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Calculus :early transcendentals /

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Calculus :James Stewart.
其他題名:	early transcendentals /
作者:	Stewart, James,
出版者:	Belmont, CA :Thomson Brooks/Cole,c2008.
面頁冊數:	1 v. (various pagings) :ill. (some col.) ;26 cm.
附註:	Includes index.
標題:	Calculus
電子資源:	http://catdir.loc.gov/catdir/enhancements/fy1104/2006939532-b.html
電子資源:	http://catdir.loc.gov/catdir/enhancements/fy1104/2006939532-d.html
電子資源:	http://catdir.loc.gov/catdir/enhancements/fy1215/2006939532-t.html
ISBN:	9780495011668

Calculus :early transcendentals /
Stewart, James,1941-

Calculus :early transcendentals /James Stewart. - 6th ed. - Belmont, CA :Thomson Brooks/Cole,c2008. - 1 v. (various pagings) :ill. (some col.) ;26 cm.

Includes index.

Preface -- To the student -- Diagnostic tests -- A preview of calculus -- 1. Functions and models -- 1.1. Four ways to represent a function -- 1.2. Mathematical models : a catalog of essential functions -- 1.3. New functions from old functions -- 1.4. Graphing calculators and computers -- 1.5. Exponential functions -- 1.6. Inverse functions and logarithms -- Review -- Principles of problem solving -- 2. Limits and derivatives -- 2.1. The tangent and velocity problems -- 2.2. The limit of a function -- 2.3. Calculating limits using the limit laws -- 2.4. The precise definition of a limit -- 2.5. Continuity -- 2.6. Limits at infinity ; horizontal asymptotes -- 2.7. Derivatives and rates of change -- Writing project : early methods for finding tangents -- 2.8. The derivative as a function -- Review -- Problems plus -- 3. Differentiation rules -- 3.1. Derivatives of polynomials and exponential functions -- Applied project : building a better roller coaster -- 3.2. The product and quotient rules -- 3.3. Derivatives of trigonometric functions -- 3.4. The chain rule -- Applied project : where should a pilot start descent? -- 3.5. Implicit differentiation -- 3.6. Derivatives of logarithmic functions -- 3.7. Rates of change in the natural and social sciences -- 3.8. Exponential growth and decay -- 3.9. Related rates -- 3.10. Linear approximations and differentials -- Laboratory project : Taylor polynomials -- 3.11. Hyperbolic functions -- Review -- Problems plus --

ISBN: 9780495011668

LCCN: 2006939532

Nat. Bib. No.: GBA783943bnbSubjects--Topical Terms:

