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Although we present topics numerically, graphically, analytically,
and literally, we are not just another reformed textbook. Our goal
is to present calculus as a coherent body of knowledge and to do so with
as much rigor as is possible for students in a first course. However,
great care has been taken to present the calculus content in a way that
incorporates what is known about how students best learn mathematics.
** ***Calculus: A Modern Approach* begins with the differentiation
of polynomials, because the derivative of a polynomial can be defined
algebraically. We then introduce the limit as a means of extending the theory
of the derivative to a broader class of functions. The Mean Value
Theorem is introduced and used to complete the elementary theory of the
derivative, although the Mean Value Theorem is not proven at this time.

**Once the theory of the derivative is completed, the exponential, logarithmic
and trigonometric functions are defined and studied. Much of this study
is motivated and developed using the fact that the elementary functions
are either the solutions or inverses of the solutions to linear differential
equations.**

**Chapter 4 introduces integration with a modern definition of the Riemann
integral. Antiderivatives are intimately connected to the Fundamental
theorem.
Applications of the integral, differential equations and modeling, Taylor's series, and
Fourier series then
follow. <Back to home page>**