Applied Calculus

Stefan Waner and Steven R. Costenoble both received their Ph.D.s from the University of Chicago, having studied several years apart with the same advisor, J. Peter May. Their paths merged when Dr. Waner joined Dr. Costenoble at Hofstra University in 1987. Since then, they have coauthored 18 research papers as well as a research-level monograph in algebraic topology. By the early 1990s, they had become dissatisfied with many of the finite mathematics and applied calculus textbooks available. They wanted textbook choices that were more readable and relevant to students' interests -- texts that contained engaging examples and exercises and texts that reflected the interactive approaches and techniques they found worked well with their own students. It, therefore, seemed natural to extend their research collaboration to a joint textbook writing project that expressed these ideals. To this day, they continue to work together on textbook projects, research in algebraic topology and in their teaching. Stefan Waner and Steven R. Costenoble both received their Ph.D.s from the University of Chicago, having studied several years apart with the same advisor, J. Peter May. Their paths merged when Dr. Waner joined Dr. Costenoble at Hofstra University in 1987. Since then, they have coauthored 18 research papers as well as a research-level monograph in algebraic topology. By the early 1990s, they had become dissatisfied with many of the finite mathematics and applied calculus textbooks available. They wanted textbook choices that were more readable and relevant to students' interests -- texts that contained engaging examples and exercises and texts that reflected the interactive approaches and techniques they found worked well with their own students. It, therefore, seemed natural to extend their research collaboration to a joint textbook writing project that expressed these ideals. To this day, they continue to work together on textbook projects, research in algebraic topology and in their teaching.

0. PRECALCULUS REVIEW.
Real Numbers. Exponents and Radicals. Using Exponent Identities Multiplying and Factoring Algebraic Equations. Rational Expressions. Solving Polynomial Equations. Solving Miscellaneous Equations. The Coordinate Plane. Logarithms.
1. FUNCTIONS AND APPLICATIONS.
Functions from the Numerical, Algebraic, and Graphical Viewpoints. Functions and Models. Linear Functions and Models. Linear Regression.
2. NONLINEAR FUNCTIONS AND MODELS.
Quadratic Functions and Models. Exponential Functions and Models. The Number e and Exponential Growth and Decay. Logistic and Logarithmic Functions and Models..
3. INTRODUCTION TO THE DERIVATIVE.
Limits: Numerical and GraphicalViewpoints. Limits and Continuity. Limits: Algebraic Viewpoint. Average Rate of Change. Derivatives: Numerical and Graphical Viewpoints. Derivatives: Algebraic Viewpoint.
4. TECHNIQUES OF DIFFERENTIATION.
Derivatives of Powers, Sums, and Constant Multiples. A First Application: Marginal Analysis. The Product and Quotient Rules. The Chain Rule. Derivatives of Logarithmic and Exponential Functions. Implicit Differentiation.
5. APPLICATIONS OF THE DERIVATIVE.
Maxima and Minima. Applications of Maxima and Minima. Higher Order Derivatives: Acceleration and Concavity. Analyzing Graphs. Related Rates. Elasticity.
6. THE INTEGRAL.
The Indefinite Integral. Substitution. The Definite Integral. The Fundamental Theorem of Calculus.
7. FURTHER INTEGRATION TECHNIQUES AND APPLICATIONS OF THE INTEGRAL.
Integration by Parts. Area Between Two Curves. Averages and Moving Averages. Applications to Business and Economics: Consumers' and Producers' Surplus and Continuous Income Streams. Improper Integrals and Applications. Differential Equations and Applications.
8. FUNCTIONS OF SEVERAL VARIABLES.
Functions of Several Variables from the Numerical, Algebraic, and Graphical Viewpoints. Partial Derivatives. Maxima and Minima. Constrained Maxima and Minima and Applications. Double Integrals and Applications.
9. TRIGONOMETRIC MODELS.
Trigonometric Functions, Models, and Regression. Derivatives of Trigonometric Functions and Applications. Integrals of Trigonometric Functions and Applications.