|
|
|
|
LEADER |
00000cam a2200000 a 4500 |
001 |
b1538020 |
003 |
MWH |
005 |
20080807012318.0 |
008 |
070329s2007 njua 001 0 eng c |
010 |
|
|
|a 2006939343
|
020 |
|
|
|a 0691131538 (cloth)
|
020 |
|
|
|a 9780691131535 (cloth)
|
020 |
|
|
|a 0691130884 (pbk.)
|
020 |
|
|
|a 9780691130880 (pbk.)
|
029 |
1 |
|
|a YDXCP
|b 2509596
|
029 |
1 |
|
|a AU@
|b 000041593435
|
029 |
1 |
|
|a NZ1
|b 11294457
|
035 |
|
|
|a (OCoLC)100000310
|
035 |
|
|
|a (OCoLC)100000310
|
040 |
|
|
|a B@L
|c B@L
|d EYE
|d IXA
|d YDXCP
|d BTCTA
|d BAKER
|d MUQ
|d SHH
|d DLC
|d OBE
|d CRH
|d NOR
|
042 |
|
|
|a pcc
|
049 |
|
|
|a HCQS
|
050 |
0 |
0 |
|a QA303.2
|b .B36 2007
|
100 |
1 |
|
|a Banner, Adrian D.,
|d 1975-
|
245 |
1 |
4 |
|a The calculus lifesaver :
|b all the tools you need to excel at calculus /
|c Adrian Banner.
|
260 |
|
|
|a Princeton, N.J. :
|b Princeton University Press,
|c c2007.
|
300 |
|
|
|a xxi, 728 p. :
|b ill. ;
|c 26 cm.
|
440 |
|
0 |
|a Princeton lifesaver study guide
|
500 |
|
|
|a Includes index.
|
505 |
0 |
0 |
|t Welcome --
|t How to use this book to study for an exam --
|t Two all-purpose study tips --
|t Key sections for exam review (by topic) --
|t Acknowledgments --
|g 1.
|t Functions, graphs, and lines --
|g 1.1.
|t Functions --
|g 1.1.1.
|t Interval notation --
|g 1.1.2.
|t Finding the domain --
|g 1.1.3.
|t Finding the range using the graph --
|g 1.1.4. The
|t vertical line test --
|g 1.2.
|t Inverse functions --
|g 1.2.1. The
|t horizontal line test --
|g 1.2.2.
|t Finding the inverse --
|g 1.2.3.
|t Restricting the domain --
|g 1.2.4.
|t Inverses of inverse functions --
|g 1.3.
|t Composition of functions --
|g 1.4.
|t Odd and even functions --
|g 1.5.
|t Graphs of linear functions --
|g 1.6.
|t Common functions and graphs --
|g 2.
|t Review of trigonometry --
|g 2.1. The
|t basics --
|g 2.2.
|t Extending the domain of trig functions --
|g 2.2.1. The
|t ASTC method --
|g 2.2.2.
|t Trig functions outside [0,2[pi]] --
|g 2.3. The
|t graphs of trig functions --
|g 2.4.
|t Trig identities --
|g 3.
|t Introduction to limits --
|g 3.1.
|t Limits : the basic idea --
|g 3.2.
|t Left-hand and right-hand limits --
|g 3.3.
|t When the limit does not exist --
|g 3.4.
|t Limits at [infinity] and -[infinity] --
|g 3.4.1.
|t Large number and small numbers --
|g 3.5.
|t Two common misconceptions about asymptotes --
|g 3.6. The
|t sandwich principle --
|g 3.7.
|t Summary of basic types of limits --
|
505 |
0 |
0 |
|g 4.
|t How to solve limit problems involving polynomials --
|g 4.1.
|t Limits involving rational functions as x -> a[alpha] --
|g 4.2.
|t Limits involving square roots as x -> a[alpha] --
|g 4.3.
|t Limits involving rational functions as x -> [infinity] --
|g 4.3.1.
|t Method and examples --
|g 4.4.
|t Limits involving poly-type functions as x -> [infinity] --
|g 4.5.
