Calculus - Revision history

Maintenance script: Fix broken external PDF/book links (pdfdrive, epdf, dead PDFs)

2026-07-06T01:14:11Z

Fix broken external PDF/book links (pdfdrive, epdf, dead PDFs)

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	Dr. David Tall, from the University of Warwick, develops an interesting way to teach calculus [https://~~homepages~~.warwick.ac.uk/~~staff~~/~~David.Tall~~/~~pdfs~~/~~dot1990d~~-versatile-calc-nm.pdf#:~:text=David%20Tall%20A%20Versatile%20Approach%20to%20Calculus%20%26,of%20stages%20in%20the%20development%20of%20numerical%20methods. here], he describes it thus: "The fundamental ideas are those of ''change'', the ''rate'' of change, and the ''accumulation'' due to change. Symbolically these are represented by the ''function'' concept, the ''derivative'' and the ''integral''."		Dr. David Tall, from the University of Warwick, develops an interesting way to teach calculus [https://wrap.warwick.ac.uk/id/eprint/509/1/WRAP_Tall_dot1990d-versatile-calc-nm.pdf#:~:text=David%20Tall%20A%20Versatile%20Approach%20to%20Calculus%20%26,of%20stages%20in%20the%20development%20of%20numerical%20methods. here], he describes it thus: "The fundamental ideas are those of ''change'', the ''rate'' of change, and the ''accumulation'' due to change. Symbolically these are represented by the ''function'' concept, the ''derivative'' and the ''integral''."

	I never really "got" calculus until I read his work.		I never really "got" calculus until I read his work.

Milllo at 00:29, 7 April 2021

2021-04-07T00:29:52Z

← Older revision		Revision as of 18:29, 6 April 2021
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	Dr. David Tall, from the University of Warwick, develops an interesting way to teach calculus [https://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1990d-versatile-calc-nm.pdf#:~:text=David%20Tall%20A%20Versatile%20Approach%20to%20Calculus%20%26,of%20stages%20in%20the%20development%20of%20numerical%20methods. here], he describes it thus: "The fundamental ideas are those of ''change'', the ''rate'' of change, and the ''accumulation'' due to change. Symbolically these are represented by the ''function'' concept, the ''derivative'' and the ''integral''." I never really "got" calculus until I read his work.		Dr. David Tall, from the University of Warwick, develops an interesting way to teach calculus [https://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1990d-versatile-calc-nm.pdf#:~:text=David%20Tall%20A%20Versatile%20Approach%20to%20Calculus%20%26,of%20stages%20in%20the%20development%20of%20numerical%20methods. here], he describes it thus: "The fundamental ideas are those of ''change'', the ''rate'' of change, and the ''accumulation'' due to change. Symbolically these are represented by the ''function'' concept, the ''derivative'' and the ''integral''."

			I never really "got" calculus until I read his work.

	Even though [[Numerical Methods]] are used to do calculations, not calculus, the ''ideas'' underlying calculus are interesting, particularly the concept of infinitesimal, which blew my mind when I first heard of it.		Even though [[Numerical Methods]] are used to do calculations, not calculus, the ''ideas'' underlying calculus are interesting, particularly the concept of infinitesimal, which blew my mind when I first heard of it.

Milllo at 00:29, 7 April 2021

2021-04-07T00:29:25Z

← Older revision		Revision as of 18:29, 6 April 2021
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	Dr. David Tall, from the University of Warwick, ~~describes~~ an interesting way to teach calculus [https://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1990d-versatile-calc-nm.pdf#:~:text=David%20Tall%20A%20Versatile%20Approach%20to%20Calculus%20%26,of%20stages%20in%20the%20development%20of%20numerical%20methods. here], he describes it thus: "The fundamental ideas are those of ''change'', the ''rate'' of change, and the ''accumulation'' due to change. Symbolically these are represented by the ''function'' concept, the ''derivative'' and the ''integral''." I never really "got" calculus until I read his work.		Dr. David Tall, from the University of Warwick, develops an interesting way to teach calculus [https://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1990d-versatile-calc-nm.pdf#:~:text=David%20Tall%20A%20Versatile%20Approach%20to%20Calculus%20%26,of%20stages%20in%20the%20development%20of%20numerical%20methods. here], he describes it thus: "The fundamental ideas are those of ''change'', the ''rate'' of change, and the ''accumulation'' due to change. Symbolically these are represented by the ''function'' concept, the ''derivative'' and the ''integral''." I never really "got" calculus until I read his work.

