Calculus, with analytic geometry
The aim of this major revision is to create a contemporary text which incorporates the best features of calculus reform yet preserves the main structure of an established and well-tested calculus course. The multivariate calculus material is completely rewritten to include the concept of a vector field and focuses on major physics and engineering applications of vector analysis. Covers such new topics as Jacobians, Kepler's laws, conics in polar coordinates and parametric representation of surfaces. Contains expanded use of calculator computations and numerous exercises.
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Coordinates Graphs Lines
Functions and Limits
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3-space angle antiderivative apply approximate arc length axis calculus called chain rule circle constant continuous cos2 cosh curve cylindrical decreasing defined definite integral denote distance diverges domain ellipse endpoint Evaluate Example Exercise Set expression Find the area formula function geometric given hyperbola IMPROPER INTEGRALS increasing indeterminate form INFINITE SERIES intersection inverse L'Hopital's rule lim f(x limit line segment LOGARITHM Maclaurin series mathematics mean-value theorem minimum value notation obtain open interval parabola parallel parametric equations PARTIAL DERIVATIVES particle moving perpendicular plane polar coordinates polynomial positive problem Proof Prove radius real number rectangle region relative extremum relative maximum result satisfies sec2 secant line sequence series converges shown in Figure sides sigma notation sin2 sinh Sketch the graph slope Solution subintervals Substituting surface tangent line Taylor series trigonometric variables vector velocity vertical volume x-axis yields