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Calculus 8th edition by James Stewart, ISBN-13: 978-1285740621

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Calculus 8th edition by James Stewart, ISBN-13: 978-1285740621
[PDF eBook eTextbook]

1392 pages
Publisher: Cengage Learning; 8 edition (May 19, 2015)
Language: English
ISBN-10: 1285740629
ISBN-13: 978-1285740621

Note: Access code NOT included.

Success in your calculus course starts here! James Stewart’s CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS, Eighth Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course!

About the Author

The late James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart was most recently Professor of Mathematics at McMaster University, and his research field was harmonic analysis. Stewart was the author of a best-selling calculus textbook series published by Cengage Learning, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.

Table of contents:

Front Cover……Page 1
Title Page……Page 2
Copyright Page……Page 4
CONTENTS……Page 5
Preface……Page 13
To the Student……Page 25
Calculators, Computers, and Other Graphing Devices……Page 26
Diagnostic Tests……Page 28
A Preview of Calculus……Page 33
1. Functions and Limits……Page 41
1.1 Four Ways to Represent a Function……Page 42
1.2 Mathematical Models: A Catalog of Essential Functions……Page 55
1.3 New Functions from Old Functions……Page 68
1.4 The Tangent and Velocity Problems……Page 77
1.5 The Limit of a Function……Page 82
1.6 Calculating Limits Using the Limit Laws……Page 94
1.7 The Precise Definition of a Limit……Page 104
1.8 Continuity……Page 114
Review……Page 126
Principles of Problem Solving……Page 130
2. Derivatives……Page 137
2.1 Derivatives and Rates of Change……Page 138
2.2 The Derivative as a Function……Page 149
2.3 Differentiation Formulas……Page 162
2.4 Derivatives of Trigonometric Functions……Page 176
2.5 The Chain Rule……Page 184
2.6 Implicit Differentiation……Page 193
2.7 Rates of Change in the Natural and Social Sciences……Page 201
2.8 Related Rates……Page 213
2.9 Linear Approximations and Differentials……Page 220
Review……Page 227
Problems Plus……Page 232
3. Applications of Differentiation……Page 235
3.1 Maximum and Minimum Values……Page 236
3.2 The Mean Value Theorem……Page 247
3.3 How Derivatives Affect the Shape of a Graph……Page 253
3.4 Limits at Infinity; Horizontal Asymptotes……Page 263
3.5 Summary of Curve Sketching……Page 276
3.6 Graphing with Calculus and Calculators……Page 283
3.7 Optimization Problems……Page 290
3.8 Newton’s Method……Page 304
3.9 Antiderivatives……Page 310
Review……Page 317
Problems Plus……Page 321
4. Integrals……Page 325
4.1 Areas and Distances……Page 326
4.2 The Definite Integral……Page 338
4.3 The Fundamental Theorem of Calculus……Page 352
4.4 Indefinite Integrals and the Net Change Theorem……Page 362
4.5 The Substitution Rule……Page 372
Review……Page 380
Problems Plus……Page 384
5. Applications of Integration……Page 387
5.1 Areas between Curves……Page 388
5.2 Volumes……Page 398
5.3 Volumes by Cylindrical Shells……Page 409
5.4 Work……Page 415
5.5 Average Value of a Function……Page 421
Review……Page 425
Problems Plus……Page 427
6. Inverse Functions……Page 431
6.1 Inverse Functions……Page 432
6.2 Exponential Functions and Their Derivatives……Page 440
6.3 Logarithmic Functions……Page 453
6.4 Derivatives of Logarithmic Functions……Page 460
