Modern Calculus One

Throughout Modern calculus one you will find examples and exercises that present classical ideas and techniques as well as modern applications and methods. Derivations and explanations are based on years of classroom experience onthe partof long-time calculus professors, striving for a balance of clarity and rigor that has proven successful with their students. Motivational applications cover important topics in probability, biology, ecology, business, and economics, as well as areasof physics, chemistry, engineering, and computer science. Student Projects in each chapter give students opportunities to explore interesting sidelights in pure and applied mathematics, from determining a safe distance between the grandstand and the track at a Formula One racetrack, to calculating the center of mass of the Grand Canyon Skywalk or the terminal speed of a skydiver. Chapter Opening Applications pose problems that are solved later in the chapter, using the ideas covered in that chapter. Problems include the hydraulic force against the Hoover Dam, and the comparison of relative intensity of twoearthquakes. Definitions, Rules, and Theorems are highlighted throughout the text, including over 60 Proofs of theorems.Modern calculus one is designed to accommodate both Early and Late Transcendental approaches to calculus. Exponential and logarithmic functions are introduced informally in Chapter 1 and presented in more rigorous termsin Chapter 6.Differentiation and integration of these functions is covered in Chapters 3-5 for instructors who want to include them with other types of functions. These discussions, however, are in separate sections that can be skipped for instructors who preferto wait until the integral definitions are given before teaching the calculus derivations of exponentials and logarithms.