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Calculus : early transcendentals

Author: James Stewart
Publisher: Belmont, CA : Thomson Brooks/Cole, ©2008.
Edition/Format:   Print book : English : 6th edView all editions and formats
Summary:
Appropriate for the traditional 2 or 3-term college calculus course, this textbook presents the fundamentals of calculus. Topics include, but are not limited to: a review of polynomials, trigonometric, exponential, and logarithmic functions, followed by discussions of limits, derivatives, applications of differential calculus to real-world problem areas, an overview of integration, basic techniques for integration,  Read more...
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Genre/Form: Textbooks
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: James Stewart
ISBN: 9780495011668 0495011665 9780495383437 0495383430 9780495382737 0495382736
OCLC Number: 144526840
Notes: Includes index.
Description: 1 volume (various pagings) : illustrations (some color) ; 26 cm
Contents: 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. 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. Applications of integration --
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. 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. 12. Vectors and the 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. 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.
Responsibility: James Stewart.
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Abstract:

'Calculus' covers exponential and logarithmic functions. It looks at their limits, derivatives, polynomials and other elementary functions.  Read more...

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1. Functions and Models. Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Graphing Calculators and Computers. Exponential Read more...

 
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