	Even though [[Numerical Methods]] are used to do calculations, not calculus, the ''ideas'' underlying calculus are interesting, particularly the concept of infinitesimal, which blew my mind when I first heard of it.		Even though [[Numerical Methods]] are used to do calculations, not calculus, the ''ideas'' underlying calculus are interesting, particularly the concept of infinitesimal, which blew my mind when I first heard of it.

Milllo at 00:29, 7 April 2021

2021-04-07T00:29:00Z

← Older revision		Revision as of 18:29, 6 April 2021
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	3 Dr. David Tall, from the University of Warwick, describes an interesting way to teach calculus [https://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1990d-versatile-calc-nm.pdf#:~:text=David%20Tall%20A%20Versatile%20Approach%20to%20Calculus%20%26,of%20stages%20in%20the%20development%20of%20numerical%20methods. here], he describes it thus: "The fundamental ideas are those of ''change'', the ''rate'' of change, and the ''accumulation'' due to change. Symbolically these are represented by the ''function'' concept, the ''derivative'' and the ''integral''." I never really "got" calculus until I read his work.		Dr. David Tall, from the University of Warwick, describes an interesting way to teach calculus [https://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1990d-versatile-calc-nm.pdf#:~:text=David%20Tall%20A%20Versatile%20Approach%20to%20Calculus%20%26,of%20stages%20in%20the%20development%20of%20numerical%20methods. here], he describes it thus: "The fundamental ideas are those of ''change'', the ''rate'' of change, and the ''accumulation'' due to change. Symbolically these are represented by the ''function'' concept, the ''derivative'' and the ''integral''." I never really "got" calculus until I read his work.

	Even though [[Numerical Methods]] are used to do calculations, not calculus, the ''ideas'' underlying calculus are interesting, particularly the concept of infinitesimal, which blew my mind when I first heard of it.		Even though [[Numerical Methods]] are used to do calculations, not calculus, the ''ideas'' underlying calculus are interesting, particularly the concept of infinitesimal, which blew my mind when I first heard of it.

Milllo at 00:28, 7 April 2021

2021-04-07T00:28:41Z

← Older revision		Revision as of 18:28, 6 April 2021
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	3 Dr. David Tall, from the University of Warwick, describes an interesting way to teach calculus [https://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1990d-versatile-calc-nm.pdf#:~:text=David%20Tall%20A%20Versatile%20Approach%20to%20Calculus%20%26,of%20stages%20in%20the%20development%20of%20numerical%20methods. here], he describes it thus: "The fundamental ideas are those of ''change'', the ''rate'' of change, and the ''accumulation'' due to change. Symbolically these are represented by the ''function'' concept, the ''derivative'' and the ''integral''." If I ~~had learned higher math like this then~~ I ~~would have picked it up much faster~~.		3 Dr. David Tall, from the University of Warwick, describes an interesting way to teach calculus [https://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1990d-versatile-calc-nm.pdf#:~:text=David%20Tall%20A%20Versatile%20Approach%20to%20Calculus%20%26,of%20stages%20in%20the%20development%20of%20numerical%20methods. here], he describes it thus: "The fundamental ideas are those of ''change'', the ''rate'' of change, and the ''accumulation'' due to change. Symbolically these are represented by the ''function'' concept, the ''derivative'' and the ''integral''." I never really "got" calculus until I read his work.

	Even though [[Numerical Methods]] are used to do calculations, not calculus, the ''ideas'' underlying calculus are interesting, particularly the concept of infinitesimal, which blew my mind when I first heard of it.		Even though [[Numerical Methods]] are used to do calculations, not calculus, the ''ideas'' underlying calculus are interesting, particularly the concept of infinitesimal, which blew my mind when I first heard of it.

