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>