Calculus : single and multivariable

著者

書誌事項

Calculus : single and multivariable

Deborah Hughes-Hallett ... [et al.]

Wiley, c2013

6th ed.

  • : cloth
  • : binder-ready

タイトル別名

Calculus : single & multivariable

大学図書館所蔵 件 / 全2件

この図書・雑誌をさがす

注記

Includes index

Produced by the Calculus Consortium and initially funded by a National Science Foundation Grant.

内容説明・目次

内容説明

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.

目次

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

「Nielsen BookData」 より

詳細情報

ページトップへ