Milllo at 22:29, 6 April 2021

2021-04-06T22:29:57Z

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	3 Dr. David Tall, from the University of Warwick, describes an interesting way to teach calculus [https://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1990d-versatile-calc-nm.pdf#:~:text=David%20Tall%20A%20Versatile%20Approach%20to%20Calculus%20%26,of%20stages%20in%20the%20development%20of%20numerical%20methods. here], he describes it thus: "The fundamental ideas are those of ''change'', the ''rate'' of change, and the ''accumulation'' due to change. Symbolically these are represented by the ''function'' concept, the ''derivative'' and the ''integral''." If I had learned higher math like this then I would have picked it up much faster		3 Dr. David Tall, from the University of Warwick, describes an interesting way to teach calculus [https://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1990d-versatile-calc-nm.pdf#:~:text=David%20Tall%20A%20Versatile%20Approach%20to%20Calculus%20%26,of%20stages%20in%20the%20development%20of%20numerical%20methods. here], he describes it thus: "The fundamental ideas are those of ''change'', the ''rate'' of change, and the ''accumulation'' due to change. Symbolically these are represented by the ''function'' concept, the ''derivative'' and the ''integral''." If I had learned higher math like this then I would have picked it up much faster.

	Even though [[Numerical Methods]] are used to do calculations, not calculus, the ''ideas'' underlying calculus are interesting, particularly the concept of infinitesimal, which blew my mind when I first heard of it.		Even though [[Numerical Methods]] are used to do calculations, not calculus, the ''ideas'' underlying calculus are interesting, particularly the concept of infinitesimal, which blew my mind when I first heard of it.

Milllo at 22:29, 6 April 2021

2021-04-06T22:29:38Z

← Older revision		Revision as of 16:29, 6 April 2021
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	3 Dr. David Tall, from the University of Warwick, describes an interesting way to teach calculus [https://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1990d-versatile-calc-nm.pdf#:~:text=David%20Tall%20A%20Versatile%20Approach%20to%20Calculus%20%26,of%20stages%20in%20the%20development%20of%20numerical%20methods. here], he describes is thus: "The fundamental ideas are those of ''change'', the ''rate'' of change, and the ''accumulation'' due to change. Symbolically these are represented by the ''function'' concept, the ''derivative'' and the ''integral''." If I had learned higher math like this then I would have picked it up much faster		3 Dr. David Tall, from the University of Warwick, describes an interesting way to teach calculus [https://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1990d-versatile-calc-nm.pdf#:~:text=David%20Tall%20A%20Versatile%20Approach%20to%20Calculus%20%26,of%20stages%20in%20the%20development%20of%20numerical%20methods. here], he describes it thus: "The fundamental ideas are those of ''change'', the ''rate'' of change, and the ''accumulation'' due to change. Symbolically these are represented by the ''function'' concept, the ''derivative'' and the ''integral''." If I had learned higher math like this then I would have picked it up much faster

	Even though [[Numerical Methods]] are used to do calculations, not calculus, the ''ideas'' underlying calculus are interesting, particularly the concept of infinitesimal, which blew my mind when I first heard of it.		Even though [[Numerical Methods]] are used to do calculations, not calculus, the ''ideas'' underlying calculus are interesting, particularly the concept of infinitesimal, which blew my mind when I first heard of it.

Milllo at 22:29, 6 April 2021

2021-04-06T22:29:20Z

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	3 Dr. David Tall, from the University of Warwick, describes an interesting way to teach calculus [https://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1990d-versatile-calc-nm.pdf#:~:text=David%20Tall%20A%20Versatile%20Approach%20to%20Calculus%20%26,of%20stages%20in%20the%20development%20of%20numerical%20methods. here], he describes is thus: "The fundamental ideas are those of ''change'', the ''rate'' of change, and the ''accumulation'' due to change. Symbolically these are represented by the ''function'' concept, the ''derivative'' and the ''integral''." If I had learned higher math like this then I would have picked it up much faster		3 Dr. David Tall, from the University of Warwick, describes an interesting way to teach calculus [https://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1990d-versatile-calc-nm.pdf#:~:text=David%20Tall%20A%20Versatile%20Approach%20to%20Calculus%20%26,of%20stages%20in%20the%20development%20of%20numerical%20methods. here], he describes is thus: "The fundamental ideas are those of ''change'', the ''rate'' of change, and the ''accumulation'' due to change. Symbolically these are represented by the ''function'' concept, the ''derivative'' and the ''integral''." If I had learned higher math like this then I would have picked it up much faster

