MATHEMATICS   Formulas, Graphs, Tables, . . .  < High School to University Level >
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
 
 
 
 
 
 
 
 
 
Copyright © 2004 - 2020, Nabla Ltd.  All rights reserved.