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Written by acclaimed author and mathematician George Simmons, this revision is designed for the calculus course offered in two and four year colleges and universities. It takes an intuitive approach to calculus and focuses on the application of methods to real-world problems. Throughout the text, calculus is treated as a problem solving science of immense capability.
Instructor's Manual to Accompany Calculus with Analytic Geometry is an instructor's manual on calculus with analytic geometry. It contains answers to even-numbered exercises and solutions of selected even- and odd-numbered exercises. Comments on selected exercises are included. Comprised of 18 chapters, this book first presents answers and solutions to exercises relating to functions and graphs. The next chapter is about derivatives and covers topics ranging from the slope problem to limits, sums and products, and quotients and square roots, along with limits and continuity. Subsequent chapters deal with applications of differentiation; exponential and trigonometric functions; techniques and applications of integration; inverse functions; and plane analytic geometry. The rest of the book focuses on approximation and convergence; power series; space geometry and vectors; vector functions and curves; higher partials and their applications; and double and multiple integrals. This monograph will be a useful resource for undergraduate students of mathematics and algebra.
Designed for prospective mathematics majors and students interested in engineering, computer science, physics, business or the life sciences. The program covers all topics in the Advanced Placement Calculus AB and Calculus BC syllabi. Instruction takes full advantage of graphing calculators, using them for visual demonstrations of concepts and confirming calculations.
A revision of McGraw-Hill's leading calculus text for the 3-semester sequence taken primarily by math, engineering, and science majors. The revision is substantial and has been influenced by students, instructors in physics, engineering, and mathematics, and participants in the national debate on the future of calculus. Revision focused on these key areas: Upgrading graphics and design, expanding range of problem sets, increasing motivation, strengthening multi-variable chapters, and building a stronger support package.
Introduction to calculus for both undergraduate math majors and those pursuing other areas of science and engineering for whom calculus will be a vital tool. Solutions available as free downloads. 1967 edition.
A NEW APPROACH TO CALCULUS THAT BETTER ENABLES STUDENTS TO PROGRESS TO MORE ADVANCED COURSES AND APPLICATIONS Calculus and Analysis: A Combined Approach bridges the gap between mathematical thinking skills and advanced calculus topics by providing an introduction to the key theory for understanding and working with applications in engineering and the sciences. Through a modern approach that utilizes fully calculated problems, the book addresses the importance of calculus and analysis in the applied sciences, with a focus on differential equations. Differing from the common classical approach to the topic, this book presents a modern perspective on calculus that follows motivations from Otto Toeplitz's famous genetic model. The result is an introduction that leads to great simplifications and provides a focused treatment commonly found in the applied sciences, particularly differential equations. The author begins with a short introduction to elementary mathematical logic. Next, the book explores the concept of sets and maps, providing readers with a strong foundation for understanding and solving modern mathematical problems. Ensuring a complete presentation, topics are uniformly presented in chapters that consist of three parts: Introductory Motivations presents historical mathematical problems or problems arising from applications that led to the development of mathematical solutions Theory provides rigorous development of the essential parts of the machinery of analysis; proofs are intentionally detailed, but simplified as much as possible to aid reader comprehension Examples and Problems promotes problem-solving skills through application-based exercises that emphasize theoretical mechanics, general relativity, and quantum mechanics Calculus and Analysis: A Combined Approach is an excellent book for courses on calculus and mathematical analysis at the upper-undergraduate and graduate levels. It is also a valuable resource for engineers, physicists, mathematicians, and anyone working in the applied sciences who would like to master their understanding of basic tools in modern calculus and analysis.