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Calculus
Discussion, etc. goes here.
Topics in calculus
Fundamental theorem | Function | Limits of functions | Continuity | Calculus with polynomials | Mean value theorem | Vector calculus | Tensor calculus
Differentiation
Product rule | Quotient rule | Chain rule | Implicit differentiation | Taylor's theorem | Related rates
Integration
Integration by substitution | Integration by parts | Integration by trigonometric substitution | Solids of revolution | Integration by disks | Integration by cylindrical shells | Improper integrals | Lists of integrals
For other uses of the term calculus see calculus (disambiguation)
Calculus is a central branch of mathematics, developed from algebra and geometry, and built on two major complementary ideas.
 
One concept is differential calculus. It studies rates of change, which are usually illustrated by the slope of a line. Differential calculus is based on the problem of finding the instantaneous rate of change of one quantity relative to another. Examples of typical differential calculus problems are finding the following quantities:
 
The acceleration and speed of a free-falling body at a particular moment.
The loss in speed and trajectory of a fired projectile, such as an artillery shell or bullet.
Change in profitability over time of a growing business at a particular point in time.
The other key concept is integral calculus. It studies the accumulation of quantities, such as areas under a curve, linear distance traveled, or volume displaced. Examples of integral calculus problems include finding the following quantities:


The amount of water pumped by a pump with a set power input but varying conditions of pumping losses and pressure.
----
The amount of money accumulated by a business under varying business conditions.
The amount of parking lot plowed by a snowplow of given power with varying rates of snowfall.
The two concepts, differentiation and integration, define inverse operations in a sense made precise by the fundamental theorem of calculus. In teaching calculus, either concept may be given priority. The usual educational approach is to introduce differential calculus first.


Contents [hide]
<h1>Migrating to Mozilla Thunderbird</h1>
1 History
2 Differential calculus
3 Integral calculus
4 Foundations
5 Fundamental theorem of calculus
6 Applications
7 See also
8 Further reading
9 External links


<h2>Getting Started</h2>


[edit]
<p>If you're a new Mozilla Thunderbird user, you almost certainly have old e-mail stored in the archives of another e-mail client.  If you use e-mail frequently, you might also have an address book full of contacts and settings fully tweaked to your liking.  Thankfully Thunderbird makes transferring your e-mail, settings, and address books a painless process in nearly all circumstances.  With its support for migrating e-mail, settings, and your address book from Eudora, Outlook, Outlook Express, and Netscape Communicator 4.x (not to mention its support for e-mail stored in Thunderbird's own format, used by Netscape 6/7, KMail, Evolution, and many other clients), getting your e-mail out of your old program and into Thunderbird is a simple process. </p>
History
Main article: History of calculus


Though the origins of integral calculus are generally regarded as going no farther back than to the ancient Greeks, there is evidence that the ancient Egyptians may have harbored such knowledge as well. (See Moscow Mathematical Papyrus.) Eudoxus is generally credited with the method of exhaustion, which made it possible to compute the area and volume of regions and solids. Archimedes developed this method further, while also inventing heuristic methods which resemble modern day concepts. An Indian Mathematician, Bhaskara (1114-1185), gave an example of what is now called the "differential coefficient" and the basic idea of what is now known as "Rolle's theorem". The 14th century Indian mathematician Madhava along with other mathematicians of the Kerala school made major inroads into Calculus that were not repeated anywhere in the world until the 17th century by Newton and Leibniz. Leibniz and Newton are usually designated the inventors of calculus, mainly for their separate discoveries of the fundamental theorem of calculus and work on notation.
<h2>Importing Your E-mail</h2>


There has been considerable debate about whether Newton or Leibniz was first to come up with the important concepts of calculus. The truth of the matter will likely never be known. Leibniz' greatest contribution to calculus was his notation; he often spent days trying to come up with the appropriate symbol to represent a mathematical idea. This controversy between Leibniz and Newton was unfortunate in that it divided English-speaking mathematicians from those in Europe for many years, setting back British analysis (i.e. calculus-based mathematics) for a very long time. Newton's terminology and notation was clearly less flexible than that of Leibniz, yet it was retained in British usage until the early 19th century, when the work of the Analytical Society successfully saw the introduction of Leibniz's notation in Great Britain. It is now thought that Newton had discovered several ideas related to calculus earlier than Leibniz had; however, Leibniz was the first to publish. Today, both Leibniz and Newton are considered to have discovered calculus independently.
<p>Start the import process by selecting Tools > Import. The import process consists of a series of dialogs which will lead you through the process of migrating your e-mail, address book, and settings.</p>


