Calculus With Applications for the Life Sciences was written for the one- or two-semester applied calculus course for life science students with a focus on incorporating interesting, relevant, and realistic applications. This text includes many citations from current data sources. It also offers many opportunities for use of technology, allowing for increased visualization and a better understanding of difficult concepts.

Table of Contents

R. Algebra Reference. Polynomials. Factoring. Rational Expressions. Equations. Inequalities. Exponents. Radicals. 1. Functions. Lines and Linear Functions. The Least Squares Line. Properties of Functions. Quadratic Functions; Translation and Reflection. Polynomial and Rational Functions. 2. Exponential, Logarithmic, and Trigonometric Functions. Exponential Functions. Logarithmic Functions. Applications: Growth and Decay. Trigonometric Functions. 3. The Derivative. Limits. Continuity. Rates of Change. Definition of the Derivative. Graphical Differentiation. 4. Calculating the Derivative. Techniques for Finding Derivatives. Derivatives of Products and Quotients. The Chain Rule. Derivatives of Exponential Functions. Derivatives of Logarithmic Functions. Derivatives of Trigonometric Functions. 5. Graphs and the Derivative. Increasing and Decreasing Functions. Relative Extrema. Higher Derivatives, Concavity, and the Second Derivative Test. Curve Sketching. 6. Applications of the Derivative. Absolute Extrema. Applications of Extrema. Implicit Differentiation. Related Rates. Differentials: Linear Approximation. 7. Integration. Antiderivatives. Substitution. Area and the Definite Integral. The Fundamental Theorem of Calculus. Integrals of Trigonometric Functions. The Area Between Two Curves. 8. Further Techniques and Applications of Integration. Numerical Integration. Integration by Parts. Volume and Average Value. Improper Integrals. 9. Multivariable Calculus. Functions of Several Variables. Partial Derivatives. Maxima and Minima. Total Differentials and Approximations. Double Integrals. 10. Linear Algebra. Solution of Linear Systems. Addition and Subtraction of Matrices. Multiplication of Matrices. Matrix Inverses. Eigenvalues and Eigenvectors. 11. Differential Equations. Solutions of Elementary and Separable Differential Equations. Linear First-Order Differential Equations. Euler's Method. Linear Systems of Differential Equations. Nonlinear Systems of Differential Equations. Applications of Differential Equations. 12. Probability. Sets. Introduction to Probability. Conditional Probability; Independent Events; Bayes' Theorem. Discrete Random Variables; Applications to Decision Making. 13. Probability and Calculus. Continuous Probability Models. Expected Value and Variance of Continuous Random Variables. Special Probability Density Functions.