[Book Cover]

Calculus for Biological and Medical Sciences, 1/e

Claudia Neuhauser, University of Minnesota

Coming December, 1999 by Prentice Hall Engineering/Science/Mathematics

Copyright 2000, 860 pp.
Cloth
ISBN 0-13-085137-X


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Summary

For a two-semester course in Calculus for Life Sciences. The first calculus that adequately addresses the special needs of students in the biological sciences, this volume teaches calculus in the biology context without compromising the level of regular calculus. It is a essentially a calculus text, written so that a math professor without a biology background can teach from it successfully. The material is organized in the standard way and explains how the different concepts are logically related. Each new concept is typically introduced with a biological example; the concept is then developed without the biological context and then the concept is tied into additional biological examples. This allows students to first see why a certain concept is important, then lets them focus on how to use the concepts without getting distracted by applications, and then, once students feel more comfortable with the concepts, it revisits the biological applications to make sure that they can apply the concepts. The text features exceptionally detailed, step-by-step, worked-out examples and a variety of problems, including an unusually large number of word problems in a biological context.

Features


Calculus taught in the context of biology—But not in a watered down way, as in many of the brief calculus versions.

  • Enables math professors without a biology background to use the text successfully. Enables biology majors to acquire a firm foundation in calculus (in preparation for future studies in mathematics) and to develop skills in applying calculus concepts specifically to problems in the biological sciences.
Less emphasis on integration techniques and more coverage of differential equations and systems of differential equations—Compared to standard calculus books. The discussion includes both solution methods, and, to a larger extent, a qualitative discussion.
Examples worked out in step-by-step detail—Each subsection contains a number of examples which increase in difficulty. The examples are completely worked out with a lot of detail on how one step follows from the previous—unlike in regular calculus texts which often simply provide lengthy calculations without any explanations.
  • Better addresses the learning style of biology students who do better when they see the equations embedded in text where the equations are explained.
A variety of problems after each section—The problems are arranged so that they correspond to subsections and they start out as drill problems which follow the material covered in the respective subsection. These problems are then followed by increasingly harder, more conceptual problems. Finally, word problems tie the concepts into biology. The problems take into account that computers and graphing calculators can do much of the routine work.
  • Drill problems make students comfortable with the concepts, conceptual problems deepen their understanding of the concepts, and word problems taken from biology texts and research papers help them build analytical skills.


Table of Contents
    1. Preview and Review.

      A Brief History. Preliminaries. Elementary Functions. Graphing. Review Problems.

    2. Limits and Continuity.

      Limits. Continuity. Review Problems.

    3. Derivatives, Part I.

      Formal Definition of Derivatives. Basic Rules. Product Rule and Quotient Rule. Chain Rule. Derivatives of Trigonometric Functions. Exponential Function. Inverse Functions and Logarithms. Approximation and Local Linearity.

    4. Derivatives, Part II.

      Local Extrema and the Mean Value Theorem. Monotonicity and Concavity. Extrema, Inflection Points and Graphing. Optimization. L'Hospital's Rule. Numerical Methods (optional). Antiderivatives. Review Problems.

    5. Integration.

      The Definite Integral. The Fundamental Theorem of Calculus. Some Applications. Problems.

    6. Integration Techniques.

      The Substitution Rule. Integration by Parts. Improper Integrals. Numerical Integration. Tables of Integration.

    7. Differential Equations.

      Solving Differential Equations. Equilibria, Stability and Beyond. Systems of Autonomous Equations. Problems.

    8. Applications.

      Densities and Histograms. Average Values. Age-Structured Populations. Taylor Approximation. Problems.

    9. Linear Algebra and Analytic Geometry.

      Linear Systems. Matrices. Applications. Linear Maps, Eigenvectors and Eignvalues. Analytic Geometry.

    10. Multivariable Calculus.

      Two or More Independent Variables. Limits and Continuity. Partial Derivatives. Linearization. The Chain Rule. Derivatives. Vector Valued Functions.

    11. Systems of Differential Equations.

      Linear Systems—Theory. Linear Systems—Applications. Nonlinear Autonomous Systems—Theory. Nonlinear Systems—Applications.

    12. Probability and Statistics.

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