Differential Calculus
Calculus Contents D
Applications of the derivative
Tangent, normal, subtangent and subnormal
Property of the parabola
Property of power functions
Property of the exponential function
Angle between two curves
Angle between two curves examples
Differential of a function
Use of differential to approximate the value of a function
Rules for differentials
Differentials of some basic functions
Higher order derivatives and higher order differentials
Higher order derivatives
Higher order derivatives examples
Higher derivative formula for the product - Leibniz formula
Higher derivatives of composite functions
Higher derivatives of composite functions examples
Higher derivatives of implicit functions
Higher derivatives of implicit functions examples
Higher derivatives of parametric functions
Higher derivatives of parametric functions examples
Higher order differentials
Higher order differentials examples
Applications of differentiation - the graph of a function and its derivative
Definition of increasing and decreasing
Increasing/decreasing test
Rolle's theorem
The mean value theorem
Generalization of the mean value theorem
Cauchy's mean value theorem or generalized mean value theorem
L'Hospital's rule - limits of indeterminate forms
Applications of L'Hospital's rule - evaluation of limits of indeterminate forms, examples
a)
Applications of differentiation - the graph of a function and its derivatives
Generalization of the mean value theorem, concavity of the graph of a function
Concavity of the graph of a function
Concave up and concave down definition
Points of inflection
Points of inflection and concavity of the sine function
Points of inflection and concavity of the cubic polynomial
Approximate solution to an equation, Newton's method (or the Newton-Raphson method)
Use of Newton's method example
b)
Applications of differentiation - the graph of a function and its derivatives
Taylor's theorem (Taylor's formula) - The extended mean value theorem
The proof of Thaylor's theorem
Maclaurin's formula or Maclaurin's theorem
Representing polynomial using Maclaurin's and Taylor's formula
Representing polynomial using Maclaurin's and Taylor's formula examples
The approximation of the exponential function by polynomial using Taylor's or Maclaurin's formula
Properties of the power series expansion of the exponential function
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
Finding extreme points
Points of inflection
Finding points of inflection
Finding and classifying critical (or stationary) points examples
Copyright © 2004 - 2020, Nabla Ltd. All rights reserved.
