Calculus: Early Transcendentals 7th Edition is a book that assists students in discovering calculus. The emphasis is on understanding concepts as this should be the primary goal of calculus instruction. In writing seventh edition of Calculus, author’s premise has been that it is possible to achieve conceptual understanding and still retain the best traditions of traditional calculus. Stewart Calculus contains elements of reform, but within the context of a traditional curriculum.
What is Calculus: Early Transcendentals 7th Edition Book all about?
In the seventh edition, some material has been rewritten for greater clarity or for better motivation.
Examples and Projects
Also, some new examples and solutions to some of the existing examples have been amplified. New three projects have been added: The Gini Index (explores how to measure income distribution among inhabitants of a given country and is a nice application of areas between curves), Families of Implicit Curves (investigates the changing shapes of implicitly defined curves as parameters in a family are varied) and Families of Polar Curves (exhibits the fascinating shapes of polar curves and how they evolve within a family). Additionally, in Calculus: Early Transcendentals 7th Edition, more than 25% of the exercises in each chapter are new.
Each exercise set in this book is carefully graded, progressing from basic conceptual exercises and skill-development problems to more challenging problems involving applications and proofs. Many of the examples and exercises include interesting real-world data to introduce, motivate, and illustrate the concepts of calculus. As a result, these examples deal with functions defined by such numerical data or graphs.
One way of involving students and making them active learners is to have them work on extended projects that give a feeling of substantial accomplishment when completed. As a result, four kinds of projects are included in Calculus 7th edition: Applied Projects (they involve applications that are designed to appeal to the imagination of students), Laboratory Projects (they involve technology), Writing Projects (they ask students to compare present-day methods with those of the founders of calculus) and Discovery Projects (anticipate results to be discussed later or encourage discovery through pattern recognition).
This textbook can be used either with or without technology and there are two special symbols to indicate clearly when a particular type of machine is required.
– this icon indicates an exercise that definitely requires the use of such technology, but that is not to say that it can’t be used on the other exercises as well.
– this symbol is reserved for problems in which the full resources of a computer algebra system are required.
Homework Hints presented in the form of questions try to imitate an effective teaching assistant by functioning as a silent tutor. Hints for representative exercises (usually oddnumbered) are included in every section of the text, indicated by printing the exercise number in red.
EduReads Final Word
This book contains more material than can be covered in any one course, it can also serve as a valuable resource for a working scientist or engineer. Reading a calculus textbook is different from reading a newspaper or a novel, or even a physics book. Don’t be discouraged if you have to read a passage more than once in order to understand it. You should have pencil and paper and calculator at hand to sketch a diagram or make a calculation.
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Keep this book for reference purposes after you finish the course. Because you will likely forget some of the specific details of calculus, the book will serve as a useful reminder when you need to use calculus in subsequent courses.
Complete and Detailed Table of Contents
- Diagnostic Tests – The book begins with four diagnostic tests, in Basic Algebra, Analytic Geometry, Functions, and Trigonometry.
- A Preview of Calculus – This is an overview of the subject and includes a list of questions to motivate the study of calculus.
- Functions and Models – From the beginning, multiple representations of functions are stressed: verbal, numerical, visual, and algebraic. A discussion of mathematical models leads to a review of the standard functions, including exponential and logarithmic functions, from these four points of view.
- Limits and Derivatives – The material on limits is motivated by a prior discussion of the tangent and velocity problems. Limits are treated from descriptive, graphical, numerical, and algebraic points of view. Section 2.4, on the precise definition of a limit, is an optional section. Sections 2.7 and 2.8 deal with derivatives (especially with functions defined graphically and numerically) before the differentiation rules are covered in Chapter 3. Here the examples and exercises explore the meanings of derivatives in various contexts. Higher derivatives are introduced in Section 2.8.
- Differentiation Rules – All the basic functions, including exponential, logarithmic, and inverse trigonometric functions, are differentiated here. When derivatives are computed in applied situations, students are asked to explain their meanings. Exponential growth and decay are covered in this chapter.
- Applications of Differentiation – The basic facts concerning extreme values and shapes of curves are deduced from the Mean Value Theorem. Graphing with technology emphasizes the interaction between calculus and calculators and the analysis of families of curves. Some substantial optimization problems are provided, including an explanation of why you need to raise your head 42° to see the top of a rainbow.
- Integrals – The area problem and the distance problem serve to motivate the definite integral, with sigma notation introduced as needed. (Full coverage of sigma notation is provided in Appendix E.) Emphasis is placed on explaining the meanings of integrals in various contexts and on estimating their values from graphs and tables.