Lesser credit for the development of calculus is given to Barrow, Descartes, de Fermat, Huygens, and Wallis. A Japanese mathematician, Kowa Seki, lived at the same time as Leibniz and Newton and also elaborated some of the fundamental principles of integral calculus, though this was not known in the West at the time, and he had no contact with Western scholars. [1]
<h3>TheBat to Thunderbird mail conversion</h3>


[edit]
'''UPDATE 2011-07:''' Use extension '''[https://addons.mozilla.org/thunderbird/addon/birdimport/ Bird Import]''' for importing e-mail messages from The Bat. E-mail flags, parked/flagged status is preserved during the import.
Differential calculus
Main article: Derivative


The derivative measures the sensitivity of one variable to small changes in another variable. Consider the formula:
'''Note: This workaround sucks. The read/unread flags are buggy (only) when used in a dual-boot environment. Strange error.. seems like TheBat exports different MBX-files. Actual "state of the art" is to use an imap-server in between TheBat and Thunderbird.... ahhhh'''


for an object moving at constant speed.  
There does not seem to be any smooth converter around (except commercial aid4mail maybe). But you can export the mails from TheBat folder by folder as .MBX files. These files can be imported by Thunderbird. Mail flags, colors, filters etc. will not be exported to the MBX-files and therfore will also not be imported by Thunderbird. This works for your attachments. The addressbook can be exported&imported, but not by this workaround. Here is how to do it step by step:
One's speed in a car describes the change in location relative to the change in time. However, the speed itself may be changing and the formula above cannot account for that. Calculus deals with this more complex but natural and familiar situation.


Differential calculus determines the instantaneous speed, at any given specific instant in time, not just average speed during an interval of time. The formula Speed = Distance/Time applied to a single instant is the meaningless quotient "zero divided by zero". This is avoided, however, because the quotient Distance/Time is not used for a single instant (as in a still photograph), but for intervals of time that are very short.
This was tested using TheBat 3.5.25 and Thunderbird 1.0.7


The derivative answers the question: as the elapsed time approaches zero, what does the average speed computed by Distance/Time approach? In mathematical language, this is an example of "taking a limit."
* Create a new email account in Thunderbird. In the account-properties look at the ''Server settings'' tab and remember the ''Local directory folder''. This folder is whereto we will export the mails from TheBat. (For migrating mailaccounts it is usually a good idea to select ''Leave messages on server'' in the account properies.) 


More formally, differential calculus defines the instantaneous rate of change (the derivative) of a mathematical function's value, with respect to changes of the variable. The derivative is defined as a limit of a difference quotient.
* In TheBat click into a folder and select all mails by pressing ctrl-a.


The derivative of a function gives information about small pieces of its graph. It is directly relevant to finding the maxima and minima of a function — because at those points the graph is flat (i.e. the slope of the graph is zero). Another application of differential calculus is Newton's method, an algorithm to find zeroes of a function by approximating the function by its tangent lines. Differential calculus has been applied to many questions that are not first formulated in the language of calculus.
* From the menu select -> Tools -> Export messages to Unix mailbox. Save the file with the name of the mailfolder in the Thunderbird-account's ''Local directory folder''.


The derivative lies at the heart of the physical sciences. Newton's law of motion, Force = Mass × Acceleration, has meaning in calculus because acceleration is a derivative. Maxwell's theory of electromagnetism and Einstein's theory of gravity (general relativity) are also expressed in the language of differential calculus, as is the basic theory of electrical circuits and much of engineering.
* Restart Thunderbird and the folders should appear.  


[edit]
To reproduce a higher-level folderstructure you will have to restart Thunderbird a lot of times and export/import level by level. Depending on the number of mailfolders , you might want to create a keyboard shotcut in TheBat. This can be done by clicking: select view -> toolbars -> customize -> select container -> main menu -> tools@carret items -> exportz message to MBX -> at bottom right you can assign a shortcut -> ok&save.
Integral calculus
Main article: Integral


The definite integral evaluates the cumulative effect of many small changes in a quantity. The simplest instance is the formula
<h2>Importing Address Books </h2>


Note: For this to work, you need to have KAddressBook.
for calculating the distance a car moves during a period of time when it is traveling at constant speed. The distance moved is the cumulative effect of the small distances moved in each of the many seconds the car is on the road. The calculus is able to deal with the natural situation in which the car moves with changing speed.


