\begin{theindex}

  \item ``area function'' $A(u)$, 137
  \item ``distance traveled'', 142
  \item ``dummy variable'', 145
  \item ``fundamental theorem of calculus'', 145
  \item {\bf EVERYTHING}, 139
  \item {\bf variable of integration}, 136
  \item 5-th left endpoint Riemann sum, 136

  \indexspace

  \item  absolute error, 36
  \item  acceleration, 43
  \item  acceleration due to gravity, 44
  \item  acre, 36
  \item  amplitude, 56, 59
  \item  angular velocity, 158
  \item  antiderivatives, 45
  \item  asymptote, 10
  \item  average velocity, 21, 24, 25
  \item  bicycle, 39, 44, 48
  \item  bicycle tire, 61
  \item  bicycle wheel, 60
  \item  caption, 152
  \item  car, 39
  \item  car rental, 6
  \item  Celsius, 6
  \item  chain rule, 45, 46, 50
  \item  chord, 19
  \item  clockwise angle, 55
  \item  collaborative groups, 151
  \item  composition of  two functions, 45
  \item  Conclusions, 152
  \item  connecting rod, 158
  \item  corners, 26
  \item  Cover Page, 152
  \item  crank, 158
  \item  crankshaft, 158
  \item  crude oil, 53
  \item  cusp, 27
  \item  Cusps, 26
  \item  cylinder, 37
  \item  degree $2$, 5
  \item  dependent variable, 11
  \item  derivative, 20, 25
  \item  Derivative Function, 25
  \item  Derivative of Trig Functions, 63
  \item  Difference Quotient, 19
  \item  distance function, 48
  \item  domain of a function, 10
  \item  drawbridge, 60
  \item  elementary functions, 17
  \item  ellipse, 14, 49
  \item  English, 151
  \item  explicit form, 49
  \item  Fahrenheit, 6
  \item  Falling Body Formula, 44
  \item  foxes, 60
  \item  fractional powers, 49
  \item  function, 9
  \item  golds coins, 6
  \item  Graphical Differentiation, 27
  \item  Graphs of Trig Functions, 56
  \item  gravity, 44, 155
  \item  guidelines, 151
  \item  Horizontal expansion., 14
  \item  horizontal ledge, 65
  \item  Horizontal shifts, 13
  \item  horizontal tangent, 41
  \item  hyperbola, 53
  \item  implicit  form, 49
  \item  Implicit Differentiation, 49
  \item  implicit differentiation, 50, 51
  \item  implicit equation, 49, 51
  \item  Implicit Functions, 49
  \item  implicitly defined curve, 65
  \item  income tax, 2
  \item  independent variable, 11
  \item  instantaneous velocity, 22, 24, 25
  \item  internal combustion engine, 158
  \item  interpretations, 153
  \item  Lab projects, 151
  \item  ladder, 48
  \item  light intensity, 52, 53
  \item  limit, 20
  \item  limiting value, 20
  \item  linear combination, 39
  \item  Linearity of the Derivative, 39
  \item  lower semicircle function, 50
  \item  magician, 155
  \item  Maple worksheet, 152
  \item  mathematical biology, 60
  \item  Mathematics Teacher, 60
  \item  mean daily temperature, 58, 60
  \item  Michael Moshen, 155
  \item  natural domain, 10
  \item  negative angle, 55
  \item  negative powers, 49
  \item  Newton's method, 51
  \item  normal mean temperature, 58
  \item  open-top box, 11
  \item  paperweights, 37
  \item  parabola, 22
  \item  pebble, 61
  \item  percent error, 34, 36
  \item  period, 59
  \item  period , 56
  \item  phase shift, 58, 59
  \item  photocopy, 6
  \item  piston, 158
  \item  point-slope, 3
  \item  polygonal graph, 7
  \item  polygonal line, 2
  \item  power function, 31
  \item  Power Rule, 31
  \item  predator-prey, 60
  \item  product rule, 40
  \item  Pythagorean theorem, 4
  \item  quadrant, 1
  \item  quotient rule, 41
  \item  rabbits, 60
  \item  radian measure, 55
  \item  recurring decimal, 34
  \item  rope, 65
  \item  second derivative, 42, 43
  \item  semicircle, 46
  \item  semicircle function, 49
  \item  semimajor axis, 14, 49
  \item  semiminor axis, 14
  \item  Shifts and Expansions, 13
  \item  sine wave, 58
  \item  sinusoidal function, 56
  \item  Sinusoidal Functions, 55
  \item  slope, 2
  \item  slope of the tangent line, 63
  \item  slope\nonbreakingspace of\nonbreakingspace chord, 19
  \item  smooth, 26
  \item  speed, 158
  \item  spring, 61
  \item  tangent line, 19, 20
  \item  Tangent Line Approximation, 31
  \item  tangent line approximation, 31, 40, 45, 48, 51, 64, 65
  \item  tangent line approximation formula, 32
  \item  tank, 53
  \item  tax, 7, 45
  \item  Taylor polynomials, 33
  \item  tile, 36
  \item  triangular sculpture, 155
  \item  Trig Derivatives, 64
  \item  Trig Functions, 55
  \item  unit circle, 4, 55
  \item  velocity, 43, 61, 156, 158
  \item  Vertical expansion, 14
  \item  vertical line, 3
  \item  vertical line test, 10
  \item  vertical shift, 58, 59
  \item  Vertical shifts, 13
  \item  waves, 65
  \item  wrist pin, 158
  \item  y-intercept, 2

