[教材书籍] [《托马斯微积分》.第12版习题答案].Thomas Calculus 12th Edition Solutions [推广有奖]

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Thomas 12th Single Variable Solutions.pdf (27.92 MB, 需要: 5 个论坛币)

Thomas 12th Multivariable Solutions.pdf (12.69 MB, 需要: 5 个论坛币)
TABLE OF CONTENTS
1 Functions 1
1.1 Functions and Their Graphs 1
1.2 Combining Functions; Shifting and Scaling Graphs 8
1.3 Trigonometric Functions 19
1.4 Graphing with Calculators and Computers 26
Practice Exercises 30
Additional and Advanced Exercises 38
2 Limits and Continuity 43
2.1 Rates of Change and Tangents to Curves 43
2.2 Limit of a Function and Limit Laws 46
2.3 The Precise Definition of a Limit 55
2.4 One-Sided Limits 63
2.5 Continuity 67
2.6 Limits Involving Infinity; Asymptotes of Graphs 73
Practice Exercises 82
Additional and Advanced Exercises 86
3 Differentiation 93
3.1 Tangents and the Derivative at a Point 93
3.2 The Derivative as a Function 99
3.3 Differentiation Rules 109
3.4 The Derivative as a Rate of Change 114
3.5 Derivatives of Trigonometric Functions 120
3.6 The Chain Rule 127
3.7 Implicit Differentiation 135
3.8 Related Rates 142
3.9 Linearizations and Differentials 146
Practice Exercises 151
Additional and Advanced Exercises 162
4 Applications of Derivatives 167
4.1 Extreme Values of Functions 167
4.2 The Mean Value Theorem 179
4.3 Monotonic Functions and the First Derivative Test 188
4.4 Concavity and Curve Sketching 196
4.5 Applied Optimization 216
4.6 Newton's Method 229
4.7 Antiderivatives 233
Practice Exercises 239
Additional and Advanced Exercises 251
5 Integration 257
5.1 Area and Estimating with Finite Sums 257
5.2 Sigma Notation and Limits of Finite Sums 262
5.3 The Definite Integral 268
5.4 The Fundamental Theorem of Calculus 282
5.5 Indefinite Integrals and the Substitution Rule 290
5.6 Substitution and Area Between Curves 296
Practice Exercises 310
Additional and Advanced Exercises 320
6 Applications of Definite Integrals 327
6.1 Volumes Using Cross-Sections 327
6.2 Volumes Using Cylindrical Shells 337
6.3 Arc Lengths 347
6.4 Areas of Surfaces of Revolution 353
6.5 Work and Fluid Forces 358
6.6 Moments and Centers of Mass 365
Practice Exercises 376
Additional and Advanced Exercises 384
7 Transcendental Functions 389
7.1 Inverse Functions and Their Derivatives 389
7.2 Natural Logarithms 396
7.3 Exponential Functions 403
7.4 Exponential Change and Separable Differential Equations 414
7.5 Indeterminate Forms and L'Ho^pital's Rule 418
7.6 Inverse Trigonometric Functions 425
7.7 Hyperbolic Functions 436
7.8 Relative Rates of Growth 443
Practice Exercises 447
Additional and Advanced Exercises 458
8 Techniques of Integration 461
8.1 Integration by Parts 461
8.2 Trigonometric Integrals 471
8.3 Trigonometric Substitutions 478
8.4 Integration of Rational Functions by Partial Fractions 484
8.5 Integral Tables and Computer Algebra Systems 491
8.6 Numerical Integration 502
8.7 Improper Integrals 510
Practice Exercises 518
Additional and Advanced Exercises 528
9 First-Order Differential Equations 537
9.1 Solutions, Slope Fields and Euler's Method 537
9.2 First-Order Linear Equations 543
9.3 Applications 546
9.4 Graphical Solutions of Autonomous Equations 549
9.5 Systems of Equations and Phase Planes 557
Practice Exercises 562
Additional and Advanced Exercises 567
10 Infinite Sequences and Series 569
10.1 Sequences 569
10.2 Infinite Series 577
10.3 The Integral Test 583
10.4 Comparison Tests 590
10.5 The Ratio and Root Tests 597
10.6 Alternating Series, Absolute and Conditional Convergence 602
10.7 Power Series 608
