Calculus: Analytic Geometry and Calculus, with Vectors | Date: 15 April 2011, 11:50
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ASIN: B000OETBGG
Table of Contents
CHAPTER 1
Analytic geometry in two dimensions 1
1.1 Real numbers 1
1.2 Slopes and equations of lines 10
1.3 Lines and linear equations; parallelism and perpendicularity
1.4 Distances, circles, and parabolas 24
1.5 Equations, statements, and graphs 35
1.6 Introduction to velocity and acceleration 41
CHAPTER 2
Vectors and geometry in three dimensions 48
2.1 Vectors in E3 48
2.2 Coordinate systems and vectors in E3 59
2.3 Scalar products, direction cosines, and lines in E3 67
2.4 Planes and lines in E3 78
2.5 Determinants and applications 87
2.6 Vector products and changes of coordinates in E3 97
CHAPTER 3
Functions, limits, derivatives 111
3.1 Functional notation 111
3.2 Limits 122
3.3 Unilateral limits and asymptotes 133
3.4 Continuity 144
3.5 Difference quotients and deriva tives 152
3.6 The chain rule and differentiation of elementary functions
3.7 Rates, velocities 176
3.8 Related rates 188
3.9 Increments and differentials 193
CHAPTER 4
Integrals 202
4.1 Indefinite integrals 202
4.2 Riemann sums and integrals 212
4.3 Properties of integrals 224
4.4 Areas and integrals 235
4.5 Volumes and integrals 244
4.6 Riemann-Cauchy integrals and work 250
4.7 Mass, linear density, and moments 259
4.8 Moments and centroids in E2 and Es 269
4.9 Simpson and other approximations to integrals 276
CHAPTER 5
Functions, graphs, and numbers 284
5.1 Graphs, slopes, and tangents 284
5.2 Trends, maxima, and minima 294
5.3 Second derivatives, convexity, and flexpoints 304
5.4 Theorems about continuous and differentiable funetions 313
5.5 The Rolle theorem and the mean-value theorem 324
5.6 Sequences, series, and decimals 334
5.7 Darboux sums and Riemann integrals 344
CHAPTER 6
Cones and conics 354
6.1 Parabolas 354
6.2 Geometry of cones and conics
6.3 Ellipses 369
6.4 Hyperbolas 379
6.5 Translation and rotation of axes
6.6 Quadric surfaces 402
CHAPTER 7
Curves, lengths. and curvatures 408
7.1 Curves and lengths 408
7.2 Lengths and integrals 417
7.3 Center and radius of curvature 428
CHAPTER 8
Trigonometric functions 438
8.1 Trigonometric functions and their derivatives 438
8.2 Trigonometric integrands 449
8.3 Inverse trigonometrie functions 458
8.4 Integration by trigonometric and other substitutions 469
8.5 Integration by substituting z = tan x/2 477
CHAPTER 9
Exponential and logarithmic functions 480
9.1 Exponentiais and Iogarithms 480
9.2 Derivatives and integrais of exponentiais and logarithms 491
9.3 Hyperbolic functions 505
9.4 Parti al fractions 511
9.5 Integration by parts 518
CHAPTER 10
Polar, cylindrical, and spherical coordinates 526
10.1 Geometry of coordinate systems 526
10.2 Polar curves, tangents, and lengths 538
10.3 Areas and integrals involving polar coordinates 547
CHAPTER 11
Partial derivatives 553
11.1 Elementary partial derivatives 553
11.2 Increments, chain ruIe, and gradients 562
11.3 Formulas involving partiai derivatives 576
CHAPTER 12
Series 587
12.1 Definitions and basic theorems 587
12.2 Ratio test and integraI test 599
12.3 Alternating seriea and Fourier series 610
12.4 Power series 619
12.5 TayIor formulas with remainders 632
12.6 EuIer-Maclaurin summation formulas 640
CHAPTER 13
Iterated and multiple integrals 652
13.1 Iterated integrais 652
13.2 Iterated integrais and volumes 659
13.3 Double integrals 667
13.4 Rectanguiar coordinate applications of double and iterated integrals
676
13.5 Integrals in polar coordinates 687
13.6 Triple integrals; rectangular coordinates 695
13.7 Triple integrals; cylindrical coordinates
13.8 Triple integrals; spherical coordinates
APPENDIX 1
Proofs of basic theorems on limits 715
APPENDIX 2
Volumes 721
INDEX 725
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