Integral calculus determines the exact distance traveled during an interval of time by creating a series of better and better approximations, called Riemann sums, that approach the exact distance.
To import address book from evolution 2.4, first select all the contacts by pressing Ctrl+A. This shall select all the contacts. Now, right click and click on Save As VCard. Save the file with a .vcf extension. Open Kaddressbook and click on Import VCF file; select the vcf file you exported. This will move all contacts in KAddressbook. Now, click on export in Kaddressbook and export contacts as ldif file.  


More formally, we say that the definite integral of a function on an interval is a limit of Riemann sum approximations.
Open TB, select import -> address book -> ldif file. Select the ldif file you exported from KAddressbook and let TB do the magic. Works like a charm.


Applications of integral calculus arise whenever the problem is to compute a number that is in principle (approximately) equal to the sum of the solutions of many, many smaller problems.
<h2>Importing Filters</h2>


The classic geometric application is to area computations. In principle, the area of a region can be approximated by chopping it up into many very tiny squares and adding the areas of those squares. (If the region has a curved boundary, then omitting the squares overlapping the edge does not cause too great an error.) Surface areas and volumes can also be expressed as definite integrals.
Currently, there is no way to import filters from Eudora to Thunderbird. For many of us, who would like to migrate, this is too much of an obstacle. Is someone going to fix this??


Many of the functions that are integrated are rates, such as a speed. An integral of a rate of change of a quantity on an interval of time tells how much that quantity changes during that time period. It makes sense that if one knows their speed at every instant in time for an hour (i.e. they have an equation that relates their speed and time), then they should be able to figure out how far they go during that hour. The definite integral of their speed presents a method for doing so.
Product version:


Many of the functions that are integrated represent densities. If, for example, the pollution density along a river (tons per mile) is known in relation to the position, then the integral of that density can determine how much pollution there is in the whole length of the river.
Evolution 2.4.1
Thunderbird 1.0.7
KDE 3.5.0
Ubuntu Breezy


Probability, the basis for statistics, provides one of the most important applications of integral calculus.
<h2>vCard or .vcf</h2>
 
[edit]
Foundations
The rigorous foundation of calculus is based on the notions of a function and of a limit; the latter has a theory ultimately depending on that of the real numbers as a continuum. Its tools include techniques associated with elementary algebra, and mathematical induction.
 
The modern study of the foundations of calculus is known as real analysis. This includes full definitions and proofs of the theorems of calculus. It also provides generalisations such as measure theory and distribution theory.
 
[edit]
Fundamental theorem of calculus
The fundamental theorem of calculus states that differentiation and integration are, in a certain sense, inverse operations. More precisely, antiderivatives can be calculated with definite integrals, and vice versa.
 
This connection allows us to recover the total change in a function over some interval from its instantaneous rate of change, by integrating the latter.
 
This realization, made by both Newton and Leibniz, was key to the massive proliferation of analytic results after their work became known.
 
The fundamental theorem provides an algebraic method of computing many definite integrals --without performing limit processes--by finding formulas for antiderivatives. It is also a prototype solution of a differential equation. Differential equations relate an unknown function to its derivatives, and are ubiquitous in the sciences.
 
1st Fundamental Theorem of Calculus: If a function f is continuous on the interval [a, b] and F is an antiderivative of f on the interval [a, b], then
 
2nd Fundamental Theorem of Calculus: If f is continuous on an open interval I containing a, then, for every x in the interval,
 
[edit]
Applications
The development and use of calculus has had wide reaching effects on nearly all areas of modern living. It underlies nearly all of the sciences, especially physics. Virtually all modern developments such as building techniques, aviation, and other technologies make fundamental use of calculus. Many algebraic formulas now used for ballistics, heating and cooling, and other practical sciences were worked out through the use of calculus. In a handbook, an algebraic formula based on calculus methods may be applied without knowing its origins.


