Calculus Single and Multivariable 6th Edition by William McCallum, Deborah Hughes Hallett, Andrew Gleason – Ebook PDF Instant Download/Delivery: 1118547854, 978-1118547854
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ISBN 10: 1118547854
ISBN 13: 978-1118547854
Author: William McCallum, Deborah Hughes Hallett, Andrew Gleason
This Sixth Edition of Calculus continues the effort to promote courses in which understanding and computation reinforce each other. Calculus: Single and Multivariable 6th Edition reflects the many voices of users at research universities, four-year colleges, community colleges, and secondary schools. This new edition has been streamlined to create a flexible approach to both theory and modeling. For instructors wishing to emphasize the connection between calculus and other fields, the text includes a variety of problems and examples from the physical, health, and biological sciences, engineering and economics. In addition, new problems on the mathematics of sustainability and new case studies on calculus in medicine by David E. Sloane, MD have been added.
Calculus Single and Multivariable 6th Table of contents:
1 A Library of Functions 1
1.1 Functions and Change 2
1.2 Exponential Functions 12
1.3 New Functions From Old 21
1.4 Logarithmic Functions 29
1.5 Trigonometric Functions 36
1.6 Powers, Polynomials, and Rational Functions 45
1.7 Introduction To Continuity 53
1.8 Limits 57
Review Problems 68
Projects 73
2 Key Concept: The Derivative 75
2.1 How Do We Measure Speed? 76
2.2 The Derivative At A Point 83
2.3 The Derivative Function 90
2.4 Interpretations of The Derivative 98
2.5 The Second Derivative 104
2.6 Differentiability 111
Review Problems 116
Projects 122
3 Short-Cuts To Differentiation 123
3.1 Powers and Polynomials 124
3.2 The Exponential Function 132
3.3 The Product and Quotient Rules 136
3.4 The Chain Rule 142
3.5 The Trigonometric Functions 149
3.6 The Chain Rule and Inverse Functions 156
3.7 Implicit Functions 162
3.8 Hyperbolic Functions 165
3.9 Linear Approximation and The Derivative 169
3.10 Theorems About Differentiable Functions 175
Review Problems 180
Projects 184
4 Using The Derivative 185
4.1 Using First and Second Derivatives 186
4.2 Optimization 196
4.3 Optimization and Modeling 205
4.4 Families of Functions and Modeling 216
4.5 Applications To Marginality 224
4.6 Rates and Related Rates 233
4.7 L’hopital’s Rule, Growth, and Dominance 242
4.8 Parametric Equations 249
Review Problems 260
Projects 267
5 Key Concept: The Definite Integral 271
5.1 How Do We Measure Distance Traveled? 272
5.2 The Definite Integral 281
5.3 The Fundamental Theorem and Interpretations 289
5.4 Theorems About Definite Integrals 298
Review Problems 309
Projects 316
6 Constructing Antiderivatives 319
6.1 Antiderivatives Graphically and Numerically 320
6.2 Constructing Antiderivatives Analytically 326
6.3 Differential Equations and Motion 332
6.4 Second Fundamental Theorem of Calculus 340
Review Problems 345
Projects 350
7 Integration 353
7.1 Integration By Substitution 354
7.2 Integration By Parts 364
7.3 Tables of Integrals 371
7.4 Algebraic Identities and Trigonometric Substitutions 376
7.5 Numerical Methods For Definite Integrals 387
7.6 Improper Integrals 395
7.7 Comparison of Improper Integrals 403
Review Problems 408
Projects 412
8 Using The Definite Integral 413
8.1 Areas and Volumes 414
8.2 Applications To Geometry 422
8.3 Area and Arc Length In Polar Coordinates 431
8.4 Density and Center of Mass 439
8.5 Applications To Physics 449
8.6 Applications To Economics 459
8.7 Distribution Functions 466
8.8 Probability, Mean, and Median 473
Review Problems 481
Projects 486
9 Sequences and Series 491