10.8 Taylor and Maclaurin Series 617
10.9 Convergence of Taylor Series 621
10.10 The Binomial Series and Applications of Taylor Series 627
Practice Exercises 634
Additional and Advanced Exercises 642
11 Parametric Equations and Polar Coordinates 647
11.1 Parametrizations of Plane Curves 647
11.2 Calculus with Parametric Curves 654
11.3 Polar Coordinates 662
11.4 Graphing in Polar Coordinates 667
11.5 Areas and Lengths in Polar Coordinates 674
11.6 Conic Sections 679
11.7 Conics in Polar Coordinates 689
Practice Exercises 699
Additional and Advanced Exercises 709
10 Infinite Sequences and Series 569
10.1 Sequences 569
10.2 Infinite Series 577
10.3 The Integral Test 583
10.4 Comparison Tests 590
10.5 The Ratio and Root Tests 597
10.6 Alternating Series, Absolute and Conditional Convergence 602
10.7 Power Series 608
10.8 Taylor and Maclaurin Series 617
10.9 Convergence of Taylor Series 621
10.10 The Binomial Series and Applications of Taylor Series 627
Practice Exercises 634
Additional and Advanced Exercises 642
11 Parametric Equations and Polar Coordinates 647
11.1 Parametrizations of Plane Curves 647
11.2 Calculus with Parametric Curves 654
11.3 Polar Coordinates 662
11.4 Graphing in Polar Coordinates 667
11.5 Areas and Lengths in Polar Coordinates 674
11.6 Conic Sections 679
11.7 Conics in Polar Coordinates 689
Practice Exercises 699
Additional and Advanced Exercises 709
12 Vectors and the Geometry of Space 715
12.1 Three-Dimensional Coordinate Systems 715
12.2 Vectors 718
12.3 The Dot Product 723
12.4 The Cross Product 728
12.5 Lines and Planes in Space 734
12.6 Cylinders and Quadric Surfaces 741
Practice Exercises 746
Additional Exercises 754
13 Vector-Valued Functions and Motion in Space 759
13.1 Curves in Space and Their Tangents 759
13.2 Integrals of Vector Functions; Projectile Motion 764
13.3 Arc Length in Space 770
13.4 Curvature and Normal Vectors of a Curve 773
13.5 Tangential and Normal Components of Acceleration 778
13.6 Velocity and Acceleration in Polar Coordinates 784
Practice Exercises 785
Additional Exercises 791
Copyright © 2010 Pearson Education Inc. Publishing as Addison-Wesley.
14 Partial Derivatives 795
14.1 Functions of Several Variables 795
14.2 Limits and Continuity in Higher Dimensions 804
14.3 Partial Derivatives 810
14.4 The Chain Rule 816
14.5 Directional Derivatives and Gradient Vectors 824
14.6 Tangent Planes and Differentials 829
14.7 Extreme Values and Saddle Points 836
14.8 Lagrange Multipliers 849
14.9 Taylor's Formula for Two Variables 857
14.10 Partial Derivatives with Constrained Variables 859
Practice Exercises 862
Additional Exercises 876
15 Multiple Integrals 881
15.1 Double and Iterated Integrals over Rectangles 881
15.2 Double Integrals over General Regions 882
15.3 Area by Double Integration 896
15.4 Double Integrals in Polar Form 900
15.5 Triple Integrals in Rectangular Coordinates 904
15.6 Moments and Centers of Mass 909
15.7 Triple Integrals in Cylindrical and Spherical Coordinates 914
15.8 Substitutions in Multiple Integrals 922
Practice Exercises 927
Additional Exercises 933
16 Integration in Vector Fields 939
16.1 Line Integrals 939
16.2 Vector Fields and Line Integrals; Work, Circulation, and Flux 944
16.3 Path Independence, Potential Functions, and Conservative Fields 952
16.4 Green's Theorem in the Plane 957
16.5 Surfaces and Area 963
16.6 Surface Integrals 972
16.7 Stokes's Theorem 980
16.8 The Divergence Theorem and a Unified Theory 984
Practice Exercises 989
Additional Exercises 997
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