تحميل حلول و كتاب Thomas' Calculus Twelfth Edition (كالكولاس توماس الطبعة الثانية عشر 12e ) من الميديا فاير

تحميل حلول و كتاب Thomas' Calculus Twelfth Edition (كالكولاس توماس الطبعة الثانية عشر 12e ) من الميديا فاير

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CONTENTS
Preface ix
1 I Functions 1
1.1 Functions and Their Graphs I
1.2 CombiJring Functions; Shifting and Scaling Graphs 14
1.3 Trigonometric Functions 22
1.4 Graphing with Calcolators and Computers 30
QuEsTIONS TO GUIDE YOUR REVIEW 34


PRACTICE EXERCISES 35
AoDmONAL AND ADvANCED EXERCISES 37

2 Limits and Continuity 39
2.1 Rates of Change and Tangents to Curves 39
2.2 Limit of a Function and Limit Laws 46
2.3 The Precise Definition of a Limit 57
2.4 One-Sided Limits 66
2.5 Continuity 73
2.6 Limits Involving Infinity; Asymptotes of Graphs 84
QuEsTIONS TO GUIDE YOUR REVIEW 96
PRACTICE EXERCISES 97
AoDmONAL AND ADvANCED EXERCISES 98

3 Differentiation 102
3.1 Tangents and the Derivative at a Point 102
3.2 The Derivative as a Function 106
3.3 Differentiation Rules 115
3.4 The Derivative as a Rate of Change 124
3.5 Derivatives of Trigonometric Functions 135
3.6 The Chain Rule 142
3.7 Implicit Differentiation 149
3.8 Related Rates 155
3.9 Linearization and Differentials 164
QuESTIONS TO GUIDE YOUR REVIEW 175
PRACTICE EXERCISES 176
ADDITIONAL AND ADvANCED EXERCISES 180

4 Applications of Derivatives 184
4.1 Extreme Values of Functions 184


4.2 The Mean Value Theorem 192
4.3 Monotonic Functions and the First Derivative Test 198
4.4 Concavity and Curve Sketching 203
4.5 Applied Optimization 214
4.6 Newton's Method 225
4.7 Antiderivatives 230
QuESTIONS TO GUIDE YOUR REVIEW 239
PRACTICE EXERCISES 240
ADDITIONAL AND ADvANCED EXERCISES 243


5 I Integration 246
5.1 Area and Estimating with Finite Sums 246
5.2 Sigma Notation and Limits of Finite Sums 256
5.3 The Definite Integral 262
5.4 The Fundamental Theorem of calculus 274
5.5 Indefinite Integrals and the Substitution Method 284
5.6 Substitution and Area Between Curves 291
QuESTIONS TO GUIDE YOUR REVIEW 300
PRACTICE EXERCISES 301
ADDITIONAL AND ADvANCED EXERCISES 304


6 Applications of Definite Integrals 308
6.1 Volumes Using Cross-Sections 308
6.2 Volumes Using Cylindrical Shells 319
6.3 Arc Length 326
6.4 Areas of Surfaces of Revolution 332
6.5 Work and Fluid Forces 337
6.6 Moments and Centers of Mass 346
QuESTIONS TO GUIDE YOUR REVIEW 357
PRACTICE EXERCISES 357
ADDITIONAL AND ADvANCED EXERCISES 359


7 Transcendental Functions 361
7.1 Inverse Functions and Their Derivatives 361
7.2 Natural Logarithms 369
7.3 Exponential Functions 377
7.4 Exponential Change and Separable Differential Equations 387
7.5 Indeterminate Forms and VHopitai's Rule 396
7.6 Inverse Trigonometric Functions 404
7.7 Hyperbolic Functions 416
7.8 Relative Rates of Growth 424
QuEsTIONS TO GUIDE YOUR REVIEW 429
PRACTICE EXERCISES 430
ADDmONAL AND ADvANCED EXERCISES 433


8 Techniques of Integration
8.1 Integration by Parts 436
8.2 Trigonometric Integrals 444
8.3 Trigonometric Substitotions 449
8.4 Integration of Rational Functions by Partial Fractions 453
8.5 Integral Tables and Computer Algebra Systems 463
8.6 Numerical Integration 468
8.7 Improper Integrals 478
QuEsTIONS TO GUIDE YOUR REVIEW 489
PRACTICE EXERCISES 489
ADDmONAL AND ADvANCED EXERCISES 491


9 First-Order Differential Equations
9.1 Solutions, Slope Fields, and Euler's Method 496
9.2 First-Order Linear Equations 504
9.3 Applications 510
9.4 Graphical Solutions of Autonomous Equations 516
9.5 Systems of Equations and Phase Planes 523
QuEsTIONS TO GUIDE YOUR REVIEW 529
PRACTICE EXERCISES 529
ADDmONAL AND ADVANCED EXERCISES 530


