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Calculus for Life Sciences: A Modeling Approach

Calculus for Life Sciences: A Modeling Approach


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About the Book

With an emphasis on model building, this text explores the fundamental concepts of the derivative, integral, and multiple theorems in a context of biological processes. Students will find this hands-on, straight forward approach to calculus engaging and easy to learn. Each math topic is motivated by some matching idea in introductory biology. There is a strong emphasis on modeling real data throughout every chapter.

Table of Contents:
1. Data, Graphs, and Equations. Linear Relations. Parabolic or Quadratic Relations. Hyperbolic Relations. Tangents to Graphs. Summary. 2. Mathematical Models of Biological Processes. Mathematical Modeling. Experimental Data, Bacterial Growth. Steps Towards Building a Mathematical Model. Solution to the Dynamic Equation Pt+1-Pt=rPt. Experimental Data: Sunlight Depletion Below the Surface of a Lake or Ocean. Penicillin Loss. Quadratic Solution Equations. Summary. 3. Exponents and Logarithms. Doubling Time and Half-Life. Semilogarithm and Log-Log Coordinates. Summary. Some More Tangents. Solutions to the Dynamic Equation Pt+1-Pt=A-rPt. 4. Functions as Descriptions of Biological Processes. Environmental Sex Determination in Turtles. Functions. Linear and Polynomial Functions. New Functions from Old. Rescaling Data. Periodic Functions and Oscillations. 5. The Derivative. Average and Instantaneous Rates of Change. Gets Close To. Instantaneous Rates of Change for Three More Functions. Chemical Kinetics: Rates of Chemical Reactions. The Derivative and the Derivative of t^n. Derivatives of Polynomials, Sum and Constant Factor Rules. The Derivative Requires Continuity. The Generalized Power Rule. The Derivative of t^n for negative n and fractions. 6. Derivatives of Exponential and Logarithmic Functions. Exponential Functions. The number e. The Natural Logarithm. The Derivative Equation P(t)=k X P(t). Instantaneous Rate of Change of the Natural Logarithm Function. The Generalized Exponential and Logarithm Rules. Derivatives of Products and Quotients. 7. Derivatives of the Trigonometric Functions. Rates of Change of Trigonometric Functions. 8. Applications of Derivatives. Some Geometry of the Instantaneous Rate of Change. Some Traditional Max-Min Problems. Approximating Functions with Polynomials. Optimum Performance. Some Functions Without Instantaneous Rates of Change. Problems. Some Additional Commonly Used Notation. Lung Compliance. Problems from the Literature. Summary and Review. Derivative Formulas. Problems. 9. Difference Equations. Solutions of Difference Equations. Graphs of Solutions to Difference Equations and Graphs of Iteration Equations. Populations Without and With Environmental Limits. Equilibrium Points, Stable and Nonstable. Alternate Notation and Application of Difference Equations. Pharmacokinetics of Penicillin. 10. The Integral. Areas of Irregular Regions. Areas Under Some Algebraic Curves. A General Procedure for Computing Areas. Estimates That Are Better Than Upper and Lower Sums. The Integral. Properties of the Integral. Cardiac Output. 11. The Fundamental Theorem of Calculus. Continuity. The Fundamental Theorem of Calculus. Application of the Fundamental Theorem of Calculus. The Parallel Graph Theorem. The Second Form of the Fundamental Theorem of Calculus. Integral Formulas. Summary. 12. Differential Equations. Solution to y= Ky. Chemical Kinetics. Population Models. Mold Growth. Butyl Chloride. Interacting Populations. Equilibria Values for Differential Equations. Numerical Solutions to Differential Equations. Uniqueness of Solutions.


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Product Details
  • ISBN-13: 9780137794300
  • Publisher: Pearson Education (US)
  • Publisher Imprint: Pearson
  • Height: 254 mm
  • No of Pages: 900
  • Width: 203 mm
  • ISBN-10: 0137794304
  • Publisher Date: 28 Nov 2007
  • Binding: Hardback
  • Language: English
  • Sub Title: A Modeling Approach


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