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Calculus, International Metric Edition (Englisch) Gebundene Ausgabe – 23. Oktober 2011

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Table of Contents: Diagnostic Tests. A Preview of Calculus. 1. FUNCTIONS AND LIMITS. Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Review. Principles of Problem Solving. 2. DERIVATIVES. Derivatives and Rates of Change. Writing Project: Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Differentiation Formulas. Applied Project: Building a Better Roller Coaster. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Laboratory Project: Families of Implicit Curves. Rates of Change in the Natural and Social Sciences. Related Rates. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials. Review. Problems Plus. 3. APPLICATIONS OF DIFFERENTIATION. Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. The Mean Value Theorem. How Derivatives Affect the Shape of a Graph. Limits at Infinity; Horizontal Asymptotes. Summary of Curve Sketching. Graphing with Calculus and Calculators. Optimization Problems. Applied Project: The Shape of a Can. Newton's Method. Antiderivatives. Review. Problems Plus. 4. INTEGRALS. Areas and Distances. The Definite Integral. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theorem. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Review. Problems Plus. 5. APPLICATIONS OF INTEGRATION. Areas Between Curves. Applied Project: The Gini Index. Volume. Volumes by Cylindrical Shells. Work. Average Value of a Function. Review. Problems Plus. 6. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS. Inverse Functions. Instructors may cover either Sections 6.2-6.4 or Sections 6.2*-6.4*. See the Preface. Exponential Functions and Their Derivatives. Logarithmic Functions. Derivatives of Logarithmic Functions. The Natural Logarithmic Function. The Natural Exponential Function. General Logarithmic and Exponential Functions. Exponential Growth and Decay. Inverse Trigonometric Functions. Applied Project: Where to Sit at the Movies. Hyperbolic Functions. Indeterminate Forms and l'Hospital's Rule. Writing Project: The Origins of l'Hospital's Rule. Review. Problems Plus. 7. TECHNIQUES OF INTEGRATION. Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integration of Rational Functions by Partial Fractions. Strategy for Integration. Applied Project: Calculus and Baseball. Integration Using Tables and Computer Algebra Systems. Discovery Project: Patterns in Integrals. Approximate Integration. Improper Integrals. Review. Problems Plus. 8. FURTHER APPLICATIONS OF INTEGRATION. Arc Length. Discovery Project: Arc Length Contest. Area of a Surface of Revolution. Discovery Project: Rotating on a Slant. Applications to Physics and Engineering. Discovery Project: Complementary Coffee Cups. Applications to Economics and Biology. Probability. Review. Problems Plus. 9. DIFFERENTIAL EQUATIONS. Modeling with Differential Equations. Direction Fields and Euler's Method. Separable Equations. Applied Project: How Fast Does a Tank Drain? Applied Project: Which is Faster, Going Up or Coming Down? Models for Population Growth. Linear Equations. Predator-Prey Systems. Review. Problems Plus. 10. PARAMETRIC EQUATIONS AND POLAR COORDINATES. Curves Defined by Parametric Equations. Laboratory Project: Families of Hypocycloids. Calculus with Parametric Curves. Laboratory Project: Bezier Curves. Polar Coordinates. Laboratory Project: Families of Polar Curves. Areas and Lengths in Polar Coordinates. Conic Sections. Conic Sections in Polar Coordinates. Review. Problems Plus. 11. INFINITE SEQUENCES AND SERIES. Sequences. Laboratory Project: Logistic Sequences. Series. The Integral Test and Estimates of Sums. The Comparison Tests. Alternating Series. Absolute Convergence and the Ratio and Root Tests. Strategy for Testing Series. Power Series. Representations of Functions as Power Series. Taylor and Maclaurin Series . Laboratory Project: An Elusive Limit. Writing Project: How Newton Discovered the Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Review. Problems Plus. 12. VECTORS AND THE GEOMETRY OF SPACE. Three-Dimensional Coordinate Systems. Vectors. The Dot Product. The Cross Product. Discovery Project: The Geometry of a Tetrahedron. Equations of Lines and Planes. Cylinders and Quadric Surfaces. Review. Problems Plus. 13. VECTOR FUNCTIONS. Vector Functions and Space Curves. Derivatives and Integrals of Vector Functions. Arc Length and Curvature. Motion in Space: Velocity and Acceleration. Applied Project: Kepler's Laws. Review. Problems Plus. 14. PARTIAL DERIVATIVES. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Tangent Planes and Linear Approximation. The Chain Rule. Directional Derivatives and the Gradient Vector. Maximum and Minimum Values. Applied Project: Designing a Dumpster. Discovery Project: Quadratic Approximations and Critical Points. Lagrange Multipliers. Applied Project: Rocket Science. Applied Project: Hydro-Turbine Optimization. Review. Problems Plus. 15. MULTIPLE INTEGRALS. Double Integrals over Rectangles. Iterated Integrals. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals. Triple Integrals. Discovery Project: Volumes of Hyperspheres. Triple Integrals in Cylindrical Coordinates. Discovery Project: The Intersection of Three Cylinders. Triple Integrals in Spherical Coordinates. Applied Project: Roller Derby. Change of Variables in Multiple Integrals. Review. Problems Plus. 16. VECTOR CALCULUS. Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Green's Theorem. Curl and Divergence. Parametric Surfaces and Their Areas. Surface Integrals. Stokes' Theorem. Writing Project: Three Men and Two Theorems. The Divergence Theorem. Summary. Review. Problems Plus. 17. SECOND-ORDER DIFFERENTIAL EQUATIONS. Second-Order Linear Equations. Nonhomogeneous Linear Equations. Applications of Second-Order Differential Equations. Series Solutions. Review. Problems Plus. APPENDIXES. A. Intervals, Inequalities, and Absolute Values. B. Coordinate Geometry and Lines. C. Graphs of Second-Degree Equations. D. Trigonometry. E. Sigma Notation. F. Proofs of Theorems. G. Graphing Calculators and Computers . H. Complex Numbers. I. Answers to Odd-Numbered Exercises.

