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Calculus for the Life Sciences

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Table of Contents

R. Algebra Reference R.1 Polynomials R.2 Factoring R.3 Rational Expressions R.4 Equations R.5 Inequalities R.6 Exponents R.7 Radicals 1. Functions 1.1 Lines and Linear Functions 1.2 The Least Squares Line 1.3 Properties of Functions 1.4 Quadratic Functions; Translation and Reflection 1.5 Polynomial and Rational Functions Chapter Review Extended Application: Using Extrapolation to Predict Life Expectancy 2. Exponential, Logarithmic, and Trigonometric Functions 2.1 Exponential Functions 2.2 Logarithmic Functions 2.3 Applications: Growth and Decay 2.4 Trigonometric Functions Chapter Review Extended Application: Power Functions 3. The Derivative 3.1 Limits 3.2 Continuity 3.3 Rates of Change 3.4 Definition of the Derivative 3.5 Graphical Differentiation Chapter Review Extended Application: A Model For Drugs Administered Intravenously 4. Calculating the Derivative 4.1 Techniques for Finding Derivatives 4.2 Derivatives of Products and Quotients 4.3 The Chain Rule 4.4 Derivatives of Exponential Functions 4.5 Derivatives of Logarithmic Functions 4.6 Derivatives of Trigonometric Functions Chapter Review Extended Application: Managing Renewable Resources 5. Graphs and the Derivative 5.1 Increasing and Decreasing Functions 5.2 Relative Extrema 5.3 Higher Derivatives, Concavity, and the Second Derivative Test 5.4 Curve Sketching Chapter Review Extended Application: A Drug Concentration Model for Orally Administered Medications 6. Applications of the Derivative 6.1 Absolute Extrema 6.2 Applications of Extrema 6.3 Implicit Differentiation 6.4 Related Rates 6.5 Differentials: Linear Approximation Chapter Review Extended Application: A Total Cost Model for a Training Program 7. Integration 7.1 Antiderivatives 7.2 Substitution 7.3 Area and the Definite Integral 7.4 The Fundamental Theorem of Calculus 7.5 The Area Between Two Curves Chapter Review Extended Application: Estimating Depletion Dates for Minerals 8. Further Techniques and Applications of Integration 8.1 Numerical Integration 8.2 Integration by Parts 8.3 Volume and Average Value 8.4 Improper Integrals Chapter Review Extended Application: Flow Systems 9. Multivariable Calculus 9.1 Functions of Several Variables 9.2 Partial Derivatives 9.3 Maxima and Minima 9.4 Total Differentials and Approximations 9.5 Double Integrals Chapter Review Extended Application: Optimization for a Predator 10. Matrices 10.1 Solution of Linear Systems 10.2 Addition and Subtraction of Matrices 10.3 Multiplication of Matrices 10.4 Matrix Inverses 10.5 Eigenvalues and Eigenvectors Chapter Review Extended Application: Contagion 11. Differential Equations 11.1 Solutions of Elementary and Separable Differential Equations 11.2 Linear First-Order Differential Equations 11.3 Euler's Method 11.4 Linear Systems of Differential Equations 11.5 Non-Linear Systems of Differential Equations 11.6 Applications of Differential Equations Chapter Review Extended Application: Pollution of the Great Lakes 12. Probability 12.1 Sets 12.2 Introduction to Probability 12.3 Conditional Probability; Independent Events; Bayes' Theorem 12.4 Discrete Random Variables; Applications to Decision Making Chapter Review Extended Application: Medical Diagnosis 13. Probability and Calculus 13.1 Continuous Probability Models 13.2 Expected Value and Variance of Continuous Random Variables. 13.3 Special Probability Density Functions Chapter Review Extended Application: Exponential Waiting Times 14. Discrete Dynamical Systems 14.1 Sequences 14.2 Equilibrium Points 14.3 Determining Stability Chapter Review Extended Application: Mathematical Modeling in a Dynamic World Special Topics (available online) Sequences and Series Geometric Sequences Annuities: An Application of Sequences Taylor Polynomials Infinite Series Taylor Series Newton's Method L'Hopital's Rule Markov Chains

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