	Even though [[Numerical Methods]] are used to do calculations, not calculus, the ''ideas'' underlying calculus are interesting, particularly the concept of infinitesimal, which blew my mind when I first heard of it.		Even though [[Numerical Methods]] are used to do calculations, not calculus, the ''ideas'' underlying calculus are interesting, particularly the concept of infinitesimal, which blew my mind when I first heard of it.

	An infinitesimal is some quantity that is explicitly nonzero and yet smaller in absolute value than any real quantity. A change in this quantity is called a differential, usually notated as dx, if x is the variable. The useful thing about infinitesimals is that they can be used to determine totals via ''integrals'' (from the Latin 'integratus' to 'make whole').		An infinitesimal is some quantity that is explicitly nonzero and yet smaller in absolute value than any real quantity. A change in this quantity is called a differential, usually notated as dx, if x is the variable. The useful thing about infinitesimals is that they can be used to determine totals via ''integrals'' (from the Latin 'integratus' to 'make whole').

Milllo at 22:28, 6 April 2021

2021-04-06T22:28:59Z

← Older revision		Revision as of 16:28, 6 April 2021
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	Even though [[Numerical Methods]] are used to do calculations, not calculus, the ''ideas'' underlying calculus are interesting, particularly the concept of infinitesimal, which blew my mind when I first heard of it.
			3 Dr. David Tall, from the University of Warwick, describes an interesting way to teach calculus [https://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1990d-versatile-calc-nm.pdf#:~:text=David%20Tall%20A%20Versatile%20Approach%20to%20Calculus%20%26,of%20stages%20in%20the%20development%20of%20numerical%20methods. here], he describes is thus: "The fundamental ideas are those of ''change'', the ''rate'' of change, and the ''accumulation'' due to change. Symbolically these are represented by the ''function'' concept, the ''derivative'' and the ''integral''." If I had learned higher math like this then I would have picked it up much faster

			Even though [[Numerical Methods]] are used to do calculations, not calculus, the ''ideas'' underlying calculus are interesting, particularly the concept of infinitesimal, which blew my mind when I first heard of it.

	An infinitesimal is some quantity that is explicitly nonzero and yet smaller in absolute value than any real quantity. A change in this quantity is called a differential, usually notated as dx, if x is the variable. The useful thing about infinitesimals is that they can be used to determine totals via ''integrals'' (from the Latin 'integratus' to 'make whole').		An infinitesimal is some quantity that is explicitly nonzero and yet smaller in absolute value than any real quantity. A change in this quantity is called a differential, usually notated as dx, if x is the variable. The useful thing about infinitesimals is that they can be used to determine totals via ''integrals'' (from the Latin 'integratus' to 'make whole').

Milllo at 09:23, 2 April 2021

2021-04-02T09:23:26Z

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	A great resource for calculating integrals can be found here: [https://www.integral-calculator.com/ integration]		A great resource for calculating integrals can be found here: [https://www.integral-calculator.com/ integration]

			----
	Calculus can be used to create equations for model systems, which are then calculated on computers and compared to the real result. In these cases integrals within limits can be useful, but even here the integrations of various equations are listed in tables so there is no need to memorize them. In addition, as with all math, calculus only approximates reality.		Calculus can be used to create equations for model systems, which are then calculated on computers and compared to the real result. In these cases integrals within limits can be useful, but even here the integrations of various equations are listed in tables so there is no need to memorize them. In addition, as with all math, calculus only approximates reality.