216672
Calculus

LC Class. No.: QA303.2 / S 7315

Dewey Class. No.: 515

Calculus :early transcendentals /
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020 $a 0495383430 (instructor's ed.)
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082 0 0 $a 515 $2 22
100 1 $a Stewart, James, $d 1941- $3 211662
245 1 0 $a Calculus : $b early transcendentals / $c James Stewart.
250 $a 6th ed.
260 $a Belmont, CA : $b Thomson Brooks/Cole, $c c2008.
300 $a 1 v. (various pagings) : $b ill. (some col.) ; $c 26 cm.
500 $a Includes index.
505 0 $a Preface -- To the student -- Diagnostic tests -- A preview of calculus -- 1. Functions and models -- 1.1. Four ways to represent a function -- 1.2. Mathematical models : a catalog of essential functions -- 1.3. New functions from old functions -- 1.4. Graphing calculators and computers -- 1.5. Exponential functions -- 1.6. Inverse functions and logarithms -- Review -- Principles of problem solving -- 2. Limits and derivatives -- 2.1. The tangent and velocity problems -- 2.2. The limit of a function -- 2.3. Calculating limits using the limit laws -- 2.4. The precise definition of a limit -- 2.5. Continuity -- 2.6. Limits at infinity ; horizontal asymptotes -- 2.7. Derivatives and rates of change -- Writing project : early methods for finding tangents -- 2.8. The derivative as a function -- Review -- Problems plus -- 3. Differentiation rules -- 3.1. Derivatives of polynomials and exponential functions -- Applied project : building a better roller coaster -- 3.2. The product and quotient rules -- 3.3. Derivatives of trigonometric functions -- 3.4. The chain rule -- Applied project : where should a pilot start descent? -- 3.5. Implicit differentiation -- 3.6. Derivatives of logarithmic functions -- 3.7. Rates of change in the natural and social sciences -- 3.8. Exponential growth and decay -- 3.9. Related rates -- 3.10. Linear approximations and differentials -- Laboratory project : Taylor polynomials -- 3.11. Hyperbolic functions -- Review -- Problems plus --
505 0 $a 4. Applications of differentiation -- 4.1. Maximum and minimum values -- Applied project : the calculus of rainbows -- 4.2. The mean value theorem -- 4.3. How derivatives affect the shape of a graph -- 4.4. Indeterminate forms and L'Hospital's rule -- Writing project : the origins of L'Hospital's rule -- 4.5. Summary of curve sketching -- 4.6. Graphing with calculus and calculators -- 4.7. Optimization problems -- Applied project : the shape of a can -- 4.8. Newton's method -- 4.9. Antiderivatives -- Review -- Problems plus -- 5. Integrals -- 5.1. Areas and distances -- 5.2. The definite integral -- Discovery project : area functions -- 5.3. The fundamental theorem of calculus -- 5.4. Indefinite integrals and the net change theorem -- Writing project : Newton, Leibniz, and the invention of calculus -- 5.5. The substitution rule -- Review -- Problems plus -- 6. Integrals -- 6.1. Areas between curves -- 6.2. Volumes -- 6.3. Volumes by cylindrical shells -- 6.4. Work -- 6.5. Average value of a function -- Applied projects : where to sit at the movies -- Review -- Problems plus -- 7. Techniques of integration -- 7.1. Integration by parts -- 7.2. Trigonometric integrals -- 7.3. Trigonometric substitution -- 7.4. Integration of rational functions by partial fractions -- 7.5. Strategy for integration -- 7.6. Integration using tables and computer algebra systems -- Discovery project : patterns in integrals -- 7.7. Approximate integration -- 7.8. Improper integrals -- Review -- Problems plus --
505 0 $a 8. Further applications of integration -- 8.1. Arc length -- Discovery project : arc length contest -- 8.2. Area of a surface of revolution -- Discovery project : rotating on a slant -- 8.3. Applications to physics and engineering -- Discovery project : complementary coffee cups -- 8.4. Applications to economics and biology -- 8.5. Probability -- Review -- Problems plus -- 9. Differential equations -- 9.1. Modeling with differential equations -- 9.2. Direction fields and Euler's method -- 9.3. Separable equations -- Applied project : how fast does a tank drain? -- Applied project : which is faster, going up or coming down? -- 9.4. Models for population growth -- Applied project : calculus and baseball -- 9.5. Linear equations -- 9.6. Predator-prey systems -- Review -- Problems plus -- 10. Parametric equations and polar coordinates -- 10.1. Curves defined by parametric equations -- Laboratory project : running circles around circles -- 10.2. Calculus with parametric curves -- Laboratory project : Bézier curves -- 10.3. Polar coordinates -- 10.4. Areas and lengths in polar coordinates -- 10.5. Conic sections -- 10.6. Conic sections in polar coordinates -- Review -- Problems plus -- 11. Infinite sequences and series -- 11.1. Sequences -- Laboratory project : logistic sequences -- 11.2. Series -- 11.3. The integral test and estimates of sums -- 11.4. The comparison tests -- 11.5. Alternating series -- 11.6. Absolute convergence and the ratio and root tests -- 11.7. Strategy for testing series -- 11.8. Power series -- 11.9. Representations of functions as power series -- 11.10. Taylor and Maclaurin series -- Laboratory project : an elusive limit -- Writing project : how Newton discovered the binomial series -- 11.11. Applications of Taylor polynomials -- Applied project : radiation from the stars -- Review -- Problems plus --
505 0 $a 12. Vectors and geometry of space -- 12.1. Three-dimensional coordinate systems -- 12.2. Vectors -- 12.3. The dot product -- 12.4. The cross product -- Discovery project : the geometry of a tetrahedrom -- 12.5. Equations of lines and planes -- Laboratory project : putting 3D in perspective -- 12.6. Cylinders and quadric surfaces -- Review -- Problems plus -- 13. Vector functions -- 13.1. Vector functions and space curves -- 13.2. Derivatives and integrals of vector functions -- 13.3. Arc length and curvature -- 13.4. Motion in space : velocity and acceleration -- Applied project : Kepler's laws -- Review -- Problems plus -- 14. Partial derivatives -- 14.1. Functions of several variables -- 14.2. Limits and continuity -- 14.3. Partial derivatives -- 14.4. Tangent planes and linear approximations -- 14.5. The chain rule -- 14.6. Directional derivatives and the gradient vector -- 14.7. Maximum and minimum values -- Applied project : designing a dumpster -- Discovery project : quadratic approximation and critical points -- 14.8. Lagrange multipliers -- Applied project : rocket science -- Applied project : hydro-turbine optimization -- Review -- Problems plus --
505 0 $a 15. Multiple integrals -- 15.1. Double integrals over rectangles -- 15.2. Iterated integrals -- 15.3. Double integrals over general regions -- 15.4. Double integrals in polar coordinates -- 15.5. Applications of double integrals -- 15.6. Triple integrals -- Discovery project : volumes of hyperspheres -- 15.7. Triple integrals in cylindrical coordinates -- Discovery project : the intersection of three cylinders -- 15.8. Triple integrals in spherical coordinates -- Applied project : roller derby -- 15.9. Change of variables in multiple integrals -- Review -- Problems plus -- 16. Vector calculus -- 16.1. Vector fields -- 16.2. Line integrals -- 16.3. The fundamental theorem for line integrals -- 16.4. Green's theorem -- 16.5. Curl and divergence -- 16.6. Parametric surfaces and their areas -- 16.7. Surface integrals -- 16.8. Stokes' theorem -- Writing project : three men and two theorems -- 16.9. The divergence theorem -- 16.10. Summary -- Review -- Problems plus -- 17. Second-order differential equations -- 17.1. Second-order linear equations -- 17.2. Nonhomogeneous linear equations -- 17.3. Applications of second-order differential equations -- 17.4. Series solutions -- Review -- Appendixes -- A. Numbers, 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. The logarithm defined as an integral -- H. Complex numbers -- I. Answers to odd-numbered exercises.
650 0 $a Calculus $3 216672
650 0 $a Transcendental functions $v Textbooks. $3 708242
650 0 7 $a Analysis. $3 273775
856 4 2 $3 Contributor biographical information $u http://catdir.loc.gov/catdir/enhancements/fy1104/2006939532-b.html
856 4 2 $3 Publisher description $u http://catdir.loc.gov/catdir/enhancements/fy1104/2006939532-d.html
856 4 1 $3 Table of contents only $u http://catdir.loc.gov/catdir/enhancements/fy1215/2006939532-t.html

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http://catdir.loc.gov/catdir/enhancements/fy1104/2006939532-b.html
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