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Full Description
Calculus for Biology and Medicine, Third Edition, addresses the needs of readers 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 readers with the knowledge and skills necessary to analyze and interpret mathematical models of a diverse array of phenomena in the living world. This book is suitable for a wide audience, as all examples were chosen so that no formal training in biology is needed.
Contents
1. Preview and Review1.1 Preliminaries1.2 Elementary Functions1.3 Graphing2. Discrete Time Models, Sequences, and Difference Equations2.1 Exponential Growth and Decay2.2 Sequences2.3 More Population Models3. Limits and Continuity3.1 Limits3.2 Continuity3.3 Limits at Infinity3.4 The Sandwich Theorem and Some Trigonometric Limits3.5 Properties of Continuous Functions3.6 A Formal Definition of Limits (Optional)4. Differentiation4.1 Formal Definition of the Derivative4.2 The Power Rule, the Basic Rules of Differentiation, and the Derivatives of Polynomials4.3 The Product and Quotient Rules, and the Derivatives of Rational and Power Functions4.4 The Chain Rule and Higher Derivatives4.5 Derivatives of Trigonometric Functions4.6 Derivatives of Exponential Functions4.7 Derivatives of Inverse Functions, Logarithmic Functions, and the Inverse Tangent Function4.8 Linear Approximation and Error Propagation5. Applications of Differentiation5.1 Extrema and the Mean-Value Theorem5.2 Monotonicity and Concavity5.3 Extrema, Inflection Points, and Graphing5.4 Optimization5.5 L'Hopital's Rule5.6 Difference Equations: Stability (Optional)5.7 Numerical Methods: The Newton-Raphson Method (Optional)5.8 Antiderivatives6. Integration6.1 The Definite Integral6.2 The Fundamental Theorem of Calculus6.3 Applications of Integration7. Integration Techniques and Computational Methods7.1 The Substitution Rule7.2 Integration by Parts and Practicing Integration7.3 Rational Functions and Partial Fractions7.4 Improper Integrals7.5 Numerical Integration7.6 The Taylor Approximation7.7 Tables of Integrals (Optional)8. Differential Equations8.1 Solving Differential Equations8.2 Equilibria and Their Stability8.3 Systems of Autonomous Equations (Optional)9. Linear Algebra and Analytic Geometry9.1 Linear Systems9.2 Matrices9.3 Linear Maps, Eigenvectors, and Eigenvalues9.4 Analytic Geometry10. Multivariable Calculus10.1 Functions of Two or More Independent Variables10.2 Limits and Continuity10.3 Partial Derivatives10.4 Tangent Planes, Differentiability, and Linearization10.5 More about Derivatives (Optional)10.6 Applications (Optional)10.7 Systems of Difference Equations (Optional)11. Systems of Differential Equations11.1 Linear Systems: Theory11.2 Linear Systems: Applications11.3 Nonlinear Autonomous Systems: Theory11.4 Nonlinear Systems: Applications12. Probability and Statistics12.1 Counting12.2 What is Probability?12.3 Conditional Probability and Independence12.4 Discrete Random Variables and Discrete Distributions12.5 Continuous Distributions12.6 Limit Theorems12.7 Statistical Tools