|t Limits involving rational functions as x -> -[infinity] --
|g 4.6.
|t Limits involving absolute values --
|g 5.
|t Continuity and differentiability --
|g 5.1.
|t Continuity --
|g 5.1.1.
|t Continuity at a point --
|g 5.1.2.
|t Continuity on an interval --
|g 5.1.3.
|t Examples of continuous functions --
|g 5.1.4. The
|t intermediate value theorem --
|g 5.1.5. A
|t harder IVT example --
|g 5.1.6.
|t Maxima and minima of continuous functions --
|g 5.2.
|t Differentiability --
|g 5.2.1.
|t Average speed --
|g 5.2.2.
|t Displacement and velocity --
|g 5.2.3.
|t Instantaneous velocity --
|g 5.2.4. The
|t graphical interpretation of velocity --
|g 5.2.5.
|t Tangent lines --
|g 5.2.6. The
|t derivative function --
|g 5.2.7. The
|t derivative as a limiting ration --
|g 5.2.8. The
|t derivative of linear functions --
|g 5.2.9.
|t Second and higher-order derivatives --
|g 5.2.10.
|t When the derivative does not exist --
|g 5.2.11.
|t Differentiability and continuity --
|
505 |
0 |
0 |
|g 6.
|t How to solve differentiation problems --
|g 6.1.
|t Finding derivatives using the definition --
|g 6.2.
|t Finding derivatives (the nice way) --
|g 6.2.1.
|t Constant multiples of functions --
|g 6.2.2.
|t Sums and differences of functions --
|g 6.2.3.
|t Products of functions via the product rule --
|g 6.2.4.
|t Quotients of functions via the quotient rule --
|g 6.2.5.
|t Composition of functions via the chain rule --
|g 6.2.6. A
|t nasty example --
|g 6.2.7.
|t Justification of the product rule and the chain rule --
|g 6.3.
|t Finding the equation of a tangent line --
|g 6.4.
|t Velocity and acceleration --
|g 6.4.1.
|t Constant negative acceleration --
|g 6.5.
|t Limits which are derivatives in disguise --
|g 6.6.
|t Derivatives of piecewise-defined functions --
|g 6.7.
|t Sketching derivative graphs directly --
|g 7.
|t Trig limits and derivatives --
|g 7.1.
|t Limits involving trig functions --
|g 7.1.1. The
|t small case --
|g 7.1.2.
|t Solving problems, the small case --
|g 7.1.3. The
|t large case --
|g 7.1.4. The
|t "other" case --
|g 7.1.5.
|t Proof of an important limit --
|g 7.2.
|t Derivatives involving trig functions --
|g 7.2.1.
|t Examples of differentiating trig functions --
|g 7.2.2.
|t Simple harmonic motion --
|g 7.2.3. A
|t curious function --
|
505 |
0 |
0 |
|g 8.
|t Implicit differentiation and related rates --
|g 8.1.
|t Implicit differentiation --
|g 8.1.1.
|t Techniques and examples --
|g 8.1.2.
|t Finding the second derivative implicitly --
|g 8.2.
|t Related rates --
|g 8.2.1. A
|t simple example --
|g 8.2.2. A
|t slightly harder example --
|g 8.2.3. A
|t much harder example --
|g 8.2.4. A
|t really hard example --
|g 9.
|t Exponentials and logarithms --
|g 9.1. The
|t basics --
|g 9.1.1.
|t Review of exponentials --
|g 9.1.2.
|t Review of logarithms --
|g 9.1.3.
|t Logarithms, exponentials, and inverses --
|g 9.1.4.
|t Log rules --
|g 9.2.
|t Definition of e --
|g 9.2.1. A
|t question about compound interest --
|g 9.2.2. The
|t answer to our question --
|g 9.2.3.
|t More about e and logs --
|g 9.3.
|t Differentiation of logs and exponentials --
|g 9.3.1.
|t Examples of differentiating exponentials and logs --
|g 9.4.
|t How to solve limit problems involving exponentials or logs --
|g 9.4.1.
