《calculus (fifth edition) P699》求取 ⇩
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1 Functions and Models10
1.1Four Ways to Represent a Function11
1.2 Mathematical Models: A Catalog of Essential Functions25
1.3 New Functions from Old Functions38
1.4 Graphing Calculators and Computers48
1.5 Exponential Functions55
1.6 Inverse Functions and Logarithms63
Review77
Principles of Problem Solving80
2 Limits and Derivatives86
2.1The Tangent and Velocity Problems87
2.2 The Limit of a Function92
2.3 Calculating Limits Using the Limit Laws104
2.4 The Precise Definition of a Limit114
2.5 Continuity124
2.6 Limits at Infinity; Horizontal Asymptotes135
2.7 Tangents, Velocities, and Other Rates of Change149
2.8 Derivatives158
Writing Project · Early Methods for Finding Tangents164
2.9 The Derivative as a Function165
Review176
Problems Plus180
3 Differentiation Rules182
3.1Derivatives of Polynomials and Exponential Functions183
3.2 The Product and Quotient Rules192
3.3 Rates of Change in the Natural and Social Sciences199
3.4 Derivatives of Trigonometric Functions211
3.5 The Chain Rule217
3.6 Implicit Differentiation227
3.7Higher Derivatives236
Applied Project · Where Should a Pilot Start Descent?243
Applied Project · Building a Better Roller Coaster243
3.8 Derivatives of Logarithmic Functions244
3.9 Hyperbolic Functions250
3.10 Related Rates256
3.11Linear Approximations and Differentials262
Laboratory Project · Taylor Polynomials269
Review270
Problems Plus274
4 AppIicatiOnS of Differentiation278
4.1Maximum and Minimum Values279
Applied Project · The Calculus of Rainbows288
4.2 The Mean Value Theorem290
4.3 How Derivatives Affect the Shape of a Graph296
4.4Indeterminate Forms and L'Hospital's Rule307
Writing Project · The Origins of L'Hospital's Rule315
4.5 Summary of Curve Sketching316
4.6 Graphing with Calculus and Calculators324
4.7Optimization Problems331
Applied Project · The Shape of a Can341
4.8 Applications to Business and Economics342
4.9 Newton's Method347
4.10 Antiderivatives353
Review361
Problems Plus365
5 Integrals368
5.1Areas and Distances369
5.2The Definite Integral380
Discovery Project · Area Functions393
5.3 The Fundamental Theorem of Calculus394
5.4Indefinite Integrals and the Net Change Theorem405
Writing Project · Newton, Leibniz, and the Invention of Calculus413
5.5 The Substitution Rule414
5.6 The Logarithm Defined as an Integral422
Review430
Problems Plus434
6 Applications of Integration436
6.1Areas between Curves437
6.2 Volumes444
6.3 Volumes by Cylindrical Shells455
6.4 Work460
6.5Average Value of a Function464
Applied Project · Where to Sit at the Movies468
Review468
Problems Plus470
7 Techniques of Integration474
7.1Integration by Parts475
7.2 Trigonometric Integrals482
7.3 Trigonometric Substitution489
7.4 Integration of Rational Functions by Partial Fractions496
7.5 Strategy for Integration505
7.6Integration Using Tables and Computer Algebra Systems511
Discovery Project · Patterns in Integrals517
7.7 Approximate Integration518
7.8 Improper Integrals530
Review540
Problems Plus543
8 Further Applications of Integration546
8.1Arc Length547
Discovery Project · Arc Length Contest554
8.2Area of a Surface of Revolution554
Discovery Project · Rotating on a slant560
8.3 Applications to Physics and Engineering561
8.4 Applications to Economics and Biology571
8.5 Probability575
Review582
Problems Plus584
9 Differential Equations586
9.1Modeling with Differential Equations587
9.2 Direction Fields and Euler's Method592
9.3Separable Equations601
Applied Project How Fast Does a Tank Drain?609
Applied Project Which Is Faster, Going Up or Coming Down?610
9.4Exponential Growth and Decay611
Applied Project · Calculus and Baseball622
9.5 The Logistic Equation623
