An innovative text that emphasizes the graphical, numerical and analytical aspects of calculus throughout and often asks students to explain ideas using words. This problem driven text introduces topics with a real-world problem and derives the general results from it. It can be used with any technology that can graph and find definite integrals numerically. The derivative, the integral, differentiation, and differential equations are among the topics covered.
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A LIBRARY OF FUNCTIONS
THE DEFINITE INTEGRAL
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acceleration annual answer antiderivative approximation Assume chain rule complex number concave constant converge cost cosx critical points decimal places decreasing definite integral density function difference quotient differential equation dy/dx equilibrium error estimate Euler's method Example Explain exponential function factor feet Find a formula Fourier ft/sec function f(x Fundamental Theorem given gives graph in Figure growth rate height horizontal improper integral increasing inflection points initial integrand interval linear look mass maxima maxima and minima maximum minima negative Notice oscillation phase plane population positive present value Problems for Section quantity radius rate of change rectangle represents Riemann sum right-hand sums root shown in Figure shows sinx Sketch a graph slice slope field solution curves solve substitution Suppose Table tangent line Taylor polynomial Taylor series temperature trapezoid vertical Write zero