|t Limits involving the definition of e --
|g 9.4.2.
|t Behavior of exponentials near 0 --
|g 9.4.3.
|t Behavior of logarithms near 1 --
|g 9.4.4.
|t Behavior of exponentials near [infinity] or -[infinity] --
|g 9.4.5.
|t Behavior of logs near [infinity] --
|g 9.4.6.
|t Behavior of logs near 0 --
|g 9.5.
|t Logarithmic differentiation --
|g 9.5.1. The
|t derivative of xa --
|g 9.6.
|t Exponential growth and decay --
|g 9.6.1.
|t Exponential growth --
|g 9.6.2.
|t Exponential decay --
|g 9.7.
|t Hyperbolic functions --
|
505 |
0 |
0 |
|g 10.
|t Inverse functions and inverse trig functions --
|g 10.1. The
|t derivative and inverse functions --
|g 10.1.1.
|t Using the derivative to show that an inverse exists --
|g 10.1.2.
|t Derivatives and inverse functions : what can go wrong --
|g 10.1.3.
|t Finding the derivative of an inverse function --
|g 10.1.4. A
|t big example --
|g 10.2.
|t Inverse trig functions --
|g 10.2.1.
|t Inverse sine --
|g 10.2.2.
|t Inverse cosine --
|g 10.2.3.
|t Inverse tangent --
|g 10.2.4.
|t Inverse secant --
|g 10.2.5.
|t Inverse cosecant and inverse cotangent --
|g 10.2.6.
|t Computing inverse trig functions --
|g 10.3.
|t Inverse hyperbolic functions --
|g 10.3.1. The
|t rest of the inverse hyperbolic functions --
|g 11. The
|t derivative and graphs --
|g 11.1.
|t Extrema of functions --
|g 11.1.1.
|t Global and local extrema --
|g 11.1.2. The
|t extreme value theorem --
|g 11.1.3.
|t How to find global maxima and minima --
|g 11.2.
|t Rolle's Theorem --
|g 11.3. The
|t mean value theorem --
|g 11.3.1.
|t Consequence of the man value theorem --
|g 11.4. The
|t second derivative and graphs --
|g 11.4.1.
|t More about points of inflection --
|g 11.5.
|t Classifying points where the derivative vanishes --
|g 11.5.1.
|t Using the first derivative --
|g 11.5.2.
|t Using the second derivative --
|
505 |
0 |
0 |
|g 12.
|t Sketching graphs --
|g 12.1.
|t How to construct a table of signs --
|g 12.1.1.
|t Making a table of signs for the derivative --
|g 12.1.2.
|t Making a table of signs for the second derivative --
|g 12.2. The
|t big method --
|g 12.3.
|t Examples --
|g 12.3.1. An
|t example without using derivatives --
|g 12.3.2. The
|t full method : example 1 --
|g 12.3.3. The
|t full method : example 2 --
|g 12.3.4. The
|t full method : example 3 --
|g 12.3.5. The
|t full method : example 4 --
|g 13.
|t Optimization and linearization --
|g 13.1.
|t Optimization --
|g 13.1.1. An
|t easy optimization example --
|g 13.1.2.
|t Optimization problems : the general method --
|g 13.1.3. An
|t optimization example --
|g 13.1.4.
|t Another optimization example --
|g 13.1.5.
|t Using implicit differentiation in optimization --
|g 13.1.6. A
|t difficult optimization example --
|g 13.2.
|t Linearization --
|g 13.2.1.
|t Linearization in general --
|g 13.2.2. The
|t differential --
|g 13.2.3.
|t Linearization summary and example --
|g 13.2.4. The
|t error in our approximation --
|g 13.3.
|t Newton's method --
|
505 |
0 |
0 |
|g 14.
|t L'Hôpital's rule and overview of limits --
|g 14.1.
|t L'Hôpital's rule --
|g 14.1.1.
|t Type A : 0/0 case --
|g 14.1.2.
|t Type A : ±[infinity]/±[infinity] case --
|g 14.1.3.
|t Type B1 ([infinity] - [infinity]) --
|g 14.1.4.
