Calculus: Mathematics and Modeling Updated Preliminary Edition by William Bauldry, Frank R. Giordano, Wade Ellis, Ed Lodi, Rich West

Drugs in the Body.
Patterns of Accumulation.
A Model for Natural Growth.
Modeling Motion.
Linear Functions as Models.
Solving Equations.

Analyzing a Discrete Function.
From Discrete to Continuous Functions.
Measuring Change: Irregular Data.
Rate of Change.
From Average Rate of Change to Instantaneous Rate of Change.
Rate of Change as a Function.

The Derivative at a Point and the Idea of a Limit.
The Derivative as a Function.
Rules, Rules, and More Rules.
Finding Features of a Continuous Function.
Optimization: Finding Global Extrema.
Implicit and Parametric Differentiation.
Partial Derivatives.

Rate and Distance.
Sums of Products.
Error Bounds for the Left and Right Endpoint Methods.
The Definite Integral.
Other Methods and Their Error Bounds.
Applications.
The Truth About Limits.@CHAPTER = The Fundamental Theorem of Calculus and its Uses.
Rate and Accumulation.
The Antiderivative Concept and The Fundamental Theorem of Calculus, Part I.
The Fundamental Theorem of Calculus, Part II.
Applications.
Using the Chain Rule in Finding Antiderivatives.
Techniques ofIntegration.
Further Techniques of Integration.

One Day in the Life of a Modeler.
Population Modeling.
Euler's Method.
Slope Fields.

Integration and Separation of Variables.
Linear Differential Equations.
Errors in the Model Construction.
Errors in Model Analysis: Euler's Method.
Advanced Numeric Techniques.
Existence and Uniqueness Theorems.
Uniqueness.
Existence.
The General Existence and Uniqueness Theorem.

Spirals of Change: You Are What You Eat.
Modeling.
Numerical Solutions: Iteration and Euler's Method.
Symbolic Solutions of Systems of Differential Equations.
Bungee Jumping.

Polynomial Appoximation of Functions.
Using Polynomial Approximations.
How Good Is a Good Polynomial Approximation?
Convergence of Series.
Power Series Solutions of Differential Equations.

Optimization with Two Variables.
Vectors, Lines, and Planes.
Tangent Vectors and Tangent Lines in Three Dimensions.
Tangent Planes.
The Gradient Search.

The Computer Algebra System Tutorial.
Troubleshooting: Things that Go Bump in the Night.