First-year calculus
By: by Einar Hille and Saturnino L. Salas.
Contributors: Salas, S. L.
Edition: 1
Series: A Blaisdell book in pure and applied mathematics
Publisher: Blaisdell Publishing Co.
Published: 1968
Place of publication: Waltham (Mass.); London
Language: eng
Number of pages: 415
Subjects: Calculus.
Other titles: First year calculus.
First sentence: This is a textbook for the first year of college calculus.
Table of contents: pagenum: 1
label: 1
class: chapter
title: Preliminaries; pagenum: 1
label: 1.1
class: part
title: Sets; pagenum: 3
label: 1.2
class: part
title: Real numbers; pagenum: 7
title: The coordinate line
class: part
label: 1.3; pagenum: 9
title: Inequalities on the line
class: part
label: 1.4; pagenum: 13
label: 1.5
class: part
title: The coordinate plane; pagenum: 15
label: 1.6
class: part
title: The straight line; pagenum: 19
label: 1.7
class: part
title: Pairs of lines; pagenum: 22
label: 1.8
class: part
title: Some subsets of the plane and their analytic representations; pagenum: 25
label: 1.9
class: part
title: Symmetry and boundedness; pagenum: 29
label: 1.10
class: part
title: Functions; pagenum: 34
label: 1.11
class: part
title: More on functions; pagenum: 38
title: Combining functions
class: part
label: 1.12; pagenum: 41
title: The axiom of induction
class: part
label: 1.13; pagenum: 44
title: The Limit of a Function
class: part
label: 2; pagenum: 44
label: 2.1
class: part
title: Preliminary intuitive discussion; pagenum: 46
label: 2.2
class: part
title: Definition of limit; pagenum: 54
title: Limit theorems
class: part
label: 2.3; pagenum: 61
label: 2.4
class: part
title: More theorems on limits; pagenum: 64
label: 2.5
class: part
title: One-sided limits; pagenum: 68
title: Continuity
class: part
label: 2.6; pagenum: 74
label: 3
class: part
title: Differentiation; pagenum: 74
title: Motivation
class: part
label: 3.1; pagenum: 76
label: 3.2
class: part
title: The derivative; pagenum: 78
title: Some rules for differentiation
class: part
label: 3.3; pagenum: 83
title: The chain rule
class: part
label: 3.4; pagenum: 87
label: 3.5
class: part
title: Derivatives of higher orders; another notation; pagenum: 88
title: The tangent line
class: part
label: 3.6; pagenum: 91
label: 3.7
class: part
title: The mean-value theorem; pagenum: 94
label: 3.8
class: part
title: The derivative and monotonicity; pagenum: 98
label: 3.9
class: part
title: Extreme values; pagenum: 104
label: 3.10
class: part
title: Concavity and points of inflection; pagenum: 107
title: Rates of change
class: part
label: 3.11; pagenum: 113
title: The notations of Newton on Leibniz
class: part
label: 3.12; pagenum: 115
title: The Integral of a Continuous Function
class: part
label: 4; pagenum: 115
label: 4.1
class: part
title: Motivation; pagenum: 118
label: 4.2
class: part
title: Definition of the definite integral; pagenum: 121
title: The function F(x) = inegral x to a f(t) dt
class: part
label: 4.3; pagenum: 126
title: The fundamental theorem of integral calculus
class: part
label: 4.4; pagenum: 132
label: 4.5
class: part
title: Some properties of the integral; pagenum: 137
title: The Logarithm and Exponential Functions
class: part
label: 5; pagenum: 137
label: 5.1
class: part
title: The logarithm function; pagenum: 145
title: The exponential funciton
class: part
label: 5.2; pagenum: 154
title: The functions p^x and log base p x; estimating e
class: part
label: 5.3; pagenum: 161
label: 5.4
class: part
title: Integration by parts; pagenum: 165
label: 5.5
class: part
title: (Optional) The equation y'(x) + P(x)y(x) = Q(x); pagenum: 169
label: 6
class: part
title: The Trigonometric Functions; pagenum: 169
label: 6.1
class: part
title: The least-upper-bound axiom; pagenum: 171
label: 6.2
class: part
title: Circular arc length; pagenum: 178
title: The trigonometric functions
class: part
label: 6.3; pagenum: 185
