Mathematics

For undergraduate courses in math modeling, and biology calculus courses in departments of math and life sciences.

Designed for students who understand the simple basics of calculus, this text focuses on the differential equations and related subjects that are commonly used today by working life scientists. It emphasizes both the mathematics and how the mathematics is employed in order to introduce some potentially useful tools and modes of thought to future experimental biologists.

• Reprints of recent research summary articles from Science and Nature —Illustrates almost all of the mathematics.

  • Demonstrates to students how the mathematics in the text is used by working biologists, so that biology majors are motivated to learn mathematics. Ex.___

• Commentary for each reprinted article.

  • Summarizes the underlying biological issues so neither students nor instructors need prior knowledge, and shows where and how the mathematics is used. Ex.___

• Exclusive focus on single and multivariable aspects of calculus—With specific emphasis on the applications of differential equations which are used in the life sciences.

  • Provides students with the mathematics that is commonly used by biologists and life scientists—as opposed to the mathematics of physicists and engineers commonly found in other texts. Ex.___

• Homework level problems in each lecture/chapter.

  • Reinforces the lecture material that is covered in class. Ex.___

• Review problems with accompanying answers.

  • Gives students the opportunity to practice applying, and test their knowledge, of what they have learned. Ex.___

• End-of-chapter summaries of the important issues.

  • Helps students to focus on the key points in each lesson.

 1. Introduction.


 2. Exponential Growth with Appendix on Taylor's Theorem.


 3. Introduction to Differential Equations.


 4. Stability in a One Component System.


 5. Systems of First Order Differential Equations.


 6. Phase Plane Analysis.


 7. Introduction to Vectors.


 8. Equilibrium in Two Component, Linear Systems.


 9. Stability in Non-Linear Systems.


10. Non-linear Stability Again.


11. Matrix Notation.


12. Remarks about Australian Predators.


13. Introduction to Advection.


14. Diffusion Equations.


15. Two Key Properties of the Advection and Diffusion Equations.


16. The No Trawling Zone.


17. Separation of Variables.


18. The Diffusion Equation and Pattern Formation.


19. Stability Criteria.


20. Summary of Advection and Diffusion.


21. Traveling Waves.


22. Traveling Wave Velocities.


23. Periodic Solutions.


24. Fast and Slow.


25. Estimating Elapsed Time.


26. Switches.


27. Testing for Periodicity.


28. Causes of Chaos.

Modeling  (Mathematics)
Differential Equations  [ODES FOR BIOLOGY]   (Mathematics)

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