MATHEMATICS
Formulas, Graphs, Tables, . . .
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High School to University Level
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CONTENTS L
111
The approximation of the sine function
by polynomial using Taylor's or Maclaurin's formula
Properties of the power series expansion of the sine function
Extreme points, local (or relative) maximum and local minimum
The first derivative test
The second derivative test and concavity
Finding and classifying critical (or stationary) points
Points of inflection
112
Finding and classifying critical (or stationary) points examples
Finding extreme points of quartic function example
Finding extreme points and points of inflections of quintic function example
113
Integral calculus
The definite integral
The area between the graph of a function and the x-axis over a closed interval
The upper sum and the lower sum
114
The definition of the definite integral
Riemann sum
Calculating a definite integral from the definition
115
Calculating a definite integral from the definition examples
Physical applications to the definite integral
116
Describing motion of objects using velocity - time graphs
Evaluating the area under the graph of a function using the definition of the definite integral examples
117
The area between the graph of a function and the x-axis over a closed interval
Geometric interpretation of the definite integral
Properties of the definite integral
The definite integral over interval of zero length
Reverse order of integration
The constant multiple rule
The integral of the sum or difference of two functions
Internal addition of the definite integral
The definite integral of an odd function
The definite integral of an even function
The definite integral of a nonnegative and non-positive functions
Relationship of the definite integrals of two functions over the same interval of integration
Absolute integrability
The mean value theorem
The average value of a function over the given interval
118
The indefinite integral
Integration - inverse of differentiation
Constant of integration, the arbitrary constant term in the expression of the indefinite integral
Evaluating the indefinite integral example
119
Differentiation of an indefinite integral with respect to upper and lower limits
The fundamental theorem of calculus
The fundamental theorem of differential calculus
Evaluating definite integrals using indefinite integrals
The fundamental theorem of integral calculus
Evaluating the definite integral examples
Cavalieri - Gregory formula for quadrature of the parabola
120
Basic rules of integration
Table of indefinite integrals
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