\BOOKMARK [0][-]{chapter.0}{Preface}{}
\BOOKMARK [0][-]{chapter.1}{The Integral}{}
\BOOKMARK [1][-]{section.1.1}{Area}{chapter.1}
\BOOKMARK [1][-]{section.1.2}{Some applications of area}{chapter.1}
\BOOKMARK [2][-]{subsection.1.2.1}{Total Accumulation as ``Area''}{section.1.2}
\BOOKMARK [2][-]{subsection.1.2.2}{Problems}{section.1.2}
\BOOKMARK [1][-]{section.1.3}{Sigma notation and Riemann sums}{chapter.1}
\BOOKMARK [2][-]{subsection.1.3.1}{Sums of areas of rectangles}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.2}{Area under a curve –– Riemann sums}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.3}{Two special Riemann sums: lower and upper sums}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.4}{Problems}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.5}{The trapazoid rule}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.6}{Simpson's rule}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.7}{Trapazoidal vs. Simpson: Which Method Is Best?}{section.1.3}
\BOOKMARK [1][-]{section.1.4}{The definite integral}{chapter.1}
\BOOKMARK [2][-]{subsection.1.4.1}{The Fundamental Theorem of Calculus}{section.1.4}
\BOOKMARK [2][-]{subsection.1.4.2}{Problems}{section.1.4}
\BOOKMARK [2][-]{subsection.1.4.3}{Properties of the definite integral}{section.1.4}
\BOOKMARK [2][-]{subsection.1.4.4}{Problems}{section.1.4}
\BOOKMARK [1][-]{section.1.5}{Areas, integrals, and anti-derivatives}{chapter.1}
\BOOKMARK [2][-]{subsection.1.5.1}{Integrals, Antiderivatives, and Applications}{section.1.5}
\BOOKMARK [1][-]{section.1.6}{Indefinite Integrals and Change}{chapter.1}
\BOOKMARK [2][-]{subsection.1.6.1}{Indefinite Integrals}{section.1.6}
\BOOKMARK [2][-]{subsection.1.6.2}{Physical Intuition}{section.1.6}
\BOOKMARK [1][-]{section.1.7}{Substitution and Symmetry}{chapter.1}
\BOOKMARK [2][-]{subsection.1.7.1}{The Substitution Rule}{section.1.7}
\BOOKMARK [2][-]{subsection.1.7.2}{Changing the variable and definite integrals}{section.1.7}
\BOOKMARK [2][-]{subsection.1.7.3}{Symmetry}{section.1.7}
\BOOKMARK [2][-]{subsection.1.7.4}{Problems}{section.1.7}
\BOOKMARK [0][-]{chapter.2}{Applications}{}
\BOOKMARK [1][-]{section.2.1}{Applications of the integral to area}{chapter.2}
\BOOKMARK [2][-]{subsection.2.1.1}{Using integration to determine areas}{section.2.1}
\BOOKMARK [1][-]{section.2.2}{Computing Volumes of Surfaces of Revolution}{chapter.2}
\BOOKMARK [2][-]{subsection.2.2.1}{Disc method}{section.2.2}
\BOOKMARK [2][-]{subsection.2.2.2}{Shell method}{section.2.2}
\BOOKMARK [1][-]{section.2.3}{Average Values}{chapter.2}
\BOOKMARK [1][-]{section.2.4}{Moments and centers of mass}{chapter.2}
\BOOKMARK [2][-]{subsection.2.4.1}{Point Masses}{section.2.4}
\BOOKMARK [2][-]{subsection.2.4.2}{Center of mass of a region in the plane}{section.2.4}
\BOOKMARK [2][-]{subsection.2.4.3}{x For A Region}{section.2.4}
\BOOKMARK [2][-]{subsection.2.4.4}{y For A Region}{section.2.4}
\BOOKMARK [2][-]{subsection.2.4.5}{Theorems of Pappus}{section.2.4}
\BOOKMARK [1][-]{section.2.5}{Arclengths}{chapter.2}
\BOOKMARK [2][-]{subsection.2.5.1}{2--d Arclength}{section.2.5}
\BOOKMARK [2][-]{subsection.2.5.2}{3--d Arclength}{section.2.5}
\BOOKMARK [0][-]{chapter.3}{Polar coordinates and complex numbers}{}
\BOOKMARK [1][-]{section.3.1}{Polar Coordinates}{chapter.3}
\BOOKMARK [1][-]{section.3.2}{Areas in Polar Coordinates}{chapter.3}
\BOOKMARK [1][-]{section.3.3}{Complex Numbers}{chapter.3}
\BOOKMARK [2][-]{subsection.3.3.1}{Polar Form}{section.3.3}
\BOOKMARK [1][-]{section.3.4}{Complex Exponentials and Trig Identities}{chapter.3}
\BOOKMARK [2][-]{subsection.3.4.1}{Trigonometry and Complex Exponentials}{section.3.4}
\BOOKMARK [1][-]{section.3.5}{Integrals of Trigonometric Functions}{chapter.3}