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Calculus: Early Transcendentals (2nd Edition) [color=rgb(85, 85, 85) !important]2nd Edition[color=rgb(85, 85, 85) !important]by William L. Briggs (Author), Lyle Cochran (Author), Bernard Gillett (Author)
蓝色封面～～～
非常非常推荐这本书！！！
calculus 讲的非常详细，认真看不存在看不懂的。这本书帮助我在所有的calculus课都得到A. 确实好好看了这本书，所以有感情。对今后学习的probability，applied statistics 都有很大的帮助。
非常高清，彩色，看起来很舒服。
复制过来目录～
contents
Preface xii credits xix
1 Functions
1.1 review of Functions 1
1.2 representing Functions 12
1.3 inverse, Exponential, and logarithmic Functions
26
1
54
1.4 Trigonometric Functions and Their inverses
38
Review Exercises 51
2 limits
2.1 The idea of limits
2.2 definitions of limits 61
2.3 Techniques for computing limits 69
2.4 infinite limits 79
2.5 limits at infinity 88
2.6 continuity 98
2.7 Precise definitions of limits 112
Review Exercises 123
3 derivatives
3.1 introducing the derivative 126
3.2 Working with derivatives
3.3 rules of differentiation 144
3.4 The Product and Quotient rules 153
3.5 derivatives of Trigonometric Functions
3.6 derivatives as rates of change 171
3.7 The chain rule 185
54
136
163
126
vii
viii Contents
3.8 implicit differentiation 195
3.9 derivatives of logarithmic and Exponential Functions
3.10 derivatives of inverse Trigonometric Functions 214
3.11 related rates 224
Review Exercises 232
4 applications of the derivative
203
236
4.1 maxima and minima 236
4.2 What derivatives Tell us 245
4.3 graphing Functions 260
4.4 optimization Problems 270
4.5 linear approximation and differentials 281
4.6 mean Value Theorem 290
4.7 l’hôpital’s rule 297
4.8 newton’s method 310
4.9 antiderivatives 318
Review Exercises 330
5 integration
5.1 approximating areas under curves 333
5.2 definite integrals 348
5.3 Fundamental Theorem of calculus 362
5.4 Working with integrals 377
5.5 substitution rule 384
Review Exercises 394
6 applications of integration
6.1 Velocity and net change 398
6.2 regions Between curves 412
6.3 Volume by slicing 420
6.4 Volume by shells 434
6.5 length of curves 445
6.6 surface area 451
6.7 Physical applications 459
6.8 logarithmic and Exponential Functions revisited
6.9 Exponential models 482
333
398
6.10 hyperbolic Functions
Review Exercises 507
491
471
7 integration Techniques
7.1 Basic approaches 511
7.2 integration by Parts 516
7.3 Trigonometric integrals 523
7.4 Trigonometric substitutions 531
7.5 Partial Fractions 541
7.6 other integration strategies 551
7.7 numerical integration 557
7.8 improper integrals 570
7.9 introduction to differential Equations 581
Review Exercises 593
8 sequences and infinite series
511
8.1 an overview 596
8.2 sequences 607
8.3 infinite series 619
8.4 The divergence and integral Tests 627
8.5 The ratio, root, and comparison Tests
641
8.6 alternating series
Review Exercises
9 Power series
649
658
Contents ix
596
9.1 approximating Functions with Polynomials 661
9.2 Properties of Power series 675
9.3 Taylor series 684
9.4 Working with Taylor series 696
Review Exercises 705
10 Parametric and Polar curves
10.1 Parametric Equations 707
10.2 Polar coordinates 719
10.3 calculus in Polar coordinates 732
10.4 conic sections 741
Review Exercises 754
661
707

x Contents
11 Vectors and Vector-Valued Functions 757
11.1 Vectors in the Plane 757
11.2 Vectors in Three dimensions 770
11.3 dot Products 781
11.4 cross Products 792
11.5 lines and curves in space 799
11.6 calculus of Vector-Valued Functions 808
11.7 motion in space 817
11.8 length of curves 830
11.9 curvature and normal Vectors 841
Review Exercises 854
12 Functions of several Variables
12.1 Planes and surfaces 858
12.2 graphs and level curves 873
12.3 limits and continuity 885
12.4 Partial derivatives 894
12.5 The chain rule 907
12.6 directional derivatives and the gradient 916
12.7 Tangent Planes and linear approximation 928
12.8 maximum/minimum Problems 939
12.9 lagrange multipliers 951
858
Review Exercises 959
13 multiple integration
13.1 double integrals over rectangular regions
13.2 double integrals over general regions 973
13.3 double integrals in Polar coordinates 984
13.4 Triple integrals 994
963
13.5 Triple integrals in cylindrical and spherical coordinates
13.6 integrals for mass calculations 1023
1007
13.7 change of Variables in multiple integrals
1034
Review Exercises 1046
14 Vector calculus
14.1 Vector Fields 1050
14.2 line integrals 1060
14.3 conservative Vector Fields
14.4 green’s Theorem 1087
1050
963
1078
14.5 divergence and curl 1100
14.6 surface integrals 1111
14.7 stokes’ Theorem 1126
14.8 divergence Theorem 1135
Review Exercises 1147
d1 differential Equations
d1.1 Basic ideas
d1.2 direction Fields and Euler’s method
d1.3 separable differential Equations
d1.4 special First-order differential Equations
d1.5 modeling with differential Equations
Review Exercises
online
Contents xi
d2 second-order differential Equations online
d2.1 Basic ideas
d2.2 linear homogeneous Equations
d2.3 linear nonhomogeneous Equations
d2.4 applications
d2.5 complex Forcing Functions
Review Exercises
appendix a algebra review 1151
appendix B Proofs of selected Theorems 1159 answers a-1
index i-1
Table of integrals
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