  \indexspace

  \item absolute maximum, 98
  \item acceleration problem, 129
  \item Acceleration to Velocity to Distance, 128
  \item angular velocity, 69
  \item antiderivative, 127
  \item area between two curves, 139
  \item area under a curve, 135
  \item asymptote of a curve, 101
  \item ATE, iii

  \indexspace

  \item concavity, 100
  \item curve sketching, 97
  \item cylinder, 158

  \indexspace

  \item definite integral, 135
  \item derivative of the area function, 138
  \item differential equation, 128
  \item downward concavity, 100

  \indexspace

  \item ellipse, 68
  \item equator, 37
  \item even functions, 101

  \indexspace

  \item falling body formula, 71
  \item falling body problem, 128
  \item focii, 49
  \item Formulas, v

  \indexspace

  \item general antiderivative, 127
  \item general principle for setting up  parametric equations, 69
  \item gravitational acceleration, 129

  \indexspace

  \item High School Algebra, iii
  \item highest value, 97
  \item horizontal asymptote, 101
  \item horizontal component, 71
  \item hypotenuse, 89, 90

  \indexspace

  \item implicit differentiation, 112
  \item indefinite integral, 127
  \item influence of gravity, 69
  \item initial velocity, 70
  \item integrand, 127
  \item iterating Newton's method, 120
  \item Iterative procedures, 119

  \indexspace

  \item Koblitz, iii

  \indexspace

  \item largest possible cone inside a sphere, 111
  \item limit of integration, 136, 146

  \indexspace

  \item magnitude and direction, 70
  \item max/min problem, 107
  \item maximize profit, 109
  \item maximum value, 107
  \item method of substitution, 130

  \indexspace

  \item Newton's method, 119
  \item NSF, iii

  \indexspace

  \item odd functions, 102

  \indexspace

  \item parabola, 110
  \item parameterized curves, 67
  \item parameterizing the cycloid, 81
  \item parameterizing the trochoid, 84
  \item parametric equations, 69
  \item parametrically, 67
  \item Plane Geometry, iii
  \item point of inflection, 100
  \item prerequisites to Ma113, iii
  \item Pythagorean Theorem, 91
  \item Pythagorean theorem, 89

  \indexspace

  \item quadratic formula, 71
  \item qualitative picture of graph, 97

  \indexspace

  \item related rates, 87
  \item related rates problem, 87
  \item related rates: airplane problem, 88
  \item related rates: balloon problem, 88
  \item related rates: puddle problem, 87
  \item related rates: swing problem, 90
  \item related rates: two roads crossing problem, 91
  \item related rates: water in cone problem, 89
  \item Riemann sum, 135
  \item Riemann sum approximation, 135

  \indexspace

  \item second derivative test, 97, 99
  \item several variables, 90
  \item subintervals, 135, 136
  \item summation symbol, 136
  \item symmetry, 101

  \indexspace

  \item the baton problem, 79
  \item time parameter, 68
  \item trajectory, 68, 71, 81
  \item Trigonometry, iii

  \indexspace

  \item upward concavity, 100

  \indexspace

  \item vector, 70
  \item velocity vector, 70
  \item vertical asymptote, 101, 109
  \item vertical component of velocity, 71
  \item vertical tangent, 98

\end{theindex}
