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Solutions Manual for James Stewart s MULTIVARIABLE CALCULUS (Seventh Edition) by Dan Clegg

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Solutions Manual for James Stewart s MULTIVARIABLE CALCULUS Seventh Edition written by Dan Clegg , Palomar College, Barbara Frank, Cape Fear Community College . This book cover the following topics.

• 10. PARAMETRIC EQUATIONS AND POLAR COORDINATES
10.1 Curves Defined by Parametric Equations, Running Circles Around Circles 15
10.2 Calculus with Parametric Curves, Bézier Curves 32
10.3 Polar Coordinates, Families of Polar Curves 48
10.4 Areas and Lengths in Polar Coordinates 51
10.5 Conic Sections 63
10.6 Conic Sections in Polar Coordinates 74

• 11. INFINITE SEQUENCES AND SERIES
11.1 Sequences, Logistic Sequences 110
11.2 Series 114
11.3 The Integral Test and Estimates of Sums 129
11.4 The Comparison Tests 138
11.5 Alternating Series 143
11.6 Absolute Convergence and the Ratio and Root Tests 149
11.7 Strategy for Testing Series 156
11.8 Power Series 160
11.9 Representations of Functions as Power Series 169
11.10 Taylor and Maclaurin , An Elusive Limit 194
11.11 Applications of Taylor Polynomials, Radiation from the Stars 209

• 12. VECTORS AND THE GEOMETRY OF SPACE
12.1 Three-Dimensional Coordinate Systems 235
12.2 Vectors 242
12.3 The Dot Product 251
12.4 The Cross Product, The Geometry of a Tetrahedron 271
12.5 Equations of Lines and Planes, Putting 3D in Perspective 285
12.6 Cylinders and Quadric Surfaces 287

• 13. VECTOR FUNCTIONS
13.1 Vector Functions and Space Curves 313
13.2 Derivatives and Integrals of Vector Functions 324
13.3 Arc Length and Curvature 333
13.4 Motion in Space: Velocity and Acceleration, Kepler’s Laws 359

• 14. PARTIAL DERIVATIVES
14.1 Functions of Several Variables 373
14.2 Limits and Continuity 391
14.3 Partial Derivatives 398
14.4 Tangent Planes and Linear Approximations 416
14.5 The Chain Rule 425
14.6 Directional Derivatives and the Gradient Vector 437
14.7 Maximum and Minimum Values, Designing a Dumpster, Quadratic Approximations and Critical Points
14.8 Lagrange Multipliers, Rocket Science, Hydro-Turbine Optimization 488

• 15. MULTIPLE INTEGRALS
15.1 Double Integrals over Rectangles 511
15.2 Iterated Integrals 516
15.3 Double Integrals over General Regions 521
15.4 Double Integrals in Polar Coordinates 534
15.5 Applications of Double Integrals 542
15.6 Surface Area 553
15.7 Triple Integrals, Volumes of Hyperspheres 574
15.8 Triple Integrals in Cylindrical Coordinates, The Intersection of Three Cylinders 582
15.9 Triple Integrals in Spherical Coordinates, Roller Derby 594
15.10 Change of Variables in Multiple Integrals 595

• 16. VECTOR CALCULUS
16.1 Vector Fields 623
16.2 Line Integrals 628
16.3 The Fundamental Theorem for Line Integrals 637
16.4 Green’s Theorem 643
16.5 Curl and Divergence 650
16.6 Parametric Surfaces and Their Areas 659
16.7 Surface Integrals 673
16.8 Stokes’ Theorem 684 v16.9 The Divergence Theorem 689

• 17. SECOND-ORDER DIFFERENTIAL EQUATIONS
17.1 Second-Order Linear Equations 711
17.2 Nonhomogeneous Linear Equations 715
17.3 Applications of Second-Order Differential Equations 720
17.4 Series Solutions 725

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