6.5 Exponential Growth and Decay……Page 498
6.6 Inverse Trigonometric Functions……Page 506
6.7 Hyperbolic Functions……Page 516
6.8 Indeterminate Forms and l’Hospital’s Rule……Page 523
Review……Page 535
Problems Plus……Page 540
7. Techniques of Integration……Page 543
7.1 Integration by Parts……Page 544
7.2 Trigonometric Integrals……Page 551
7.3 Trigonometric Substitution……Page 558
7.4 Integration of Rational Functions by Partial Fractions……Page 565
7.5 Strategy for Integration……Page 575
7.6 Integration Using Tables and Computer Algebra Systems……Page 580
7.7 Approximate Integration……Page 586
7.8 Improper Integrals……Page 599
Review……Page 609
Problems Plus……Page 612
8. Further Applications of Integration……Page 615
8.1 Arc Length……Page 616
8.2 Area of a Surface of Revolution……Page 623
8.3 Applications to Physics and Engineering……Page 630
8.4 Applications to Economics and Biology……Page 641
8.5 Probability……Page 645
Review……Page 653
Problems Plus……Page 655
9. Differential Equations……Page 657
9.1 Modeling with Differential Equations……Page 658
9.2 Direction Fields and Euler’s Method……Page 663
9.3 Separable Equations……Page 671
9.4 Models for Population Growth……Page 682
9.5 Linear Equations……Page 692
9.6 Predator-Prey Systems……Page 699
Review……Page 706
Problems Plus……Page 709
10. Parametric Equations and Polar Coordinates……Page 711
10.1 Curves Defined by Parametric Equations……Page 712
10.2 Calculus with Parametric Curves……Page 721
10.3 Polar Coordinates……Page 730
10.4 Areas and Lengths in Polar Coordinates……Page 741
10.5 Conic Sections……Page 746
10.6 Conic Sections in Polar Coordinates……Page 754
Review……Page 761
Problems Plus……Page 764
11. Infinite Sequences and Series……Page 765
11.1 Sequences……Page 766
11.2 Series……Page 779
11.3 The Integral Test and Estimates of Sums……Page 791
11.4 The Comparison Tests……Page 799
11.5 Alternating Series……Page 804
11.6 Absolute Convergence and the Ratio and Root Tests……Page 809
11.7 Strategy for Testing Series……Page 816
11.8 Power Series……Page 818
11.9 Representations of Functions as Power Series……Page 824
11.10 Taylor and Maclaurin Series……Page 831
11.11 Applications of Taylor Polynomials……Page 846
Review……Page 856
Problems Plus……Page 859
12. Vectors and the Geometry of Space……Page 863
12.1 Three-Dimensional Coordinate Systems……Page 864
12.2 Vectors……Page 870
12.3 The Dot Product……Page 879
12.4 The Cross Product……Page 886
12.5 Equations of Lines and Planes……Page 895
12.6 Cylinders and Quadric Surfaces……Page 906
Review……Page 913
Problems Plus……Page 916
13. Vector Functions……Page 919
13.1 Vector Functions and Space Curves……Page 920
13.2 Derivatives and Integrals of Vector Functions……Page 927
13.3 Arc Length and Curvature……Page 933
13.4 Motion in Space: Velocity and Acceleration……Page 942
Review……Page 953
Problems Plus……Page 956
14. Partial Derivatives……Page 959
14.1 Functions of Several Variables……Page 960
14.2 Limits and Continuity……Page 975
14.3 Partial Derivatives……Page 983
14.4 Tangent Planes and Linear Approximations……Page 999
14.5 The Chain Rule……Page 1009
14.6 Directional Derivatives and the Gradient Vector……Page 1018
14.7 Maximum and Minimum Values……Page 1031
14.8 Lagrange Multipliers……Page 1043
Review……Page 1053
Problems Plus……Page 1057
15. Multiple Integrals……Page 1059
15.1 Double Integrals over Rectangles……Page 1060