|t Type B2 (0 x ± [infinity]) --
|g 14.1.5.
|t Type C (1 ± [infinity], 0⁰, or [infinity]⁰) --
|g 14.1.6.
|t Summary of l'Hôpital's rule types --
|g 14.2.
|t Overview of limits --
|g 15.
|t Introduction to integration --
|g 15.1.
|t Sigma notation --
|g 15.1.1. A
|t nice sum --
|g 15.1.2.
|t Telescoping series --
|g 15.2.
|t Displacement and area --
|g 15.2.1.
|t Three simple cases --
|g 15.2.2. A
|t more general journey --
|g 15.2.3.
|t Signed area --
|g 15.2.4.
|t Continuous velocity --
|g 15.2.5.
|t Two special approximations --
|g 16.
|t Definite integrals --
|g 16.1. The
|t basic idea --
|g 6.1.1.
|t Some easy example --
|g 16.2.
|t Definition of the definite integral --
|g 16.2.1. An
|t example of using the definition --
|g 16.3.
|t Properties of definite integrals --
|g 16.4.
|t Finding areas --
|g 16.4.1.
|t Finding the unsigned area --
|g 16.4.2.
|t Finding the area between two curves --
|g 16.4.3.
|t Finding the area between a curve and the y-axis --
|g 16.5.
|t Estimating integrals --
|g 16.5.1. A
|t simple type of estimation --
|g 16.6.
|t Averages and the mean value theorem for integrals --
|g 16.6.1. The
|t mean value theorem for integrals --
|g 16.7. A
|t nonintegrable function --
|
505 |
0 |
0 |
|g 17. The
|t fundamental theorems of calculus --
|g 17.1.
|t Functions based on integrals of other functions --
|g 17.2. The
|t first fundamental theorem --
|g 17.2.1.
|t Introduction to antiderivatives --
|g 17.3. The
|t second fundamental theorem --
|g 17.4.
|t Indefinite integrals --
|g 17.5.
|t How to solve problems : the first fundamental theorem --
|g 17.5.1.
|t Variation 1 : variable left-hand limit on integration --
|g 17.5.2.
|t Variation 2 : one tricky limit of integration --
|g 17.5.3.
|t Variation 3 : two tricky limits of integration --
|g 17.5.4.
|t Variation 4 : limit is a derivative in disguise --
|g 17.6.
|t How to solve problems : the second fundamental theorem --
|g 17.6.1.
|t Finding indefinite integrals --
|g 17.6.2.
|t Finding definite integrals --
|g 17.6.3.
|t Unsigned areas and absolute values --
|g 17.7. A
|t technical point --
|g 17.8.
|t Proof of the first fundamental theorem --
|g 18.
|t Techniques of integration, part one --
|g 18.1.
|t Substitution --
|g 18.1.1.
|t Substitution and definite integrals --
|g 18.1.2.
|t How to decide what to substitute --
|g 18.1.3.
|t Theoretical justification of the substitution method --
|g 18.2.
|t Integration by parts --
|g 18.2.1.
|t Some variations --
|g 18.3.
|t Partial fractions --
|g 18.3.1. The
|t algebra of partial fractions --
|g 18.3.2.
|t Integrating the pieces --
|g 18.3.3. The
|t method and a big example --
|
505 |
0 |
0 |
|g 19.
|t Techniques of integration, part two --
|g 19.1.
|t Integrals involving trig identities --
|g 19.2.
|t Integrals involving powers of trig functions --
|g 19.2.1.
|t Powers of sin and/or cos --
|g 19.2.2.
|t Powers of tan --
|g 19.2.3.
|t Powers of sec --
|g 19.2.4.
|t Powers of cot --
|g 19.2.5.
|t Powers of csc --
|g 19.2.6.
|t Reduction formulas --
|g 19.3.
|t Integrals involving trig substitutions --
|g 19.3.1.
|t Type 1 : [square root] a² - x² --
|g 19.3.2.
|t Type 2 : [square root] x² + a² --
|g 19.3.3.