title: Differentiating the trigonometric functions
class: part
label: 6.4; pagenum: 189
label: 6.5
class: part
title: Integrating the trigonometric functions; pagenum: 193
title: The inverse trigonometric functions
class: part
label: 6.6; pagenum: 200
label: 6.7
class: part
title: (Optional) The differential equation y" + ay' + by = 0; pagenum: 202
label: 7
class: part
title: Some Analytic Geometry; pagenum: 202
title: The distance between a point and a line; translations
class: part
label: 7.1; pagenum: 206
label: 7.2
class: part
title: The conic sections; pagenum: 206
title: The parabola
class: part
label: 7.3; pagenum: 214
title: The ellipse
class: part
label: 7.4; pagenum: 219
label: 7.5
class: part
title: The hyperbola; pagenum: 225
label: 7.6
class: part
title: Polar coordinates; pagenum: 229
label: 7.7
class: part
title: Curves given parametrically; pagenum: 236
label: 7.8
class: part
title: Rotations: eliminating the xy-term; pagenum: 242
label: 7.9
class: part
title: Curvature; pagenum: 248
label: 8
class: part
title: The Technique of Integration; pagenum: 248
title: A short table of integrals; review
class: part
label: 8.1; pagenum: 252
label: 8.2
class: part
title: The method of partial fractions; pagenum: 260
label: 8.3
class: part
title: Integration by substitution; pagenum: 266
title: The indefinite integral notation
class: part
label: 8.4; pagenum: 267
label: 8.5
class: part
title: Approximate integration; pagenum: 272
label: 9
class: part
title: Integration as an Averaging Process: Applications; pagenum: 272
title: The average value of a function
class: part
label: 9.1; pagenum: 276
title: Area and volume
class: part
label: 9.2; pagenum: 288
label: 9.3
class: part
title: Area in polar coordinates; pagenum: 291
title: Arc length
class: part
label: 9.4; pagenum: 299
title: Area of a surface of revolution
class: part
label: 9.5; pagenum: 303
label: 9.6
class: part
title: (Optional) The notion of work; pagenum: 307
label: 9.7
class: part
title: (Optional) Moment of area; pagenum: 312
title: (Optional) Some remarks on the integral as a set function
class: section
label: 9.8; pagenum: 316
title: Sequences and Series
class: part
label: 10; pagenum: 316
title: Sequences of real numbers
class: part
label: 10.1; pagenum: 320
title: The limit of a sequence
class: part
label: 10.2; pagenum: 330
label: 10.3
class: part
title: Some important limits; pagenum: 333
title: Some comments on notation
class: part
label: 10.4; pagenum: 334
title: Infinite series
class: part
label: 10.5; pagenum: 339
title: Taylor series
class: part
label: 10.6; pagenum: 346
label: 10.7
class: part
title: The logarithm and the arc tangent; computing pi; pagenum: 349
label: 10.8
class: part
title: Series with nonnegative terms; pagenum: 357
title: Convergence and absolute convergence; alternating series
class: part
label: 10.9; pagenum: 359
label: 10.10
class: part
title: Power series; pagenum: 369
label: 11
class: part
title: Problems on Supplementary Topics; pagenum: 369
title: Limits as x -> +- infinity
class: part
label: 11.1; pagenum: 371
title: L'Hospital's rule (0/0)
class: part
label: 11.2; pagenum: 373
title: Infinite limits
class: part
label: 11.3; pagenum: 375
label: 11.4
class: part
title: L'Hospital's rule (infinity/infinity); pagenum: 377
label: 11.5
class: part
title: Improper integrals; pagenum: 382
title: More on the hyperbolic cosine and hyperbolic sine
class: part
label: 11.6; pagenum: 385
title: Appendix
class: part
label: A; pagenum: 385
label: A.1
class: part
title: The intermediate-value theorem; pagenum: 386
label: A.2
class: part
title: The maximum-minimum theorem; pagenum: 387
label: A.3
class: part
title: The integrability of continuous functions; pagenum: 391
title: Table of integrals
class: part
label: B; pagenum: 393
label: C
class: part
title: Answers to starred excercises; pagenum: 411
title: Index
class: part
label: D