Calculus Single and Multivariable 6th Edition Hughes-Hallett Test Bank

Calculus Single and Multivariable 6th Edition Hughes-Hallett Test Bank

Product details:

• ISBN-10 ‏ : ‎ 1118231147
• ISBN-13 ‏ : ‎ 978-1118231142
• Author: Deborah J. Hughes Hallett

Calculus: Single and Multivariable, 6th Edition continues the effort to promote courses in which understanding and computation reinforce each other. The 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. The text includes a variety of problems and examples from the physical, health, and biological sciences, engineering and economics; emphasizing the connection between calculus and other fields. 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.

Table 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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