189
Index
Algebra of summation, 43
Algebra of vectors, 77
Angle between vectors, 78
Anti-derivatives, 1
Area between curves, 21
Area formula for polar curves, 70
Arithmetic of vectors, 76
C (unknown constant)
in initial value problems, 35
of integration, 2
Calculus with vector curves, 85
Circles
in polar coordinates, 63
Circular integration by parts, 137
Constant
of integration, 2
unknown, 2
Constant of integration, 2
Conversion
polar to rectangular, 62
Coordinates
polar, 60
Cross product, 79
Curves
parametric, 50
Definite integral, 12
Derivative
of a parametric curve, 55
of a polar curve, 67
of a root with multiplicity, 104
Dot product
of vectors, 76
Even function, 24
integral of, 24
Factoring
polynomials, 163
Fast polynomial multiplication algorithm, 92
Finding partial fractions coefficients, 168
Function
even, 24
integral of, 24
odd, 24
integral of, 26
parametric, 49
rational, 109
Fundamental theorem of calculus I, 13
Fundamental theorem of calculus II, 13
Graph paper
polar, 62
Identities
polynomial, 112
Indefinite integral, 9
Induction
mathematical, 40
Initial value problems, 31
Integral, 1
definite, 12
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