CalcLabs with Mathematica for Stewart's Multivariable Calculus (6TH)

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CalcLabs with Mathematica for Stewart's Multivariable Calculus (6TH)

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  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 273 p.
  • 言語 ENG,ENG
  • 商品コード 9780495118909
  • DDC分類 515

Table of Contents

Prologue                                           vii
1 Vectors 1 (24)
1.1 Visualizing Vectors with Mathematica 1 (3)
1.2 Length and Arithmetic Operations 4 (4)
1.3 The Dot Product and Projections 8 (5)
Exercises 12 (1)
1.4 The Cross Product 13 (4)
1.5 Equations of Lines 17 (2)
1.6 Equations of Planes 19 (6)
Exercises 24 (1)
2 Surfaces 25 (17)
2.1 Graphs of Functions of Two Variables 25 (5)
2.2 Traces and Contours 30 (3)
Exercises 32 (1)
2.3 Cylindrical and Spherical Coordinates 33 (6)
2.4 3D Contours and the Quadric Surfaces 39 (3)
Exercises 41 (1)
3 Vector-valued Functions 42 (31)
3.1 Space Curves 42 (5)
Exercises 46 (1)
3.2 Derivatives 47 (4)
Exercises 50 (1)
3.3 Parametrization 51 (4)
3.4 Arc Length and Curvature 55 (7)
3.5 Velocity and Acceleration 62 (5)
Exercises 66 (1)
3.6 Parametric Surfaces: Vector-valued 67 (6)
Functions of Two Variables
Exercises 72 (1)
4 Multivariate Functions 73 (40)
4.1 Limits and Continuity 73 (5)
Exercises 77 (1)
4.2 Partial Derivatives 78 (5)
Exercises 82 (1)
4.3 The Tangent Plane and Linear 83 (4)
Approximation
Exercises 86 (1)
4.4 Directional Derivatives and the 87 (12)
Gradient
Exercises 98 (1)
4.5 Optimization and Lagrange Multipliers 99 (14)
Exercises 112(1)
5 Multiple Integrals 113(29)
5.1 Double Integrals 113(7)
5.2 Polar Coordinates 120(2)
5.3 Applications 122(4)
Exercises 125(1)
5.4 Triple Integrals 126(3)
5.5 Cylindrical and Spherical Coordinates 129(3)
Exercises 131(1)
5.6 Change of Variables 132(10)
Exercises 140(2)
6 Vector Calculus 142(31)
6.1 Vector Fields 142(7)
Exercises 148(1)
6.2 Line Integrals 149(7)
6.3 Green's Theorem 156(4)
Exercises 159(1)
6.4 Surface Integrals 160(6)
Exercises 165(1)
6.5 Divergence, Curl, and the Laplacian 166(1)
6.6 Stokes' Theorem 167(3)
6.7 The Divergence Theorem 170(3)
Exercises 171(2)
7 Projects 173(49)
7.1 Osculating Circles 173(1)
7.2 Coriolis Acceleration 174(2)
7.3 An Ant on a Helix 176(1)
7.4 Animating Particle Motion 176(2)
7.5 Flying the Osculating Plane 178(1)
7.6 Drawing Curves on a Sphere 179(2)
7.7 Steepest Descent Curves 181(3)
7.8 Critical Point Classification 184(4)
7.9 Least Squares and Curve Fitting 188(2)
7.10 More Curve Fitting: Nonlinear Least 190(2)
Squares
7.11 The Method of Steepest Descent 192(5)
7.12 Quadratic Approximation and 197(3)
Optimization
7.13 Newton's Method for Nonlinear 200(2)
Equations
7.14 Constrained Minimization with 202(4)
FindMinimum
7.15 3D Coordinate Systems 206(5)
7.16 Rolling Marbles on Surfaces 211(2)
7.17 Balancing a Region 213(1)
7.18 Reflecting Points 214(1)
7.19 2D Space Exploration 215(2)
7.20 Streamlines I: Velocity Fields and 217(2)
Steady Flow
7.21 Streamlines II: Incompressible 219(3)
Potential Flow
Appendix Mathematica Basics 222(48)
A.1 Getting Started 222(13)
A.2 Functions 235(6)
A.3 Equations 241(4)
A.4 Lists 245(6)
A.5 Rules 251(2)
A.6 Graphics 253(4)
A.7 Animate and Manipulate 257(3)
A.8 Avoiding and Getting Out of Trouble 260(6)
A.9 Turning a Notebook into a Report 266(2)
A.10 Miscellaneous Advice 268(2)
Index 270