|Calculus with Applications for the Life Sciences|
Raymond N. Greenwell, Hofstra University
|Table of Content|
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.
Applications: Growth and Decay.
3. The Derivative.
Rates of Change.
Definition of the Derivative.
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.
Higher Derivatives, Concavity, and the Second Derivative Test.
6. Applications of the Derivative.
Applications of Extrema.
Differentials: Linear Approximation.
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.
Integration by Parts.
Volume and Average Value.
9. Multivariable Calculus.
Functions of Several Variables.
Maxima and Minima.
Total Differentials and Approximations.
10. Linear Algebra.
Solution of Linear Systems.
Addition and Subtraction of Matrices.
Multiplication of Matrices.
Eigenvalues and Eigenvectors.
11. Differential Equations.
Solutions of Elementary and Separable Differential Equations.
Linear First-Order Differential Equations.
Linear Systems of Differential Equations.
Nonlinear Systems of Differential Equations.
Applications of Differential Equations.
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.