
Introduction to DiscreteTime Dynamical Systems 


1  (117) 


2  (4) 

Updating Functions: Describing Growth 


6  (8) 

Units and Dimensions of Measurements and Functions 


14  (8) 

Linear Functions and Their Graphs 


22  (10) 

Finding Solutions: Describing the Dynamics 


32  (7) 

Combining and Manipulating Functions 


39  (10) 

Expressing Solutions with Exponential Functions 


49  (10) 

Power Functions and Allometry 


59  (10) 

Oscillations and Trigonometry 


69  (9) 

Modeling and Graphical Analysis of Updating Functions 


78  (8) 


86  (9) 

An Example of Nonlinear Dynamics 


95  (11) 

Excitable Systems: The Heart 


106  (12) 


118  (94) 

Introduction to Derivatives 


119  (10) 


129  (9) 


138  (10) 

Computing Derivatives: Linear and Quadratic Functions 


148  (8) 

Derivatives of Sums, Powers, and Polynomials 


156  (12) 

Derivatives of Products and Quotients 


168  (8) 

The Second Derivative, Curvature, and Acceleration 


176  (8) 

Derivatives of Exponential and Logarithmic Functions 


184  (6) 

Derivatives of Trigonometric Functions 


190  (9) 


199  (13) 

Applications of Derivatives and Dynamical Systems 


212  (98) 

Stability and the Derivative 


213  (11) 


224  (13) 


237  (11) 

Reasoning About Functions 


248  (9) 


257  (11) 

Leading Behavior and L'Hopital's Rule 


268  (12) 

Approximating Functions with lines and Polynomials 


280  (9) 


289  (10) 

Panting and Deep Breathing 


299  (11) 

Differential Equations, Integrals, and Their Applications 


310  (76) 


311  (11) 

Basic Differential Equations 


322  (8) 

Solving PureTime Differential Equations 


330  (10) 

Integration of Special Functions and Integration by Substitution 


340  (8) 


348  (8) 

Definite and Indefinite Integrals 


356  (10) 

Applications of Integrals 


366  (8) 


374  (12) 

Analysis of Differential Equations 


386  (61) 

Equilibria and Display of Autonomous Differential Equations 


387  (8) 

Stable and Unstable Equilibria 


395  (7) 

Solving Autonomous Differential Equations 


402  (7) 

TwoDimensional Differential Equations 


409  (8) 


417  (8) 

Solutions in the Phase Plane 


425  (10) 


435  (12) 

Probability Theory and Descriptive Statistics 


447  (82) 

Introduction to Probabilistic Models 


448  (6) 

Stochastic Models of Diffusion 


454  (8) 

Stochastic Models of Genetics 


462  (6) 


468  (6) 


474  (6) 

Independence and Markov Chains 


480  (6) 


486  (11) 


497  (9) 


506  (9) 

Descriptive Statistics for Spread 


515  (14) 


529  (89) 


530  (8) 

Covariance and Correlation 


538  (9) 

Sums and Products of Random Variables 


547  (10) 

The Binomial Distribution 


557  (10) 

Applications of the Binomial Distribution 


567  (7) 

Waiting Times: Geometric and Exponential Distributions 


574  (10) 


584  (8) 


592  (10) 

Applying the Normal Approximation 


602  (16) 

Introduction to Statistical Reasoning 


618  (67) 

Statistics: Estimating Parameters 


619  (8) 


627  (9) 


636  (11) 


647  (7) 

Hypothesis Testing: Normal Theory 


654  (9) 

Comparing Experiments: Unpaired data 


663  (8) 


671  (14) 
Answers 

685  (92) 
Index 

777  