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10. PARAMETRIC EQUATIONS AND POLAR COORDINATES. Curves Defined by Parametric Equations. Laboratory Project: Families of Hypocycloids. Calculus with Parametric Curves. Laboratory Project: Bezier Curves. Polar Coordinates. Laboratory Project: Families of Polar Curves. Areas and Lengths in Polar Coordinates. Conic Sections. Conic Sections in Polar Coordinates. Review. Problems Plus. 11. INFINITE SEQUENCES AND SERIES. Sequences. Laboratory Project: Logistic Sequences. Series. The Integral Test and Estimates of Sums. The Comparison Tests. Alternating Series. Absolute Convergence and the Ratio and Root Tests. Strategy for Testing Series. Power Series. Representations of Functions as Power Series. Taylor and Maclaurin Series. Laboratory Project: An Elusive Limit. Writing Project: How Newton Discovered the Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Review. Problems Plus. 12. VECTORS AND THE GEOMETRY OF SPACE. Three-Dimensional Coordinate Systems. Vectors. The Dot Product. The Cross Product. Discovery Project: The Geometry of a Tetrahedron. Equations of Lines and Planes. Cylinders and Quadric Surfaces. Review. Problems Plus. 13. VECTOR FUNCTIONS. Vector Functions and Space Curves. Derivatives and Integrals of Vector Functions. Arc Length and Curvature. Motion in Space: Velocity and Acceleration. Applied Project: Kepler's Laws. Review. Problems Plus. 14. PARTIAL DERIVATIVES. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Tangent Planes and Linear Approximation. Applied Project: The Speedo LZR Race Suit. The Chain Rule. Directional Derivatives and the Gradient Vector. Maximum and Minimum Values. Applied Project: Designing a Dumpster. Discovery Project: Quadratic Approximations and Critical Points. Lagrange Multipliers. Applied Project: Rocket Science. Applied Project: Hydro-Turbine Optimization. Review. Problems Plus. 15. MULTIPLE INTEGRALS. Double Integrals over Rectangles. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals. Surface Area. Triple Integrals. Discovery Project: Volumes of Hyperspheres. Triple Integrals in Cylindrical Coordinates. Discovery Project: The Intersection of Three Cylinders. Triple Integrals in Spherical Coordinates. Applied Project: Roller Derby. Change of Variables in Multiple Integrals. Review. Problems Plus. 16. VECTOR CALCULUS. Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Green's Theorem. Curl and Divergence. Parametric Surfaces and Their Areas. Surface Integrals. Stokes' Theorem. Writing Project: Three Men and Two Theorems. The Divergence Theorem. Summary. Review. Problems Plus. 17. SECOND-ORDER DIFFERENTIAL EQUATIONS. Second-Order Linear Equations. Nonhomogeneous Linear Equations. Applications of Second-Order Differential Equations. Series Solutions. Review. Problems Plus. APPENDIXES. A Numbers, Inequalities, and Absolute Values. B Coordinate Geometry and Lines. C Graphs of Second-Degree Equations. D Trigonometry. E Sigma Notation. F Proofs of Theorems. G The Logarithm Defined as an Integral. H Complex Numbers. I Answers to Odd-Numbered Exercises. INDEX.
Posted August 3, 2010
Well, Calculus three is hard, no doubt about that and using this book didn't make it much easier for me. In any case, I really liked all the important formulae listed a the back of the book and you can just tear those sheets out if you choose to. They only have the some of the odd number answers which sucks and those are not in detail. It does not have enough proofs. It's not a very clear book, but if it is assigned to you by your professor and you have to do your homework from it, then you are essentially stuck with it. The only way I was able to sail through the class was by purchasing the student manual. Without it, i would have been lost! What I really recommend is taking the Cal 3 class with a great professor and/or having a fantastic TA. Good Luck!!!Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.
Posted July 23, 2008
I picked up this book expecting never to open it again. I was pleasantly surprised at how good this book actually was at teaching concepts, better than some other books (which were very thorough, but too in depth to keep up with my course), some online aids (which weren't in depth enough), and my professor (who was in a bit of a hurry). After using two of Stewart's others books 'Single Variable Calculus: Early Transcendentals Volumes 1 & 2', I expected that this book would be horrible. Either Stewart is far better at explaining more advanced topics, or I hadn't developed enough mathematical sense to understand how good the other books were (my teachers raved about them, though). My only complaints are these: 1. Some more in-depth proofs of some of the more difficult [to prove] theorems, or some insight as to how one might prove them would make the book better. 2. Sections should begin on a new page, not at the bottom of one so that one continually has to flip back and forth to see a theorem applied to a problem.Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.
Posted December 18, 2008
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