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Teach Yourself Calculus

by: Neill, Hugh

Teach Yourself Calculus

by: Neill, Hugh

ISBN 13:
9780071421287
ISBN 10:
0071421289
Edition: 2nd
Format: Paperback
Copyright: 07/25/2003
Publisher: McGraw-Hill
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Summary

WhileTeach Yourself Calculusis perfect for beginners who want to acquire a working knowledge of calculus, at the same time it is an excellent tool for anyone who wants to expand their knowledge beyond the basics. In a progressive, step-by-step fashion, the book builds from the ground up to offer comprehensive coverage of a range of more advanced topics such as multiple integrals. Each chapter features numerous worked examples and graded exercises.

functions

(11)

what is calculus?

(1)

functions

(2)

equations of functions

(1)

general notation for functions

(1)

notation for increases in functions

(1)

graphs of functions

(2)

using calculators or computers for plotting functions

(1)

inverse functions

(1)

implicit functions

(1)

functions of more than one variable

(1)

variations in functions; limits

(11)

variations in functions

(2)

limits

(1)

limit of a function of theorem 0/0

(2)

a trigonometric limit, lim θ → 0 sin θ/θ = 1

(1)

a geometric illustration of a limit

(1)

theorems on limits

(3)

gradient

(9)

gradient of the line joining two points

(2)

equation of a straight line

(1)

approximating to gradients of curves

(1)

towards a definition of gradient

(2)

definition of the gradient of a curve

(1)

negative gradient

(2)

rate of change

(10)

the average change of a function over an interval

(2)

the average rate of change of a non-linear function

(1)

motion of a body with non-constant velocity

(3)

graphical interpretation

(1)

a definition of rate of change

(2)

differentiation

(12)

algebraic approach to the rate of change of a function

(2)

the derived function

(1)

notation for the derivative

(1)

differentials

(1)

sign of the derivative

(1)

some examples of differentiation

(6)

some rules for differentiation

(19)

differentiating a sum

(2)

differentiating a product

(3)

differentiating a quotient

(2)

function of a function

(5)

differentiating implicit functions

(1)

successive differentiation

(2)

alternative notation for derivatives

(1)

graphs of derivatives

(2)

maxima, minima and points of inflexion

(20)

sign of the derivative

(1)

stationary values

(2)

turning points

(2)

maximum and minimum values

(3)

which are maxima and which are minima?

(1)

a graphical illustration

(2)

some worked examples

(3)

points of inflexion

(5)

differentiating the trigonometric functions

(20)

using radians

(1)

differentiating sin x

(1)

differentiating cos x

(1)

differentiating tan x

(1)

differentiating sec x, cosec x, cot x

(1)

summary of results

(1)

differentiating trigonometric functions

(2)

successive derivatives

(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

Amazon no longer offers textbook rentals. We do!

Teach Yourself Calculus

Teach Yourself Calculus

9780071421287

0071421289

Summary

Author Biography

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Teach Yourself Calculus

Teach Yourself Calculus

9780071421287

0071421289

Summary

Author Biography

Table of Contents

Supplemental Materials

Write a Review

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