Calculus, with Analytic GeometryThe 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. |
Contents
Coordinates Graphs Lines | 1 |
Functions and Limits | 55 |
Differentiation | 120 |
Copyright | |
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3-space a₁ alternating series test angle antiderivative approximate arc length axis b₁ C₁ calculator chain rule circle constant cos² cosh curve decimal place accuracy defined denote derivative differentiable distance diverges dt dt dx dx ellipse endpoint Evaluate Example Exercise Set Find the area formula function f geometric given graph of ƒ hyperbola increasing indeterminate form intersection inverse L'Hôpital's rule Let f(x lim f(x lim h→0 limit line segment Maclaurin series mathematics maximum obtain open interval parabola parallel parametric equations perpendicular plane polar coordinates polynomial positive Proof Prove radius real number rectangle region result satisfies sec² secant line sequence series converges shown in Figure sin² sinh Sketch the graph slope Solution solve subintervals Substituting surface tangent line Taylor series u₁ vector velocity vertex vertical x-axis x₁ y-axis yields