Über den Autor und weitere Mitwirkende

The late James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart was most recently Professor of Mathematics at McMaster University, and his research field was harmonic analysis. Stewart was the author of a best-selling calculus textbook series published by Cengage Learning, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.

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Amazon.com: 3.4 von 5 Sternen 122 Rezensionen
100 von 112 Kunden fanden die folgende Rezension hilfreich
2.0 von 5 Sternen The Calculus textbooks almost all the same 9. Februar 2012
Von Marc - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
Okay here is my point of view. I am not a student anymore, but my daughter is an Electrical Engineering student.

I am a severly disabled vet with a spinal cord injury, so I have alot of weird nerve and brain issues.

So math is sort of a recreation and therapy, I used to be a software engineer but my brain really does work right anymore.

I get my daughter's textbooks when they are done, plus I have a ton of other textbooks I acquire.

Looking at Stewart or Larson, they are almost the same. Larson has a bit more flash and is slighty better for me the self study. But honestly there is very little difference in the texts.
I have a few Calc textbooks which are not the popular choices for universities, and they are better, but not popular.

One issue is that online courses have forced textbook publishers to come up with online content, so all the textbooks now are geared for cashing in on internet content. So in this case the internet is not improving the educational experience for students.

As a self study, Stewart is worthless. As one reviewer stated, everything is really standardized to fit some testing model. So they present the basics. There are a few sample exercises, but none that really instruct the student on how to approach or solve the harder cases. I assume you are suppossed to figure that out yourself. Textbook to Textbook they take that approach.

As a reference I guess it is okay. But if you really want to understand and learn it, pick up Morris Kline and Adrian Banner. Start there then move onto pure mathematics. It is not an easy way to go, but you will have a better understanding.. Use Stewart as a reference and for some practice exercises.
40 von 45 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen Good book w/ some drawbacks 3. Dezember 2011
Von MP - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
Stewart's calculus textbook is a relatively standard development of basic calculus. It is readable with many examples and pictures to aid understanding. It is not a "rigorous" development in the strict (i.e. real analysis) sense - you'll need a supplementary textbook if you want to crack that egg. It does, however, provide students with the ability to solve problems using calculus that they will likely encounter in later courses.

