logarithms
- Applications
- - Applications

Chapter 4: Rules of differentiation

- Rules of computation for the derivative
- - The sum rule for differentiation
- - The product rule for differentiation
- - The quotient rule for differentiation
- - The chain rule for differentiation
- - Exponential functions and logarithmic derivatives revised
- - The derivative of an inverse function
- Applications of derivatives
- - Tangent lines revisited
- - Approximation
- - Elasticity

Chapter 5: Applications of differentiation

- Analysis of functions
- - Monotonicity
- - Local minima and maxima
- - Analysis of functions
- Higher derivatives
- - Higher derivatives
- Applications
- - Applications of differentiation

Chapter 6: Multivariate functions

- Basic notions
- - Functions of two variables
- - Functions and relations
- - Visualizing bivariate functions
- - Multivariate functions
- Partial derivatives
- - Partial derivatives of the first order
- - Chain rules for partial differentiation
- - Higher partial derivatives
- - Elasticity in two variables
- Applications
- - Applications of multivariate functions

Chapter 7: Optimization

- Extreme points
- - Stationary points
- - Minimum, maximum and saddle point
- - Criteria for extrema and saddle points
- - Convexity and concavity
- - Criterion for a global extremum
- - Hessian convexity criterion
- Applications
- - Applications of optimization

Chapter 8: Constrained Optimization

- The Lagrange multiplier method
- - Lagrange multipliers
- - Lagrange multiplier interpretation
- - Lagrange's theorem
- Sufficient conditions for optimality
- - Convexity conditions for global optimality
- - Second-order conditions for local optimality