Calculus For Biology and Medicine

For a two-semester or three-semester course in Calculus for Life Sciences. Calculus for Biology and Medicine, Third Edition, addresses the needs of students in the biological sciences by showing them how to use calculus to analyze natural phenomena-without compromising the rigorous presentation of the mathematics. While the table of contents aligns well with a traditional calculus text, all the concepts are presented through biological and medical applications. The text provides students with the knowledge and skills necessary to analyze and interpret mathematical models of a diverse array of phenomena in the living world. Since this text is written for college freshmen, the examples were chosen so that no formal training in biology is needed.1. Preview and Review 1.1 Preliminaries 1.2 Elementary Functions 1.3 Graphing 2. Discrete Time Models, Sequences, and Difference Equations 2.1 Exponential Growth and Decay 2.2 Sequences 2.3 More Population Models 3. Limits and Continuity 3.1 Limits 3.2 Continuity 3.3 Limits at Infinity 3.4 The Sandwich Theorem and Some Trigonometric Limits 3.5 Properties of Continuous Functions 3.6 A Formal Definition of Limits (Optional) 4. Differentiation 4.1 Formal Definition of the Derivative 4.2 The Power Rule, the Basic Rules of Differentiation, and the Derivatives of Polynomials 4.3 The Product and Quotient Rules, and the Derivatives of Rational and Power Functions 4.4 The Chain Rule and Higher Derivatives 4.5 Derivatives of Trigonometric Functions 4.6 Derivatives of Exponential Functions 4.7 Derivatives of Inverse Functions, Logarithmic Functions, and the Inverse Tangent Function 4.8 Linear Approximation and Error Propagation 5. Applications of Differentiation 5.1 Extrema and the Mean-Value Theorem 5.2 Monotonicity and Concavity 5.3 Extrema, Inflection Points, and Graphing 5.4 Optimization 5.5 L'Hopital's Rule 5.6 Difference Equations: Stability (Optional) 5.7 Numerical Methods: The Newton-Raphson Method (Optional) 5.8 Antiderivatives 6. Integration 6.1 The Definite Integral 6.2 The Fundamental Theorem of Calculus 6.3 Applications of Integration 7. Integration Techniques and Computational Methods 7.1 The Substitution Rule 7.2 Integration by Parts and Practicing Integration 7.3 Rational Functions and Partial Fractions 7.4 Improper Integrals 7.5 Numerical Integration 7.6 The Taylor Approximation 7.7 Tables of Integrals (Optional) 8. Differential Equations 8.1 Solving Differential Equations 8.2 Equilibria and Their Stability 8.3 Systems of Autonomous Equations (Optional) 9. Linear Algebra and Analytic Geometry 9.1 Linear Systems 9.2 Matrices 9.3 Linear Maps, Eigenvectors, and Eigenvalues 9.4 Analytic Geometry 10. Multivariable Calculus 10.1 Functions of Two or More Independent Variables 10.2 Limits and Continuity 10.3 Partial Derivatives 10.4 Tangent Planes, Differentiability, and Linearization 10.5 More about Derivatives (Optional) 10.6 Applications (Optional) 10.7 Systems of Difference Equations (Optional) 11. Systems of Differential Equations 11.1 Linear Systems: Theory 11.2 Linear Systems: Applications 11.3 Nonlinear Autonomous Systems: Theory 11.4 Nonlinear Systems: Applications