9.1 Sequences 492
9.2 Geometric Series 498
9.3 Convergence of Series 505
9.4 Tests For Convergence 512
9.5 Power Series and Interval of Convergence 521
Review Problems 529
Projects 533
10 Approximating Functions Using Series 537
10.1 Taylor Polynomials 538
10.2 Taylor Series 546
10.3 Finding and Using Taylor Series 552
10.4 The Error In Taylor Polynomial Approximations 560
10.5 Fourier Series 565
Review Problems 578
Projects 582
11 Differential Equations 585
11.1 What is A Differential Equation? 586
11.2 Slope Fields 591
11.3 Euler’s Method 599
11.4 Separation of Variables 604
11.5 Growth and Decay 609
11.6 Applications and Modeling 620
11.7 The Logistic Model 629
11.8 Systems of Differential Equations 639
11.9 Analyzing The Phase Plane 649
Review Problems 655
Projects 661
12 Functions of Several Variables 665
12.1 Functions of Two Variables 666
12.2 Graphs and Surfaces 674
12.3 Contour Diagrams 681
12.4 Linear Functions 694
12.5 Functions of Three Variables 700
12.6 Limits and Continuity 705
Review Problems 710
Projects 714
13 A Fundamental Tool: Vectors 717
13.1 Displacement Vectors 718
13.2 Vectors In General 726
13.3 The Dot Product 734
13.4 The Cross Product 744
Review Problems 752
Projects 755
14 Differentiating Functions of Several Variables 757
14.1 The Partial Derivative 758
14.2 Computing Partial Derivatives Algebraically 766
14.3 Local Linearity and The Differential 771
14.4 Gradients and Directional Derivatives In The Plane 779
14.5 Gradients and Directional Derivatives In Space 789
14.6 The Chain Rule 796
14.7 Second-Order Partial Derivatives 806
14.8 Differentiability 815
Review Problems 822
Projects 827
15 Optimization: Local and Global Extrema 829
15.1 Critical Points: Local Extrema and Saddle Points 830
15.2 Optimization 839
15.3 Constrained Optimization: Lagrange Multipliers 848
Review Problems 860
Projects 864
16 Integrating Functions of Several Variables 867
16.1 The Definite Integral of A Function of Two Variables 868
16.2 Iterated Integrals 875
16.3 Triple Integrals 884
16.4 Double Integrals In Polar Coordinates 891
16.5 Integrals In Cylindrical and Spherical Coordinates 896
16.6 Applications of Integration To Probability 906
Review Problems 911
Projects 915
17 Parameterization and Vector Fields 917
17.1 Parameterized Curves 918
17.2 Motion, Velocity, and Acceleration 927
17.3 Vector Fields 937
17.4 The Flow of A Vector Field 943
Review Problems 950
Projects 953
18 Line Integrals 957
18.1 The Idea of A Line Integral 958
18.2 Computing Line Integrals Over Parameterized Curves 967
18.3 Gradient Fields and Path-Independent Fields 974
18.4 Path-Dependent Vector Fields and Green’s Theorem 985
Review Problems 997
Projects 1002
19 Flux Integrals and Divergence 1005
19.1 The Idea of A Flux Integral 1006
19.2 Flux Integrals For Graphs, Cylinders, and Spheres 1016
19.3 The Divergence of A Vector Field 1025
19.4 The Divergence Theorem 1034
Review Problems 1040
Projects 1044
20 The Curl and Stokes’ Theorem 1047
20.1 The Curl of A Vector Field 1048
20.2 Stokes’ Theorem 1056
20.3 The Three Fundamental Theorems 1062
Review Problems 1067
Projects 1071
21 Parameters, Coordinates, and Integrals 1073
21.1 Coordinates and Parameterized Surfaces 1074
21.2 Change of Coordinates In A Multiple Integral 1084
21.3 Flux Integrals Over Parameterized Surfaces 1089
Review Problems 1093
Projects 1094
Appendix 1095
A Roots, Accuracy, and Bounds 1096
B Complex Numbers 1104
C Newton’s Method 1111
D Vectors In The Plane 1114
E Determinants 1120
Ready Reference 1123
Answers To Odd-Numbered Problems 1141
Index 1205
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Tags: William McCallum, Deborah Hughes Hallett, Andrew Gleason, Calculus Single