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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