10 Infinite Sequences and Series
10.1 Sequences 532
10.2 Infinite Series 544
10.3 The Integral Test 553
lOA Comparison Tests 558
10.5 The Ratio and Root Thsts 563
10.6 Alternating Series, Absolute and Conditional Convergence 568
10.7 Power Series 575
10.8 Taylor and Maclaurin Series 584
10.9 Convergence of Taylor Series 589
10.10 The Binomial Series and Applications of Taylor Series 596
QuESTIONS TO GUIDE YOUR REVIEW 605
PRACTICE EXERCISES 605
ADDITIONAL AND ADvANCED EXERCISES 607


11 Parametric Equations and Polar Coordinates 610
11.1 Parametrizations of Plane Curves 610
11.2 calculus with Parametric Curves 618
11.3 Polar Coordinates 627
11.4 Graphing in Polar Coordinates 631
11.5 Areas and Lengths in Polar Coordinates 635
11.6 Conic Sections 639
11.7 Conics in Polar Coordinates 648
QuESTIONS TO GUIDE YOUR REVIEW 654
PRACTICE EXERCISES 655
ADDITIONAL AND ADvANCED EXERCISES 657


12 Vectors and the Geometry of Space 660
12.1 Three-Dimensional Coordinate Systems 660
12.2 Vectors 665
12.3 The Dot Product 674
12.4 The Cross Product 682
12.5 Lines and Planes in Space 688
12.6 Cylinders and Quadric Surfaces 696
QuESTIONS TO GUIDE YOUR REVIEW 701
PRACTICE EXERCISES 702
ADDITIONAL AND ADvANCED EXERCISES 704


13 Vector-Valued Functions and Motion in Space 707
13.1 Curves in Space and Their Tangents 707
13.2 Integrals of V ector Functions; Projectile Motion 715
13.3 Arc Length in Space 724
13.4 Curvatore and Normal Vectors ofa Curve 728
13.5 Tangential and Normal Components of Acceleration 734
13.6 Velocity and Acceleration in Polar Coordinates 739
QuESTIONS TO GUIDE YOUR REVIEW 742
PRACTICE EXERCISES 743
ADDITIONAL AND ADvANCED EXERCISES 745


14 Partial Derivatives
14.1 Functions of Several Variables 747
14.2 Limits and Continuity in Higher Dimensions 755
14.3 Partial Derivatives 764
14.4 The Chain Rule 775
14.5 Directional Derivatives and Gradient Vectors 784
14.6 Tangent Planes and Differentials 791
14.7 Extreme Values and Saddle Points 802
14.8 Lagrange Multipliers 811
14.9 Taylor's Formula for Two Variables 820
14.10 Partial Derivatives with Constrained Variables 824
QUESTIONS TO GUIDE YOUR REVIEW 829
PRACTICE ExERCISES 829
ADomONAL AND ADvANCED EXERCISES 833


15 Multiple Integrals
15.1 Double and Iterated Integrals over Rectangles 836
15.2 Double Integrals over General Regions 841
15.3 Area by Double Integration 850
15.4 Double Integrals in Polar Form 853
15.5 Triple Integrals in Rectangular Coordinates 859
15.6 Moments and Centers of Mass 868
15.7 Triple Integrals in Cylindrical and Spherical Coordinates 875
15.8 Substitutions in Multiple Integrals 887
QUESTIONS TO GUIDE YOUR REVIEW 896
PRACTICE ExERCISES 896
ADomONAL AND ADvANCED EXERCISES 898


16 Integration in Vector Fields
16.1 Line Integrals 901
16.2 Vector Fields and Line Integrals: Work, Circulation, and Flux 907
16.3 Path Independence, Conservative Fields, and Potential Functions 920
16.4 Green's Theorem in the Plane 931

16.5 Surfaces and Area 943
16.6 Surface Integrals 953
16.7 Stokes' Theorem 962
16.8 The Divergence Theorem and a Unified Theory 972
QUESTIONS TO GUIDE YOUR REVIEW 983
PRACTICE ExERCISES 983
ADomONAL AND ADVANCED EXERCISES 986


17 Second-Order Differential Equations
17.1 Second-Order Linear Equations
17.2 Nonhomogeneous Linear Equations
17.3 Applications
17.4 Euler Equations
17.5 Power Series Solutions


Appendices AP-1
A.I Real Numbers and the Real Line AP-I
A.2 Mathematical Induction AP-6
A.3 Lines, Circles, and Parabolas AP-1O
AA Proofs of Limit Theorems AP-IS
A.5 Commonly Occurring Limits AP-2I
A.6 Theory of the Real Numbers AP-23
A.7 Complex Numbers AP-25
A.S The Distributive Law for Vector Cross Products AP-35
A.9 The Mixed Derivative Theorem and the Increment Theorem AP-36
Answers to Odd-Numbered Exercises A-1
Index 1-1
A Brief Table of Integrals T-1
Credits C-1




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