\begin{theindex}

  \item $ds/dt$, 20
  \item $p$-{\em series}, 165
  \item $u$-substitution technique of integration, 79
  \item {\bf eccentricity} of an ellipse, 19
  \item {\bf square} cross-sections, 12
  \item {\em Taylor series for $f$ at} $ x = a $, 192
  \item {\em power series in}  $ x - a $, 187
  \item {\em remainder after} $n$-terms, 166
  \item {\it net} distance traveled, 5
  \item {\it qualitative} information, 105
  \item {\it second order} differential equation, 114
  \item {\it total} distance traveled, 5

  \indexspace

  \item  caption, 202
  \item  collaborative groups, 201
  \item  Conclusions, 202
  \item  Cover Page, 202
  \item  English, 201
  \item  guidelines, 201
  \item  interpretations, 202
  \item  Lab projects, 201
  \item  Maple worksheet, 202

  \indexspace

  \item a solid with finite volume but infinite surface area, 59
  \item alternating series, 169
  \item angular velocity, 18
  \item antiderivative method, 21, 22
  \item antiderivative of $x^{-1}$, 50
  \item applying Taylor's formula, 129
  \item approximation, 125
  \item approximation method, 21
  \item arclength, 20
  \item arctangent, 42
  \item area enclosed by two curves, 1
  \item area out to infinity, 57
  \item ATE, iii
  \item average value of a function, 76
  \item axis of symmetry, 29

  \indexspace

  \item bad notation, 4
  \item bad notation, $\tan^{-1}x$, 42
  \item balancing point, 33
  \item bank interest problem, 63, 69
  \item best view problem, 44
  \item bounded above, 153
  \item bounded sequence, 153
  \item Brook Taylor, 126
  \item bug problem, 22
  \item bug's shadow, 23

  \indexspace

  \item c\'ordobas, 71
  \item cardiac output, 29
  \item center of mass, 33
  \item centroid, 34
  \item centroid of Nicaragua, 37
  \item circle, 17
  \item circular cross-section, 28
  \item Combined circular motion, 17
  \item common ratio, 157
  \item companion antiderivative formula, 45
  \item compounded continuously, 98
  \item concentration, 103
  \item continuous compounding, 64
  \item converge absolutely, 185
  \item convergent sequence, 147
  \item convergent series, 155
  \item converges to the limit, 147
  \item cross sectional area, 10
  \item cycloid, 18

  \indexspace

  \item daily compounding, 64
  \item damped harmonic oscillation, 116
  \item decreasing, 152
  \item degree/radian warning, 42
  \item differential equation, 69
  \item differential equation $y'=\pm ky$, 97
  \item Divergence Test, 168
  \item divergent, 147
  \item divergent series, 155
  \item dominates, 168
  \item doubling time, 71
  \item draw a picture, 14

  \indexspace

  \item effective annual interest rate, 70
  \item ellipse, 18, 19
  \item ellipse parameterized from a focus, 20
  \item erm-by-term, 189
  \item expanding $f$ in a power series, 189
  \item exponential function, 65
  \item exponential term, 102

  \indexspace

  \item finite sequences, 145
  \item first term, 145
  \item focus of an ellipse, 19
  \item force of repulsion, 94
  \item Formulas, v
  \item freeway problem, 59, 94
  \item fundamental constant of mathematics, 63
  \item Fundamental Theorem of Calculus, 1
  \item fundamental theorem of calculus, 49

  \indexspace

  \item goes backwards, 41
  \item greatest lower bound, 154

  \indexspace

  \item half-life, 72
  \item harmonic oscillation, 115
  \item harmonic series, 159
  \item hemisphere, 8
  \item home mortgages, 99
  \item horizontal asymptote, 102
  \item horizontal velocity, 17
  \item hypotenuse, 93

  \indexspace

  \item implicitly differentiate, 43
  \item improper integral, 57
  \item increasing, 152
  \item Indeterminate Form, 134
  \item indeterminate form $ 0/0 $, 135
  \item infinite decimal, 157
  \item infinite series, 145, 155
  \item initial velocity, 7, 17
  \item instantaneous birth rate, 71
  \item instantaneous interest rate, 70
  \item instantaneous rate of interest, 97
  \item integration by parts, 79
  \item integration of even powers of sin and cos, 76
  \item integration of odd powers of sin and cos, 75
  \item integration of {\bf rational functions}, 85
  \item interpolating, 29
  \item interpolation, 28
  \item interval of convergence, 187
  \item inverse function, 41
  \item inverse sine function, 45
  \item inverse tangent function, 42
  \item inverse trig substitution, 91, 94

  \indexspace

  \item Koblitz, iii

  \indexspace

  \item L'Hospital's Rule, 134
  \item law of conservation of energy, 115
  \item least upper bound, 154
  \item left endpoint Riemann sum, 27
  \item limit, 147
  \item limit problems, 139
  \item log to the base $a=2$, 53
  \item logarithmic differentiation, 53
  \item logarithms to the base 10, 53

  \indexspace

  \item Maclaurin series for $f$, 192
  \item main uses of integration by parts, 79
  \item major axis, 18
  \item method of partial fractions, 112
  \item method of substitution, 37
  \item minor axis, 18
  \item mirror images, 41, 43
  \item model for the spread of an epidemic, 112
  \item moment, 33
  \item moment integral, 37
  \item monotonic, 152

  \indexspace

  \item natural logarithm, 49
  \item Newton's law of cooling, 101
  \item Newton's method, 125
  \item nonlinear mixing problems, 113
  \item nonlinear separation of variables, 111
  \item NSF, iii
  \item numerical integration, 22

  \indexspace

  \item parabola, 2
  \item parameterized by time, 17
  \item parameterized curves, 17
  \item parametric equations, 20
  \item partial fractions, 85
  \item Pinching Principle for Sequences, 151
  \item Plutonium 239, 72
  \item point-masses, 33
  \item power series, 185
  \item principal value, 42
  \item properties of ln, 49
  \item properties of the exponential function, 65
  \item Pythagorean theorem, 60

  \indexspace

  \item radius of convergence, 187
  \item rate of inflation, 71
  \item rate of payment, 98
  \item recursively, 146
  \item Related Rate Volume Problems, 13
  \item representing $ f $ by a power series, 189
  \item Riemann sum, 25, 59
  \item Riemann sum rectangles, 9
  \item right circular cone, 8
  \item right endpoint Riemann sum, 26

  \indexspace

  \item second derivative method, 44
  \item second term, 145
  \item seesaw principle, 33
  \item separation of variables, 69
  \item sequence, 145, 146
  \item sequence of partial sums, 155
  \item shortcuts, 3
  \item significant figures, 28
  \item solid of revolution, 7
  \item sphere, 8, 10
  \item stay close, 147
  \item strictly decreasing, 152
  \item strictly increasing, 152
  \item substitution $u=\cos\theta$, 93
  \item sum of the infinite series, 155
  \item summation notation, 9

  \indexspace

  \item tangent line approximation, 44
  \item Taylor Polynomials, 126
  \item Taylor's Theorem, 125, 127
  \item technique of integration: substitution, 75
  \item terms, 145
  \item terms of the series, 156
  \item the exponential function, 63
  \item third degree Taylor polynomial, 126
  \item total moment, 35
  \item trapezoid rule, 21, 27

  \indexspace

  \item variant on the mixing problem, 114
  \item velocity $v(t)$ of a falling body, 102
  \item vertical components, 22

\end{theindex}
