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.
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Calculus for Life Sciences-Mathematics
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.
Calculus taught in the context of biologyBut
not in a watered down way, as in many of the brief calculus versions.
Less emphasis on integration techniques and more coverage
of differential equations and systems of differential equationsCompared
to standard calculus books. The discussion includes both solution
methods, and, to a larger extent, a qualitative discussion.
- 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.
Examples worked out in step-by-step detailEach
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 previousunlike in regular calculus
texts which often simply provide lengthy calculations without any
A variety of problems after each sectionThe
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
- Better addresses the learning style of biology students
who do better when they see the equations embedded in text where the
equations are explained.
- 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.
1. Preview and Review.
A Brief History. Preliminaries. Elementary Functions. Graphing.
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.
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.
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
11. Systems of Differential Equations.
Linear SystemsTheory. Linear SystemsApplications.
Nonlinear Autonomous SystemsTheory. Nonlinear SystemsApplications.
12. Probability and Statistics.