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Location Call Number / Copy Notes Barcode Shelving Location Status Due Date
Covington-Veedersburg PL - Covington 515 ABB (Text) 32572000216531 CVBPLC Adult Nonfiction Available -
Monticello-Union Twp PL - Monticello NONFICTION 515 ABBOTT (Text) 37743001682477 Adult Nonfiction Checked out 09/21/2018

Record details

  • ISBN: 0071421289 :
  • Physical Description: ix, 316 pages : illustrations ; 20 cm.
  • Edition: Rev. [ed.] / revised by Hugh Neill.
  • Publisher: London : Hodder & Stoughton Educational ; [2003]

Content descriptions

Bibliography, etc. Note:
Includes index.
Subject: Calculus.
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functions
1(11)
what is calculus?
2(1)
functions
2(2)
equations of functions
4(1)
general notation for functions
4(1)
notation for increases in functions
5(1)
graphs of functions
6(2)
using calculators or computers for plotting functions
8(1)
inverse functions
9(1)
implicit functions
9(1)
functions of more than one variable
10(1)
variations in functions; limits
11(11)
variations in functions
12(2)
limits
14(1)
limit of a function of theorem 0/0
15(2)
a trigonometric limit, lim θ → 0 sin θ/θ = 1
17(1)
a geometric illustration of a limit
18(1)
theorems on limits
19(3)
gradient
22(9)
gradient of the line joining two points
23(2)
equation of a straight line
25(1)
approximating to gradients of curves
26(1)
towards a definition of gradient
27(2)
definition of the gradient of a curve
29(1)
negative gradient
29(2)
rate of change
31(10)
the average change of a function over an interval
32(2)
the average rate of change of a non-linear function
34(1)
motion of a body with non-constant velocity
35(3)
graphical interpretation
38(1)
a definition of rate of change
39(2)
differentiation
41(12)
algebraic approach to the rate of change of a function
42(2)
the derived function
44(1)
notation for the derivative
45(1)
differentials
46(1)
sign of the derivative
47(1)
some examples of differentiation
47(6)
some rules for differentiation
53(19)
differentiating a sum
54(2)
differentiating a product
56(3)
differentiating a quotient
59(2)
function of a function
61(5)
differentiating implicit functions
66(1)
successive differentiation
67(2)
alternative notation for derivatives
69(1)
graphs of derivatives
70(2)
maxima, minima and points of inflexion
72(20)
sign of the derivative
73(1)
stationary values
74(2)
turning points
76(2)
maximum and minimum values
78(3)
which are maxima and which are minima?
81(1)
a graphical illustration
82(2)
some worked examples
84(3)
points of inflexion
87(5)
differentiating the trigonometric functions
92(20)
using radians
93(1)
differentiating sin x
93(1)
differentiating cos x
94(1)
differentiating tan x
95(1)
differentiating sec x, cosec x, cot x
95(1)
summary of results
96(1)
differentiating trigonometric functions
97(2)
successive derivatives
99(1)
graphs of the trigonometric functions
100(5)
inverse trigonometric functions
105(1)
differentiating sin-1 x and cos-1 x
105(2)
differentiating tan-1 x and cot-1 x
107(1)
differentiating sec-1 x and cosec-1 x
108(1)
summary of results
109(3)
exponential and logarithmic functions
112(12)
compound interest Law of growth
113(1)
the value of lim n → ∞ (1+1/n)n
114(1)
the compound interest law
115(1)
differentiating ex
116(2)
the exponential curve
118(1)
natural logarithms
119(1)
differentiating ln x
120(1)
differentiating general exponential functions
121(1)
summary of formulae
121(1)
worked examples
121(3)
hyperbolic functions
124(14)
definitions of hyperbolic functions
125(2)
formulae connected with hyperbolic functions
127(1)
summary
128(1)
derivatives of the hyperbolic functions
129(1)
graphs of the hyperbolic functions
130(1)
differentiating the inverse hyperbolic functions
131(2)
logarithm equivalents of the inverse hyperbolic functions
133(2)
summary of inverse functions formulae
135(3)
integration; standard integrals
138(18)
meaning of integration
139(1)
the constant of integration
140(2)
the symbol for integration
142(1)
integrating a constant factor
143(1)
integrating xn
143(2)
integrating a sum
145(1)
integrating 1/x
146(1)
a useful rule for integration
147(3)
integrals of standard forms
150(2)
additional standard integrals
152(4)
methods of integration
156(16)
introduction
157(1)
trigonometric functions
157(2)
integration by substitution
159(1)
some trigonometrical substitutions
159(2)
the substitution t = tan 1/2x
161(2)
worked examples
163(2)
algebraic substitutions
165(2)
integration by parts
167(5)
integration of algebraic fractions
172(12)
rational fractions
173(1)
denominators of the form ax2 + bx + c
174(1)
denominator a perfect square
175(1)
denominator a difference of squares
175(2)
denominator a sum of squares
177(2)
denominators of higher degree
179(1)
denominators with square roots
180(4)
area and definite integrals
184(16)
areas by integration
185(2)
definite integrals
187(2)
characteristics of a definite integral
189(3)
some properties of definite integrals
192(2)
infinite limits and infinite integrals
194(1)
infinite limits
194(2)
functions with infinite values
196(4)
the integral as a sum; areas
200(31)
approximation to area by division into small elements
201(2)
the definite integral as the limit of a sum
203(1)
examples of areas
204(9)
sign of an area
213(9)
polar coordinates
222(2)
plotting curves from their equations in polar coordinates
224(2)
areas in polar coordinates
226(2)
mean value
228(3)
approximate integration
231(7)
the need for approximate integration
232(1)
the trapezoidal rule
232(2)
Simpson's rule for area
234(4)
volumes of revolution
238(8)
solids of revolution
239(1)
volume of a cone
239(1)
general formula for volumes of solids of revolution
240(3)
volume of a sphere
243(1)
examples
243(3)
lengths of curves
246(8)
lengths of arcs of curves
247(3)
length in polar coordinates
250(4)
Taylor's and Maclaurin's series
254(9)
infinite series
255(1)
convergent and divergent series
255(1)
Taylor's expansion
256(2)
Maclaurin's series
258(3)
expansion by the differentiation and the integration of known series
261(2)
differential equations
263(19)
introduction and definitions
264(2)
type i: one variable absent
266(1)
type ii: variables separable
267(2)
type iii: linear equations
269(3)
type iv: linear differential equations with constant coefficients
272(6)
type v: homogeneous equations
278(4)
applications of differential equations
282(10)
introduction
283(1)
problems involving rates
283(2)
problems involving elements
285(7)
answers 292(21)
index 313


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