|t Type 3 : [square root] x² - a² --
|g 19.3.4.
|t Completing the square and trig substitutions --
|g 19.3.5.
|t Summary of trig substitutions --
|g 19.3.6.
|t Technicalities of square roots and trig substitutions --
|g 19.4.
|t Overview of techniques of integration --
|g 20.
|t Improper integrals : basic concepts --
|g 20.1.
|t Convergence and divergence --
|g 20.1.1.
|t Some examples of improper integrals --
|g 20.1.2.
|t Other blow-up points --
|g 20.2.
|t Integrals over unbounded regions --
|g 20.3. The
|t comparison test (theory) --
|g 20.4. The
|t limit comparison test (theory) --
|g 20.4.1.
|t Functions asymptotic to each other --
|g 20.4.2. The
|t statement of the test --
|g 20.5. The
|t p-test (theory) --
|g 20.6. The
|t absolute convergence test --
|
505 |
0 |
0 |
|g 21.
|t Improper integrals : how to solve problems --
|g 21.1.
|t How to get started --
|g 21.1.1.
|t Splitting up the integral --
|g 21.1.2.
|t How to deal with negative function values --
|g 21.2.
|t Summary of integral tests --
|g 21.3.
|t Behavior of common functions near [infinity] and -[infinity] --
|g 21.3.1.
|t Polynomials and poly-type functions near [infinity] and -[infinity] --
|g 21.3.2.
|t Trig function near [infinity] and -[infinity] --
|g 21.3.3.
|t Exponentials near [infinity] and -[infinity] --
|g 21.3.4.
|t Logarithms near [infinity] --
|g 21.4.
|t Behavior of common functions near 0 --
|g 21.4.1.
|t Polynomials and poly-type functions near 0 --
|g 21.4.2.
|t Trig functions near 0 --
|g 21.4.3.
|t Exponentials near 0 --
|g 21.4.4.
|t Logarithms near 0 --
|g 21.4.5. The
|t behavior of more general functions near 0 --
|g 21.5.
|t How to deal with problem spots not at 0 or [infinity] --
|g 22.
|t Sequences and series : basic concepts --
|g 22.1.
|t Convergence and divergence of sequences --
|g 22.1.1. The
|t connection between sequences and functions --
|g 22.1.2.
|t Two important sequences --
|g 22.2.
|t Convergence and divergence of series --
|g 22.2.1.
|t Geometric series (theory) --
|g 22.3. The
|t nth term test (theory) --
|g 22.4.
|t Properties of both infinite series and improper integrals --
|g 22.4.1. The
|t comparison test (theory) --
|g 22.4.2. The
|t limit comparison test (theory) --
|g 22.4.3. The
|t p-test (theory) --
|g 22.4.4.
|t absolute convergence test --
|g 22.5.
|t New tests for series --
|g 22.5.1. The
|t ratio test (theory) --
|g 22.5.2. The
|t root test (theory) --
|g 22.5.3. The
|t integral test (theory) --
|g 22.5.4. The
|t alternating series test (theory) --
|
505 |
0 |
0 |
|g 23.
|t How to solve series problems --
|g 23.1.
|t How to evaluate geometric series --
|g 23.2.
|t How to use the nth term test --
|g 23.3.
|t How to use the ratio test --
|g 23.4.
|t How to use the root test --
|g 23.5.
|t How to use the integral test --
|g 23.6.
|t Comparison test, limit comparison test, and p-test --
|g 23.7.
|t How to deal with series with negative terms --
|g 24.
|t Taylor polynomials, Taylor series, and power series --
|g 24.1.
|t Approximations and Taylor polynomials --
|g 24.1.1.
|t Linearization revisited --
|g 24.1.2.
|t Quadratic approximations --
|g 24.1.3.
|t Higher-degree approximations --
|g 24.1.4.
|t Taylor's theorem --
|g 24.2.
|t Power series and Taylor series --
|g 24.2.1.
|t Power series in general --
|g 24.2.2.
|t Taylor series and Maclaurin series --
|g 24.2.3.
|t Convergence of Taylor series --
|g 24.3. A
|t useful limit --
|g 25.