It is not without drawbacks, however. My primary complaint is that while I worked through the later chapters for the first time I was unsure why I was doing what I was. In particular, the chapters on vectors were rather poorly done - they seemed developed enough just to get students through the problem sets. On the other hand, anybody wishing to seriously learn vector calculus will likely have an entire book devoted to the topic.

My only other complaint is the development of differential equations. I understand the purpose of including them in the textbook (they're used in many fields), but you really can't cover much about differential equations in the small chapters devoted to them. Like I said, I understand why the author included the sections, but after learning differential equations properly, I do not feel like those chapters in this textbook served any useful purpose.

Due to the widespread usage of this textbook, it is inevitable that some struggling students (and mathematicians!) will dislike it. If you happen to be a struggling student, check out "Calculus: An Intuitive and Physical Approach" by Morris Kline. It is very cheap, thorough, and will undoubtedly make for an excellent study aid.
30 von 34 Kunden fanden die folgende Rezension hilfreich
1.0 von 5 Sternen Get it if you have to, but if you have a choice: Spivak 17. August 2012
Von Tech of all Types - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
If your course requires you to get this book, get it of course. But if you want to learn Calculus from the best Math textbook ever written, get Spivak (Calculus, 4th edition). Also, if you stumble across a copy of Apostol, that's pretty good too (Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra). But Spivak is the best - relevant, well written, engaging, comprehensive.
21 von 23 Kunden fanden die folgende Rezension hilfreich
2.0 von 5 Sternen Waste of money 13. August 2013
Von Abraham Frei-Pearson - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
This textbook was assigned when I took calculus as a freshman in college. Back then, in those ancient days of 2007, we used the fifth edition. I've seen the sixth and seventh editions, and, as far as I can tell, there is no real difference. Some of the problems have been reordered, and maybe a sentence tweaked here or there, some new pictures, but nothing really noteworthy. Seemingly the only reason to release a new edition is to stay abreast of the used book market.

If you are a professor, it is incredibly inconsiderate to assign this book. It's not a bad book, really, but there are a ton of cheap and even free alternatives that are, at the very least, just as good. If any instructors are reading this, you should really take the time to find one of these alternatives that you like and assign it, rather than forcing 200 teenagers to spend $150.00 on a textbook that's basically a dime a dozen (you might even try an older edition of Stewart. There are currently 668 used copies of the fifth edition available on Amazon, the cheapest being $1.08. That these things become worthless once a new edition comes out speaks volumes.). Also, the solutions manuals to these books hit the internet approximately three seconds after they are published, and with websites like Cramster around, assigning this thing is asking your less honest pupils to cheat.
41 von 52 Kunden fanden die folgende Rezension hilfreich
1.0 von 5 Sternen Calculus 7th Edition (7E) James Stewart 24. August 2011
Von L. S. Mayer - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
This is a horrible text, and testament as to why so many potential students of science drop their major. This book is supposed to be a first book in Calculus, provide some basis for the subject, and work students through the essentials step by step. You can be an all inclusive masterful mathematical academician, and not be able to communicate with a first level student. That is precisely what this book does.

I wish I had the time to write a Calculus book taught like my professors did 30 years ago - when it was essential to teach students, not overwhelm them as if to prove how smart you are. Explanations are terse and incomplete, there is no history as to why evaluations of limits, derivatives, and integral equations were developed, and a host of problems that are not explained and leave students clueless. Unsuspecting new professors continue to use this book, and wonder why their students struggle with their class.

Wake up and throw away this text as a standard and get one that actually teaches Calculus I. It's OK if the book you choose does not cover Calculus II or III, just cover Calculus I thoroughly. Leave students with a firm foundation, appreciation, and enjoyment in mathematics - not quitting their majors.
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