| |
| |
| (Each Chapter ends with a Summary and Review.) | |
| |
| |
| |
| Functions in the Real World | |
| |
| |
| Functions are all around us | |
| |
| |
| Describing the behavior of functions | |
| |
| |
| Representing functions symbolically | |
| |
| |
| Connecting geometric and symbolic representations | |
| |
| |
| Mathematical models | |
| |
| |
| |
| Families of Functions | |
| |
| |
| Introduction | |
| |
| |
| Linear functions | |
| |
| |
| Linear functions and Data | |
| |
| |
| Exponential growth functions | |
| |
| |
| Exponential decay functions | |
| |
| |
| Logarithmic functions | |
| |
| |
| Power functions | |
| |
| |
| Comparing Rates of Growth and Decay | |
| |
| |
| Inverse functions | |
| |
| |
| |
| Fitting Functions to Data | |
| |
| |
| Introduction to Data Analysis | |
| |
| |
| Linear regression analysis | |
| |
| |
| Fitting nonlinear functions to data | |
| |
| |
| How to fit exponential and logarithmic functions to data | |
| |
| |
| How to fit power functions to data | |
| |
| |
| How good is the fit? Linear models with several variables | |
| |
| |
| |
| Extended Families of Functions | |
| |
| |
| Introduction to polynomial functions | |
| |
| |
| The behavior of polynomial functions | |
| |
| |
| Modeling with polynomial functions | |
| |
| |
| The roots of polynomial equations: Real or complex? Finding polynomial patterns | |
| |
| |
| Building new functions from old: Operations on Functions | |
| |
| |
| Building new functions from old: Shifting, stretching, and shrinking | |
| |
| |
| Using shifting and stretching to analyze data | |
| |
| |
| The logistic and surge functions | |
| |
| |
| |
| Modeling with Difference Equations | |
| |
| |
| Eliminating drugs from the body | |
| |
| |
| Modeling with difference equations | |
| |
| |
| The logistic or inhibited growth model | |
| |
| |
| Newton's Laws of Cooling and Heating | |
| |
| |
| Geometric sequences and their sums | |
| |
| |
| |
| Introduction to Trigonometry | |
| |
| |
| The tangent of an angle | |
| |
| |
| The sine and cosine of an angle | |
| |
| |
| The sine, cosine and tangent in general | |
| |
| |
| Relationships among trigonometric functions | |
| |
| |
| The law of sines and the law of cosnes | |
| |
| |
| |
| Modeling Periodic Behavior | |
| |
| |
| Introduction to the sine and cosine functions | |
| |
| |
| Modeling periodic behavior with sine and cosine | |
| |
| |
| Solving equations with sine and cosine | |
| |
| |
| The inverse functions | |
| |
| |
| The tangent function | |
| |
| |
| |
| More About the Trigonometric Functions | |
| |
| |
| Relationships among trigonometric functions | |
| |
| |
| Approximating sine and cosine with polynomials | |
| |
| |
| Properties of complex numbers | |
| |
| |
| The road to chaos | |
| |
| |
| |
| Geometric Models | |
| |
| |
| Introduction to coordinate systems | |
| |
| |
| Analytic geometry | |
| |
| |
| Conic sections | |
| |
| |
| The Ellipse | |
| |
| |
| Conic sections | |
| |
| |
| The Hyperbola and the Parabola | |
| |
| |
| Parametric curves | |
| |
| |
| The polar coordinate system | |
| |
| |
| Families of curves in polar coordinates | |
| |
| |
| |
| Matrix Algebra and Its Applications | |
| |
| |
| Geometric vectors | |
| |
| |
| Linear models | |
| |
| |
| Scalar products | |
| |
| |
| Matrix multiplication | |
| |
| |
| Gaussian elimination | |
| |
| |
| |
| Probability Models (online only) | |
| |
| |
| Introduction to probability models | |
| |
| |
| Binomial probability and the binomial formula | |
| |
| |
| Using probability to investigate polynomials | |
| |
| |
| Geometric probability | |
| |
| |
| Estimating areas of plane regions | |
| |
| |
| The normal distribution function | |
| |
| |
| Waiting time at a red light | |
| |
| |
| Random patterns in chaos | |
| |
| |
| |
| More About Difference Equations (online only) | |
| |
| |
| Solutions of difference equations | |
| |
| |
| Constructing solutions of first order difference equations | |
| |
| |
| Modeling with first order, non-homogeneous difference equations | |
| |
| |
| Financing a car or a home | |
| |
| |
| Solving the Fibonacci and other second order difference equations | |
| |
| |
| The predator-prey model | |
| |
| |
| Competing species | |
| |
| |
| Iteration and chaos | |