|t How to solve estimation problems --
|g 25.1.
|t Summary of Taylor polynomials and series --
|g 25.2.
|t Finding Taylor polynomials and series --
|g 25.3.
|t Estimation problems using the error term --
|g 25.3.1.
|t First example --
|g 25.3.2.
|t Second example --
|g 25.3.3.
|t Third example --
|g 25.3.4.
|t Fourth example --
|g 25.3.5.
|t Fifth example --
|g 25.3.6.
|t General techniques for estimating the error term --
|g 25.4.
|t Another technique for estimating the error --
|
505 |
0 |
0 |
|g 26.
|t Taylor and power series : how to solve problems --
|g 26.1.
|t Convergence of power series --
|g 26.1.1.
|t Radius of convergence --
|g 26.1.2.
|t How to find the radius and region of convergence --
|g 26.2.
|t Getting new Taylor series from old ones --
|g 26.2.1.
|t Substitution and Taylor series --
|g 26.2.2.
|t Differentiating Taylor series --
|g 26.2.3.
|t Integrating Taylor series --
|g 26.2.4.
|t Adding and subtracting Taylor series --
|g 26.2.5.
|t Multiplying Taylor series --
|g 26.2.6.
|t Dividing Taylor series --
|g 26.3.
|t Using power and Taylor series to find derivatives --
|g 26.4.
|t Using Maclaurin series to find limits --
|g 27.
|t Parametric equations and polar coordinates --
|g 27.1.
|t Parametric equations --
|g 27.1.1.
|t Derivatives of parametric equations --
|g 27.2.
|t Polar coordinates --
|g 27.2.1.
|t Converting to and from polar coordinates --
|g 27.2.2.
|t Sketching curves in polar coordinates --
|g 27.2.3.
|t Find tangents to polar curves --
|g 27.2.4.
|t Finding areas enclosed by polar curves --
|g 28.
|t Complex numbers --
|g 28.1. The
|t basics --
|g 28.1.1.
|t Complex exponentials --
|g 28.2. The
|t complex plane --
|g 28.2.1.
|t Converting to and from polar form --
|g 28.3.
|t Taking large powers of complex numbers --
|g 28.4.
|t Solving zn = w --
|g 28.4.1.
|t Some variations --
|g 28.5.
|t Solving ez = w --
|g 28.6.
|t Some trigonometric series --
|g 28.7.
|t Euler's identity and power series --
|
505 |
0 |
0 |
|g 29.
|t Volumes, arc lengths, and surface areas --
|g 29.1.
|t Volumes of solids of revolution --
|g 29.1.1. The
|t disc method --
|g 29.1.2. The
|t shell method --
|g 29.1.3.
|t Summary... and variations --
|g 29.1.4.
|t Variation 1 : regions between a curve and the y-axis --
|g 29.1.5.
|t Variation 2 : regions between two curves --
|g 29.1.6.
|t Variation 3 : axes parallel to the coordinate axes --
|g 29.2.
|t Volumes of general solids --
|g 29.3.
|t Arc lengths --
|g 29.3.1.
|t Parametrization and speed --
|g 29.4.
|t Surface areas of solids of revolution --
|g 30.
|t Differential equations --
|g 30.1.
|t Introduction to differential equations --
|g 30.2.
|t Separable first-order differential equations --
|g 30.3.
|t First-order linear equations --
|g 30.3.1.
|t Why the integrating factor works --
|g 30.4.
|t Constant-coefficient differential equations --
|g 30.4.1.
|t Solving first-order homogeneous equations --
|g 30.4.2.
|t Solving second-order homogeneous equations --
|g 30.4.3.
|t Why the characteristic quadratic method works --
|g 30.4.4.
|t Nonhomogeneous equations and particular solutions --
|g 30.4.5.
|t Funding a particular solution --
|g 30.4.6.
|t Examples of finding particular solutions --
|g 30.4.7.
|t Resolving conflicts between yP and yH --
|g 30.4.8.
|t Initial value problems (constant-coefficient linear) --
|g 30.5.