The success of calculus has been extended over time to differential equations, vector calculus, calculus of variations, complex analysis, and differential topology.
Some address book programs use a vCard format, which cannot be imported directly by Thunderbird.  You can import both vCard and vcf using the third-party Thunderbird extension [http://nic-nac-project.de/~kaosmos/morecols-en.html MoreFunctionsForAddressBook].  An alternative is to convert the format to one which can be imported by Thunderbird. One suggestion is to use a [http://labs.brotherli.ch/vcfconvert/ online conversion utility] to convert the vCard format to LDIF, then import the LDIF format in Thunderbird. For the other direction - from LDIF format to vCard - are also [http://eclipsing.de/wiki/Wiki.jsp?page=ThunderbirdLdifToVcard_en free applications] available.

Latest revision as of 12:19, 7 July 2011

Discussion, etc. goes here.

Migrating to Mozilla Thunderbird

Getting Started

If you're a new Mozilla Thunderbird user, you almost certainly have old e-mail stored in the archives of another e-mail client. If you use e-mail frequently, you might also have an address book full of contacts and settings fully tweaked to your liking. Thankfully Thunderbird makes transferring your e-mail, settings, and address books a painless process in nearly all circumstances. With its support for migrating e-mail, settings, and your address book from Eudora, Outlook, Outlook Express, and Netscape Communicator 4.x (not to mention its support for e-mail stored in Thunderbird's own format, used by Netscape 6/7, KMail, Evolution, and many other clients), getting your e-mail out of your old program and into Thunderbird is a simple process.

Importing Your E-mail

Start the import process by selecting Tools > Import. The import process consists of a series of dialogs which will lead you through the process of migrating your e-mail, address book, and settings.

TheBat to Thunderbird mail conversion

UPDATE 2011-07: Use extension Bird Import for importing e-mail messages from The Bat. E-mail flags, parked/flagged status is preserved during the import.

Note: This workaround sucks. The read/unread flags are buggy (only) when used in a dual-boot environment. Strange error.. seems like TheBat exports different MBX-files. Actual "state of the art" is to use an imap-server in between TheBat and Thunderbird.... ahhhh

There does not seem to be any smooth converter around (except commercial aid4mail maybe). But you can export the mails from TheBat folder by folder as .MBX files. These files can be imported by Thunderbird. Mail flags, colors, filters etc. will not be exported to the MBX-files and therfore will also not be imported by Thunderbird. This works for your attachments. The addressbook can be exported&imported, but not by this workaround. Here is how to do it step by step:

This was tested using TheBat 3.5.25 and Thunderbird 1.0.7

  • Create a new email account in Thunderbird. In the account-properties look at the Server settings tab and remember the Local directory folder. This folder is whereto we will export the mails from TheBat. (For migrating mailaccounts it is usually a good idea to select Leave messages on server in the account properies.)
  • In TheBat click into a folder and select all mails by pressing ctrl-a.
  • From the menu select -> Tools -> Export messages to Unix mailbox. Save the file with the name of the mailfolder in the Thunderbird-account's Local directory folder.
  • Restart Thunderbird and the folders should appear.

To reproduce a higher-level folderstructure you will have to restart Thunderbird a lot of times and export/import level by level. Depending on the number of mailfolders , you might want to create a keyboard shotcut in TheBat. This can be done by clicking: select view -> toolbars -> customize -> select container -> main menu -> tools@carret items -> exportz message to MBX -> at bottom right you can assign a shortcut -> ok&save.

Importing Address Books

Note: For this to work, you need to have KAddressBook.

To import address book from evolution 2.4, first select all the contacts by pressing Ctrl+A. This shall select all the contacts. Now, right click and click on Save As VCard. Save the file with a .vcf extension. Open Kaddressbook and click on Import VCF file; select the vcf file you exported. This will move all contacts in KAddressbook. Now, click on export in Kaddressbook and export contacts as ldif file.

Open TB, select import -> address book -> ldif file. Select the ldif file you exported from KAddressbook and let TB do the magic. Works like a charm.

Importing Filters

Currently, there is no way to import filters from Eudora to Thunderbird. For many of us, who would like to migrate, this is too much of an obstacle. Is someone going to fix this??


Product version:

Evolution 2.4.1 Thunderbird 1.0.7 KDE 3.5.0 Ubuntu Breezy

vCard or .vcf

Some address book programs use a vCard format, which cannot be imported directly by Thunderbird. You can import both vCard and vcf using the third-party Thunderbird extension MoreFunctionsForAddressBook. An alternative is to convert the format to one which can be imported by Thunderbird. One suggestion is to use a online conversion utility to convert the vCard format to LDIF, then import the LDIF format in Thunderbird. For the other direction - from LDIF format to vCard - are also free applications available.

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