Calculus - Revision history

Milllo at 00:29, 7 April 2021

2021-04-07T00:29:52Z

Milllo at 00:29, 7 April 2021

2021-04-07T00:29:25Z

Milllo at 00:29, 7 April 2021

2021-04-07T00:29:00Z

Milllo at 00:28, 7 April 2021

2021-04-07T00:28:41Z

Milllo at 22:29, 6 April 2021

2021-04-06T22:29:57Z

Milllo at 22:29, 6 April 2021

2021-04-06T22:29:38Z

Milllo at 22:29, 6 April 2021

2021-04-06T22:29:20Z

Milllo at 22:28, 6 April 2021

2021-04-06T22:28:59Z

Milllo at 09:23, 2 April 2021

2021-04-02T09:23:26Z

Milllo at 18:30, 1 April 2021

2021-04-01T18:30:37Z

← Older revision		Revision as of 00:29, 7 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.

← Older revision		Revision as of 00:29, 7 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.

← Older revision		Revision as of 00:29, 7 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.

← Older revision		Revision as of 00:28, 7 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.

← Older revision		Revision as of 22:29, 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''." 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.

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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 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').

← Older revision		Revision as of 22:28, 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').

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 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.

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 Many problems that require determining the total value of something can be solved using integrals.
-*[[Example problems using calculus]]
+*[[Example problems using integrals]]
 *[[The same examples using numerical methods]]