Modeling the Dynamics of Life

Modeling The Dynamics of Life: Calculus and Probability for Life Scientists

Frederick R. Adler, University of Utah

Return to Brooks/Cole Mathematics Catalog

CB Š 1998
ISBN/ISSN: 0-534-34816-5
Price: US $73.95
Price: UK Ł22.50
Price: Canada $104.95

This book is designed to help students understand the role mathematics plays in the life sciences, as well as to provide a thorough grounding in the mathematical language with which these developments are created and controlled. The book follows three themes throughout: growth, diffusion, and selection. Each theme is studied in turn with the three kinds of models that structure the course: discrete-time dynamical systems, differential equations, and stochastic processes. Techniques and insights build on each other throughout the book. Along the way, students learn and apply the standard material of a calculus course (differentiation, integration, and their applications).

The final section of the book teaches probability and statistics from the modeling perspective, using discrete-time dynamical systems and differential equations to describe simple stochastic processes.
The author saves time by skipping methods made obsolete by computers, thereby providing students with the greater challenge of learning more concepts and fewer techniques.
Concepts of modeling are covered, including describing a system, translating appropriate aspects into equations, and interpreting results in terms of the original problem. By understanding the concepts, students learn that the science is central and "solving" the equations is in some ways the least important step.
The book meshes with a general biology curriculum in a logical way. The dynamical themes are distilled from the material covered in standard introductory courses: genetics, cell biology, physiology, and ecology.

PART I: INTRODUCTION TO DISCRETE DYNAMICAL SYSTEMS

1.1 Biology and Dynamics

1.2 Updating Functions: Describing Growth

1.3 Units and Dimensions

1.4 Linear Functions and Their Graphs

1.5 Finding Solutions: Describing the Dynamics

1.6 Combining and Manipulating Functions

1.7 Solutions and Exponential Functions

1.8 Power Functions and Allometry

1.9 Oscillations and Trigonometry

1.10 Modeling and Cobwebbing

1.11 Equilibria

1.12 An Example of Nonlinear Dynamics

1.13 Excitable Systems I: The Heart

PART II: LIMITS AND DERIVATIVES

2.1 Introduction to Derivatives

2.2 Limits

2.3 Continuity

2.4 Computing derivatives

2.5 Derivatives of Sums, Powers and Polynomials

2.6 Derivatives of products and quotients

2.7 The Second Derivative

2.8 Exponentials and Logarithms

2.9 Derivatives of Trigonometric Functions

2.10 The Chain Rule

PART III: APPLICATIONS OF DERIVATIVES AND DYNAMICAL SYSTEMS

3.1 Stability and the Derivative

3.2 More Complex Dynamics

3.3 Maximization

3.4 Reasoning about functions

3.5 Limits at Infinity

3.6 Leading behavior and L'Hopital's Rule

3.7 Approximating functions

3.8 Newton's method

3.9 Panting and Deep Breathing

PART IV: DIFFERENTIAL EQUATIONS, INTEGRALS, AND THEIR APPLICATIONS

4.1 Differential Equations

4.2 Basic differential equations

4.3 The Antiderivative

4.4 Special functions and substitution

4.5 Integrals and sums

4.6 Definite and indefinite integrals

4.7 Applications of integrals

4.8 Improper integrals

PART V: ANALYSIS OF DIFFERENTIAL EQUATIONS

5.1 Autonomous Differential Equations

5.2 Stable and unstable equilibria

5.3 Solving autonomous equations

5.4 Two dimensional equations

5.5 The Phase-Plane

5.6 Solutions in the phase-plane

5.7 The dynamics of a neuron

PART VI: PROBABILITY THEORY AND DESCRIPTIVE STATISTICS

6.1 Probabilistic Models

6.2 Stochastic models of diffusion

6.3 Stochastic models of genetics

6.4 Probability Theory

6.5 Conditional Probability

6.6 Independence and Markov Chains

6.7 Displaying Probabilities

6.8 Random Variables

6.9 Descriptive Statistics

6.10 Descriptive statistics for spread

PART VII: PROBABILITY MODELS

7.1 Joint distributions

7.2 Covariance and Correlation

7.3 Sums and products of random variables

7.4 The Binomial Distribution

7.5 Applications of the Binomial Distribution

7.6 Exponential distributions

7.7 The Poisson Distribution

7.8 The Normal Distribution

7.9 Applying the Normal Approximation

PART VIII: INTRODUCTION TO STATISTICAL REASONING

8.1 Statistics: Estimating Parameters

8.2 Confidence limits

8.3 Estimating the Mean

8.4 Hypothesis Testing

8.5 Hypothesis Testing: Normal Theory

8.6 Comparing experiments

8.7 Regression

Author

Frederick R. Adler, University of Utah

800 pages
Dimensions: 8 1/2 x 11
Status: Available Now!! Modeling The Dynamics of Life: Calculus and Probability for Life Scientists

Return to Brooks/Cole Mathematics Catalog

Request a Review Copy

Brooks/Cole Home Page