|t Modeling using differential equations --
|
505 |
0 |
0 |
|t Appendix A : Limits and proofs --
|g A.1.
|t Formal definition of a limit --
|g A.1.1. A
|t little game --
|g A.1.2. The
|t actual definition --
|g A.1.3.
|t Examples of using the definition --
|g A.2.
|t Making new limits from old ones --
|g A.2.1.
|t Sums and differences of limits, proofs --
|g A.2.2.
|t Products of limits, proof --
|g A.2.3.
|t Quotients of limits, proof --
|g A.2.4. The
|t sandwich principle, proof --
|g A.3.
|t Other varieties of limits --
|g A.3.1.
|t Infinite limits --
|g A.3.2.
|t Left-hand and right-hand limits --
|g A.3.3.
|t Limits at [infinity] and -[infinity] --
|g A.3.4.
|t Two examples involving trig --
|g A.4.
|t Continuity and limits --
|g A.4.1.
|t Composition of continuous functions --
|g A.4.2.
|t Proof of the intermediate value theorem --
|g A.4.3.
|t Proof of the max-min theorem --
|g A.5.
|t Exponentials and logarithms revisited --
|g A.6.
|t Differentiation and limits --
|g A.6.1.
|t Constant multiples of functions --
|g A.6.2.
|t Sums and differences of functions --
|g A.6.3.
|t Proof of the product rule --
|g A.6.4.
|t Proof of the quotient rule --
|g A.6.5.
|t Proof of the chain rule --
|g A.6.6.
|t Proof of the extreme value theorem --
|g A.6.7.
|t Proof of Rolle's theorem --
|g A.6.8.
|t Proof of the mean value theorem --
|g A.6.9. The
|t error in linearization --
|g A.6.10.
|t Derivatives of piecewise-defined functions --
|g A.6.11.
|t Proof of l'Hôspital's rule --
|g A.7.
|t Proof of the Taylor approximation theorem --
|t Appendix B : Estimating integrals --
|g B.1.
|t Estimating integrals using strips --
|g B.1.1.
|t Evenly spaced partitions --
|g B.2. The
|t trapezoidal rule --
|g B.3.
|t Simpson's rule --
|g B.3.1.
|t Proof of Simpson's rule --
|g B.4. The
|t error in our approximations --
|g B.4.1.
|t Examples of estimating the error --
|g B.4.2.
|t Proof of an error term inequality --
|t List of symbols --
|t Index.
|
650 |
|
0 |
|a Calculus.
|
856 |
4 |
2 |
|3 Contributor biographical information
|u http://catdir.loc.gov/catdir/enhancements/fy0809/2006939343-b.html
|t 0
|
856 |
4 |
2 |
|3 Publisher description
|u http://catdir.loc.gov/catdir/enhancements/fy0809/2006939343-d.html
|t 0
|
856 |
4 |
1 |
|3 Table of contents only
|u http://catdir.loc.gov/catdir/enhancements/fy0809/2006939343-t.html
|t 0
|
907 |
|
|
|a .b15380208
|b 05-23-16
|c 08-07-08
|
998 |
|
|
|a hz
|a hq
|b 09-19-08
|c m
|d a
|e -
|f eng
|g nju
|h 4
|i 0
|
994 |
|
|
|a C0
|b HCD
|
945 |
|
|
|f - -
|g 1
|h 0
|i 38400003749411
|j - -
|k 03-21-2016 12:11
|l hqcol
|o -
|p $0.00
|q -
|r -
|s -
|t 0
|u 8
|v 1
|w 8
|x 0
|y .i15891562
|z 09-19-08
|
999 |
f |
f |
|i 5e054cad-6f2d-5453-8c2c-ee38de156edc
|s d665b2a8-1818-5d93-aa75-d2437ee45ec4
|t 0
|
952 |
f |
f |
|p Can Circulate
|a College of the Holy Cross
|b Main Campus
|c Science
|d Science Library
|t 0
|e QA303.2 .B36 2007
|h Library of Congress classification
|i Book
|m 38400003749411
|