- Applications of Integration – Here Stewart presents the applications of integration—area, volume, work, average value—that can reasonably be done without specialized techniques of integration. General methods are emphasized. The goal is for students to be able to divide a quantity into small pieces, estimate with Riemann sums, and recognize the limit as an integral.
- Techniques of Integration – All the standard methods are covered but, of course, the real challenge is to be able to recognize which technique is best used in a given situation. Accordingly, in Section 7.5, The use of computer algebra systems is discussed in Section 7.6.
- Further Applications of Integration – Here are the applications of integration—arc length and surface area—for which it is useful to have available all the techniques of integration, as well as applications to biology, economics, and physics (hydrostatic force and centers of mass). I have also included a section on probability. There are more applications here than can realistically be covered in a given course. Instructors should select applications suitable for their students and for which they themselves have enthusiasm.
- Differential Equations – Modeling is the theme that unifies this introductory treatment of differential equations. Direction fields and Euler’s method are studied before separable and linear equations are solved explicitly, so that qualitative, numerical, and analytic approaches are given equal consideration. These methods are applied to the exponential, logistic, and other models for population growth. The first four or five sections of this chapter serve as a good introduction to first-order differential equations. An optional final section uses predator-prey models to illustrate systems of differential equations.
- Parametric Equations and Polar Coordinates – This chapter introduces parametric and polar curves and applies the methods of calculus to them. Parametric curves are well suited to laboratory projects; the three presented here involve families of curves and Bézier curves. A brief treatment of conic sections in polar coordinates prepares the way for Kepler’s Laws in Chapter 13.
- Infinite Sequences and Series – The convergence tests have intuitive justifications (see page 714) as well as formal proofs. Numerical estimates of sums of series are based on which test was used to prove convergence. The emphasis is on Taylor series and polynomials and their applications to physics. Error estimates include those from graphing devices.
- Vectors and The Geometry of Space – The material on three-dimensional analytic geometry and vectors is divided into two chapters. Chapter 12 deals with vectors, the dot and cross products, lines, planes, and surfaces.
- Vector Functions – This chapter covers vector-valued functions, their derivatives and integrals, the length and curvature of space curves, and velocity and acceleration along space curves, culminating in Kepler’s laws.
- Partial Derivatives – Functions of two or more variables are studied from verbal, numerical, visual, and algebraic points of view. In particular, Stewart introduces partial derivatives by looking at a specific column in a table of values of the heat index (perceived air temperature) as a function of the actual temperature and the relative humidity.
- Multiple Integrals – Contour maps and the Midpoint Rule are used to estimate the average snowfall and average temperature in given regions. Double and triple integrals are used to compute probabilities, surface areas, and (in projects) volumes of hyperspheres and volumes of intersections of three cylinders. Cylindrical and spherical coordinates are introduced in the context of evaluating triple integrals.
- Vector Calculus – Vector fields are introduced through pictures of velocity fields showing San Francisco Bay wind patterns. The similarities among the Fundamental Theorem for line integrals, Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem are emphasized.
- Second-Order Differential Equations – Since first-order differential equations are covered in Chapter 9, this final chapter deals with second-order linear differential equations, their application to vibrating springs and electric circuits, and series solutions.
Author: James Stewart
ISBN-10: 0840058454 (Paperback); 0538497904 (Hardcover)
ISBN-13: 978-0840058454 (Paperback); 978-0538497909 (Hardcover)
Release Date: January 1st, 2011.
Publisher: Thomson Brooks/Cole
Category: Science –> Mathematics –> Calculus
About James Stewart, author of “Calculus: Early Transcendentals 7th Edition”
James Stewart (born on January 1st, 1941) received the M.S. degree from Stanford University and the Ph.D. from the University of Toronto. After two years as a postdoctoral fellow at the University of London, he became Professor of Mathematics at McMaster University. His research has been in harmonic analysis and functional analysis. Stewart’s books include a series of high school textbooks as well as a best-selling series of calculus textbooks published by Brooks/Cole. He is also co-author, with Lothar Redlin and Saleem Watson, of a series of college algebra and precalculus textbooks. Translations of his books include those into Spanish, Portuguese, French, Italian, Korean, Chinese, Greek, and Indonesian.
Stewart was named a Fellow of the Fields Institute in 2002 and was awarded an honorary D.Sc. in 2003 by McMaster University. The library of the Fields Institute is named after him. The James Stewart Mathematics Centre was opened in October, 2003, at McMaster University.
View all books written by James Stewart