Title Details

Sebastian J. Schreiber received his B.A. in mathematics from Boston university in 1989 and his Ph.D. in mathematics from the University of California, Berkeley in 1995. he is currently Professor of Ecology and Evolution at the University of California, Davis. Previously, he was an Associate Professor of Mathematics at the College of William and Mary, where he was the 2005 recipient of the Simon Prize for Excellence in the Teaching of Mathematics, and Western Washington University. Professor Schreiber's research on the application of stochastic processes and nonlinear dynamics to ecology, evolution, and epidemiology has been supported by grants from the National Science Foundation and the National Oceanic and Atmospheric Administration. He is the author of over 60 scientific papers in peer-reviewed mathematics and biology journals.

Preview of Modeling and Calculus

1 Modeling with Functions

1.1 Real Numbers and Functions

1.2 Data Fitting with Linear and Periodic Functions

1.3 Power Functions and Scaling Laws

1.4 Exponential Growth

1.5 Function Building

1.6 Inverse Functions and Logarithms

1.7 Sequences and Difference Equations

2 Limits and Derivatives

2.1 Rates of Change and Tangent Lines

2.2 Limits

2.3 Limit Laws and Continuity

2.4 Asymptotes and Infinity

2.5 Sequential Limits

2.6 Derivative at a Point

2.7 Derivatives as Functions

Group Projects

3 Derivative Rules and Tools

3.1 Derivatives of Polynomials and Exponentials

3.2 Product and Quotient Rules

3.3 Chain Rule and Implicit Differentiation

3.4 Derivatives of Trigonometric Functions

3.5 Linear Approximation

3.6 Higher Derivatives and Approximations

3.7 l’Hoˆ pital’s Rule

Group Projects

4 Applications of Differentiation

4.1 Graphing Using Calculus

4.2 Getting Extreme

4.3 Optimization in Biology

4.4 Decisions and Optimization

4.5 Linearization and Difference Equations

Group Projects

5 Integration

5.1 Antiderivatives

5.2 Accumulated Change and Area under a Curve

5.3 The Definite Integral

5.4 The Fundamental Theorem of Calculus

5.5 Substitution

5.6 Integration by Parts and Partial Fractions

5.7 Numerical Integration

5.8 Applications of Integration

Group Projects

6 Differential Equations

6.1 A Modeling Introduction to Differential Equations

6.2 Solutions and Separable Equations

6.3 Linear Models in Biology

6.4 Slope Fields and Euler’s Method

6.5 Phase Lines and Classifying Equilibria

6.6 Bifurcations

Group Projects

7 Probabilistic Applications of Integration

7.1 Histograms, PDFs, and CDFs

7.2 Improper Integrals

7.3 Mean and Variance

7.4 Bell-Shaped Distributions

7.5 Life Tables

Group Projects

8 Multivariable Extensions

8.1 Multivariate Modeling

8.2 Matrices and Vectors

8.3 Eigenvalues and Eigenvectors

8.4 Systems of Linear Differential Equations

8.5 Nonlinear Systems

Group Projects