15.2 Double Integrals over General Regions……Page 1073
15.3 Double Integrals in Polar Coordinates……Page 1082
15.4 Applications of Double Integrals……Page 1088
15.5 Surface Area……Page 1098
15.6 Triple Integrals……Page 1101
15.7 Triple Integrals in Cylindrical Coordinates……Page 1112
15.8 Triple Integrals in Spherical Coordinates……Page 1117
15.9 Change of Variables in Multiple Integrals……Page 1124
Review……Page 1133
Problems Plus……Page 1137
16. Vector Calculus……Page 1139
16.1 Vector Fields……Page 1140
16.2 Line Integrals……Page 1147
16.3 The Fundamental Theorem for Line Integrals……Page 1159
16.4 Green’s Theorem……Page 1168
16.5 Curl and Divergence……Page 1175
16.6 Parametric Surfaces and Their Areas……Page 1183
16.7 Surface Integrals……Page 1194
16.8 Stokes’ Theorem……Page 1206
16.9 The Divergence Theorem……Page 1213
16.10 Summary……Page 1219
Review……Page 1220
Problems Plus……Page 1223
17. Second-Order Differential Equations……Page 1225
17.1 Second-Order Linear Equations……Page 1226
17.2 Nonhomogeneous Linear Equations……Page 1232
17.3 Applications of Second-Order Differential Equations……Page 1240
17.4 Series Solutions……Page 1248
Review……Page 1253
APPENDICES……Page 1255
A: Numbers, Inequalities, and Absolute Values……Page 1256
B: Coordinate Geometry and Lines……Page 1264
C: Graphs of Second-Degree Equations……Page 1270
D: Trigonometry……Page 1278
E: Sigma Notation……Page 1288
F: Proofs of Theorems……Page 1293
G: Complex Numbers……Page 1302
1.1……Page 1311
1.2……Page 1312
1.3……Page 1313
1.4, 1.5……Page 1314
1.7, 1.8……Page 1315
problem solving……Page 1316
2.1……Page 1317
2.2……Page 1318
2.3……Page 1319
2.5……Page 1320
2.6, 2.7……Page 1321
R……Page 1322
plus……Page 1323
3.2, 3.3……Page 1324
3.4, 3.5……Page 1326
3.6……Page 1329
3.7……Page 1330
3.8, 3.9, R……Page 1331
plus……Page 1332
4.1……Page 1333
4.2, 4.3……Page 1334
plus……Page 1335
5.2……Page 1336
R, plus……Page 1337
6.1, 6.2……Page 1338
6.3, 6.4……Page 1339
6.2*……Page 1340
6.3*……Page 1341
6.6……Page 1342
6.8……Page 1343
7.1……Page 1344
7.4……Page 1345
7.6……Page 1346
7.7, 7.8……Page 1347
8.2……Page 1348
9.1……Page 1349
9.3……Page 1350
9.4……Page 1351
9.6……Page 1352
10.1……Page 1353
10.2……Page 1354
10.3……Page 1355
10.4……Page 1356
10.6……Page 1357
R……Page 1358
11.2……Page 1359
11.9……Page 1360
11.10……Page 1361
11.11……Page 1362
12.1……Page 1363
12.4……Page 1364
12.6……Page 1365
R……Page 1366
13.1……Page 1367
13.2, 13.3……Page 1368
13.4……Page 1369
14.1……Page 1370
14.3……Page 1372
14.4……Page 1373
14.7……Page 1374
R……Page 1375
15.2, 15.3……Page 1376
15.5, 15.6, 15.7……Page 1377
15.8, 15.9, R……Page 1378
16.2……Page 1379
16.5, 16.6……Page 1380
17.2……Page 1381
B……Page 1382
C……Page 1383
E, G……Page 1384
B……Page 1385
C……Page 1386
D……Page 1387
E……Page 1388
F……Page 1389
G……Page 1390
H, I……Page 1391
J, K, L……Page 1392
M, N……Page 1393
P……Page 1394
R……Page 1395
S……Page 1396
T……Page 1397
U, V……Page 1398
W, X, Y, Z……Page 1399
Geometry……Page 1401
Trig……Page 1402
Special Functions……Page 1403
Differentiation Rules……Page 1405
Table of Integrals……Page 1406
CH 01……Page 1411
CH 02……Page 1415
CH 03……Page 1417
CH 04……Page 1419
CH 05……Page 1421
CH 06……Page 1422
CH 07……Page 1424
CH 08……Page 1425
CH 09……Page 1426
CH 10……Page 1427
CH 11……Page 1429
CH 12……Page 1431
CH 13……Page 1434
CH 14……Page 1436
CH 15……Page 1439
CH 16……Page 1443
CH 17……Page 1446
Lies my calculator and computer told me……Page 1448

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