9.6 Linear Equations632
9.7 Predator-Prey Systems638
Review644
Problems Plus648
10 Parametric Equations and Polar Coordinates650
10.1Curves Defined by Parametric Equations651
Laboratory Project · Running Circlee around Circles659
10.2Calculus with Parametric Curves660
Laboratory Project · Bezler Curves669
10.3 Polar Coordinates669
10.4 Areas and Lengths in Polar Coordinates679
10.5 Conic Sections684
10.6 Conic Sections in Polar Coordinates692
Review696
Problems Plus699
11Infinite Sequences and Series700
11.1Sequences701
Laboratory Project · Logietic sequences713
11.2 Series713
11.3 The Integral Test and Estimates of Sums723
11.4 The Comparison Tests730
11.5 Alternating Series735
11.6 Absolute Convergence and the Ratio and Root Tests740
11.7 Strategy for Testing Series747
11.8 Power Series749
11.9 Representations of Functions as Power Series754
11.10Taylor and Maclaurin Series760
Laboratory Project · An Elusive Limit772
11.11The Binomial Series772
Writing Project · How Newton Discovered the Binomial Series776
11.12Applications of Taylor Polynomials776
Applied Project · Radiation from the Stars785
Review786
Problems Plus789
12 Vectors and the Geometry of Space792
12.1Three-Dimensional Coordinate Systems793
12.2 Vectors798
12.3 The Dot Product807
12.4The Cross Product814
Discovery Project · The Geometry of a Tetrahedron822
12.5Equations of Lines and Planes822
Laboratory Project · Putting 3D in Perspective832
12.6 Cylinders and Quadric Surfaces832
12.7Cylindrical and Spherical Coordinates839
Laboratory Project · Families of Surfaces844
Review844
Problems Plus847
13 Vector Functions848
13.1Vector Functions and Space Curves849
13.2 Derivatives and Integrals of Vector Functions856
13.3 Arc Length and Curvature862
13.4Motion in Space: Velocity and Acceleration870
Applied Project · Kepler's Laws880
Review881
Problems Plus884
14 Partial Derivatives886
14.1Functions of Several Variables887
14.2 Limits and Continuity902
14.3 Partial Derivatives909
14.4 Tangent Planes and Linear Approximations923
14.5 The Chain Rule931
14.6 Directional Derivatives and the Gradient Vector940
14.7Maximum and Minimum Values953
Applied Project · Designing a Dumpster963
Discovery Project · Quadratic Approximations and Critical Points964
14.8Lagrange Multipliers965
Applied Project Rocket Science972
Applied Project Hydro-Turbine Optimization973
Review974
Problems Plus978
15 Multiple Integrals980
15.1Double Integrals over Rectangles981
15.2 Iterated Integrals989
15.3 Double Integrals over General Regions995
15.4 Double Integrals in Polar Coordinates1003
15.5 Applications of Double Integrals1009
15.6 Surface Area1019
15.7Triple Integrals1023
Discovery Project · Volumes of Hyperspheres1032
15.8Triple Integrals in Cylindrical and Spherical Coordinates1033
Applied Project · Roller Derby1039
Discovery Project · The Intersection of Three Cylinders1040
15.9 Change of Variables in Multiple Integrals1041
Review1049
Problems Plus1052
16 Vector Calculus1054
16.1Vector Fields1055
16.2 Line Integrals1062
16.3 The Fundamental Theorem for Line Integrals1074
16.4 Green's Theorem1083
16.5 Curl and Divergence1090
16.6 Parametric Surfaces and Their Areas1098
16.7 Surface Integrals1109
16.8Stokes' Theorem1121
Writing Project · Three Men and Two Theorems1126
16.9 The Divergence Theorem1127
16.10 Summary1134
Review1135
Problems Plus1138
17 Second-Order Differential Equations1140
17.1Second-Order Linear Equations1141
17.2 Nonhomogeneous Linear Equations1147
17.3 Applications of Second-Order Differential Equations1155
17.4 Series Solutions1163
Review1167
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高度相关资料
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- Calculus Third Edition
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