Integrals and differentials: general
overview
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Calculus
Differentiation Formulas, Derivatives-Chain and Power Rules,
Derivatives-Product and Quotient Rules, Curve Sketching, Integration
Formulas, Integration by Parts, Integration by Partial Fractions,
Integration by Substitution, Infinite Series: Popular Series, Infinite
Series: Popular Limits, Infinite Series: Covergance/Divergance, Infinite
Series |
| Difference equations to differential |
| eCalculus.org
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Integrals |
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Integrals |
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Integrals, Definite Integral and Differential Equations Integrals,
Definite Integral and Differential Equations |
| Karl's calculus
tutorial derivative, integral, limit, continuity, continuous, function, L'Hopital, converge, differential, number systems, real numbers, rational
numbers, counting numbers, integer, exponential, logarithm, trigonometry, min-max |
| Mathpages various mathematical topics:
number theory, calculus and differential equations, geometry, combinatorics |
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UBC calculus |
| Visual
calculus pre calculus, limits and continuity, derivatives, applications of differentiation, integration, applications of integration,
sequences and series. Javascript and flash involved a tip |
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Horizontaal |
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Differentials: topics
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| Calculus and
differential equations a tip
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Continuity and differentiability |
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Differential equations
differential equations,
First-order differential equations, Direct integration, Separable equations,
Making an equation separable by changing the variable, Finding and using an
"Integrating Factor" , Second-order differential equations, Homogeneous
constant-coefficient equations, Inhomogeneous constant-coefficient equations
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| Differential equations differential equations
and electrical circuits |
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Definition of derivative at a point
In this tutorial, we define what is meant by the derivative of a function f
at a point x = a. This concept is motivated by the definition of the tangent
line to the graph of f at a point x = a. Several examples are provided
including a couple of examples where the derivative does not exist |
| Definition
of definite integrals
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Definition of the derivative |
| Definition of the derivative
The essence of calculus is the derivative. The derivative is the
instantaneous rate of change of a function with respect to one of its
variables. This is equivalent to finding the slope of the tangent line to
the function at a point. Let's use the view of derivatives as tangents to
motivate a geometric definition of the derivative |
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Derivative pdf file |
| Derivatives
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Derivatives of exponentials & logarithms pdf file |
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Derivatives of logarithmic and exponential functions |
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Derivatives of Trigonometric Functions |
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Differential equations pdf file |
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Differential
equations
a differential equation is an equation involving an unknown function and its derivatives, first order differential equations, second
order differential equations, higher order linear equations, Laplace transform, Fourier series, Bessel's inequality and Parseval formula - the
energy theorem |
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Differentiating the exponential and logarithm functions pdf file |
| Differentiation |
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Differentiation and integration of vector valued functions |
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Differentiations definition of the derivative, chain rule, implicit differentiation |
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Euler and differentials pdf file |
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Function analysis |
| Hyperbolic
functions pdf file |
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Implicit differentiation find the derivative of an implicitly defined function using implicit differentiation |
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Implicit differentiation how Implicit differentiation works |
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Inverse trigonometric functions DIFFERENTIATION OF INVERSE TRIGONOMETRIC
FUNCTIONS |
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Limit of
a Function The following applet can be used to examine the limit of the
function f(x) as x approaches a |
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Limit definition of the derivative pdf file |
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Limits, continuity, and the derivative
This section contains a sketch of the formal mathematics that is required to
fully develop the concept of the derivative |
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logarithmic differentiation
the process of logarithmic differentiation |
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Logarithmic or inverse tangent
The following problems involve the integration of rational functions,
resulting in logarithmic or inverse tangent functions |
| Mathematics
reference: rules for differentiation |
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Partial differentiation |
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The Fundamental Theorem of Calculus The Fundamental Theorem of Calculus
expresses a relationship between integration and differentiation |
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Horizontaal |
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Integrals: topics
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Applications of the definite integral to calculating volume and length pdf file |
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Applications of the de definite integral to calculating volume and length pdf file |
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Area Between Curves Area Between Curves |
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Area Between Two Curves Recall that the area under a curve and above the
x axis can be computed by the definite integral |
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Area of a Circle
Applications of Integration |
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Average value Average Value of a Function |
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Definite Integral The Length of a Curve, Volumes of Revolution, Area of
Surface of Revolution |
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Definite Integral
The Length of a Curve |
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Finding areas by integration
Integration can be used to calculate areas.
In simple cases, the area is given by a single definite integral, pdf file |
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Finding the Area
Between Curves |
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Integrals |
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Integrals
Understand the definition of an integral, Cite the general laws of an
integration, Recognize the integrals of some common functions, Calculate an
integral |
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Integrals of Trigonometric Functions |
| Integration |
| Integration
covers the uniqueness theorem, inverse property and applications of indefinite integrals, a tip
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Integration and applications
antiderivatives, substitution, integration of exponentials and logs, the first fundamental theorem of calculus, area
between two curves, Riemann Sums, volumes of revolution |
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Integration as summation Integration as summation, pdf file |
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Integration as the reverse of differentiation Integration can be
introduced in several different ways. One way is to think of it as
differentiation in reverse. This approach is described in this leaflet, pdf file |
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Integration by parts |
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Integration by substitution Integration by substitution, This technique
involves making a substitution in order to simplify an integral before
evaluating it, pdf file |
| Integration of
inverse trigonometric functions integration of inverse trigonometric functions, pdf file |
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Integration of
rational functions integration of
rational functions, pdf file |
| Improper integrals
how Improper integrals work |
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Improper integrals |
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Mathematics
reference: rules for integration |
| Multiple
integrals double integrals, triple integrals |
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Multiple integrals multiple integrals |
| Multiple integrals multiple integrals, pdf file |
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Multiple integration iterated integrals and area, double integrals and volume, double integration in polar coordinates, center of mass and moment of inertia,
surface area, triple integrals, triple integrals in cylindrical and spherical coordinates, Jacobians |
| Table of
elementary indefinite integrals
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Techniques of integration substitution, integration by parts, partial fractions and logistics growth, trapezoidal and Simpson's rule, improper
integrals, derivatives of trigonometric functions, integrals of trigonometric functions |
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The Fundamental Theorem of Calculus The Fundamental Theorem of Calculus
expresses a relationship between integration and differentiation |
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Trigonometric functions |
| Trigonometric
substitutions solving integrals using trigonometric substitutions, pdf file |
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Volumeberekening van omwentelingslichamen ppt file |
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Volume by Discs and Washers |
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Volumes of solids of revolution The volume of a sphere, The volume of a
cone, pdf file |
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Volumes of solids of revolution
Volumes of solids of revolution |
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Last updated on:
2011-01-22
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