Single-variable calculus learning recommendations - Revision history

Vipul: /* Acquiring greater depth in calculus topics you already learned */

2014-11-02T18:06:33Z

Acquiring greater depth in calculus topics you already learned

← Older revision		Revision as of 18:06, 2 November 2014
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	\| You like a nice integrated course experience with professionally done videos, quizzes, and lecture materials. \|\| [https://www.coursera.org/course/calcsing Calculus: Single Variable by Robert Ghrist (University of Pennsylvania) on Coursera] \|\| Free		\| You like a nice integrated course experience with professionally done videos, quizzes, and lecture materials. \|\| [https://www.coursera.org/course/calcsing Calculus: Single Variable by Robert Ghrist (University of Pennsylvania) on Coursera] \|\| Free
	\|-		\|-
	\| You are looking for detailed explanations of a few important topics in single-variable calculus, without necessarily getting comprehensive coverage of all topics \|\| [http://www.youtube.com/user/vipulsclassroom Vipul's Classroom] has video playlists on some calculus-related topics, including limits, many subtopics of integration, differential equations, some subtopics of sequences and series. \|\| Free		\| You are looking for detailed explanations of a few important topics in single-variable calculus, without necessarily getting comprehensive coverage of all topics \|\| [http://www.youtube.com/user/vipulsclassroom Vipul's Classroom] has video playlists on some calculus-related topics, including limits, many subtopics of integration, differential equations, some subtopics of sequences and series. You might also be interested in [https://docs.google.com/file/d/0B66kEP2FWgm_SExEVmpSUUxyblU these notes by Eus]. \|\| Free
	\|}		\|}

Vipul at 02:08, 6 March 2014

2014-03-06T02:08:31Z

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 This page lists recommendations specific to learning [[single-variable calculus]] (called ''calculus'' for short here). This includes limits, differential calculus, integral calculus, and some auxiliary topics. This combines the calculus-related items in our [[online mathematics learning resources]] and the calculus-related items in our [[mathematics reading recommendations]] and sorts them based on your educational stage.
 ==First-time learning==
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 If, however, our previous suggestions didn't fit your needs well, and you have found Khan Academy to generally work well for you, we recommend considering [[PatrickJMT]] ([http://patrickjmt.com patrickjmt.com]) as a free but somewhat superior alternative to Khan Academy that is very similar in style. Another alternative is [https://www.coursera.org/course/calc1 Calculus One from Coursera]. Both of these have the advantage over Khan Academy that the instructors have relevant mathematical background as well as teaching experience, so they are more likely to make accurate statements that are reflective of the deeper logic of the subject.

Vipul: /* First-time learning */

2014-03-02T20:57:42Z

First-time learning

← Older revision		Revision as of 20:57, 2 March 2014
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	\| You prefer to learn from videos that offer conceptual explanations of ideas, and you don't have an aversion to long videos. \|\| The [[Center of Math]] calculus videos ([http://centerofmath.org/videos/index.html here]) and their corresponding textbooks ([http://centerofmath.org/store/index.html store]). These introduce ideas in a concepts-first fashion. \|\| The Worldwide AP Calculus book (that covers all topics) costs $14.95 digital and $39.95 print.<br>Videos require a decent Internet connection, but we expect the Internet connections of most clients to be adequate.		\| You prefer to learn from videos that offer conceptual explanations of ideas, and you don't have an aversion to long videos. \|\| The [[Center of Math]] calculus videos ([http://centerofmath.org/videos/index.html here]) and their corresponding textbooks ([http://centerofmath.org/store/index.html store]). These introduce ideas in a concepts-first fashion. \|\| The Worldwide AP Calculus book (that covers all topics) costs $14.95 digital and $39.95 print.<br>Videos require a decent Internet connection, but we expect the Internet connections of most clients to be adequate.
	\|-		\|-
	\| You just want something to get you started. \|\| Almost any book will do. Here's the [http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/ calculus online textbook] by Gilbert Strang that's reasonably good.<br>Stewart's book is also good, but expensive.<br>For video-based learning, consider [[Thinkwell]] if you're willing to pay money. \|\| Strang's book (digital version) is free.		\| You just want something to get you started. \|\| Almost any book will do. Here's the [http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/ calculus online textbook] by Gilbert Strang that's reasonably good.<br>Stewart's book is also good, but expensive.<br>For video-based learning, consider [[Thinkwell]] if you're willing to pay money. \|\| Strang's book (digital version) is free.<br>Thinkwell costs ~$150 for year-long course access.
	\|}		\|}

Vipul: /* First-time learning */

2014-03-02T20:57:17Z

First-time learning

← Older revision		Revision as of 20:57, 2 March 2014
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	\| You prefer to learn from videos that offer conceptual explanations of ideas, and you don't have an aversion to long videos. \|\| The [[Center of Math]] calculus videos ([http://centerofmath.org/videos/index.html here]) and their corresponding textbooks ([http://centerofmath.org/store/index.html store]). These introduce ideas in a concepts-first fashion. \|\| The Worldwide AP Calculus book (that covers all topics) costs $14.95 digital and $39.95 print.<br>Videos require a decent Internet connection, but we expect the Internet connections of most clients to be adequate.		\| You prefer to learn from videos that offer conceptual explanations of ideas, and you don't have an aversion to long videos. \|\| The [[Center of Math]] calculus videos ([http://centerofmath.org/videos/index.html here]) and their corresponding textbooks ([http://centerofmath.org/store/index.html store]). These introduce ideas in a concepts-first fashion. \|\| The Worldwide AP Calculus book (that covers all topics) costs $14.95 digital and $39.95 print.<br>Videos require a decent Internet connection, but we expect the Internet connections of most clients to be adequate.
	\|-		\|-
	\| You just want something ~~cheap and basic~~ to get started. \|\| Almost any book will do. Here's the [http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/ calculus online textbook] by Gilbert Strang that's reasonably good. \|\| Strang's book (digital version) is free.		\| You just want something to get you started. \|\| Almost any book will do. Here's the [http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/ calculus online textbook] by Gilbert Strang that's reasonably good.<br>Stewart's book is also good, but expensive.<br>For video-based learning, consider [[Thinkwell]] if you're willing to pay money. \|\| Strang's book (digital version) is free.
	\|}		\|}

Vipul at 20:14, 2 March 2014

2014-03-02T20:14:34Z

← Older revision		Revision as of 20:14, 2 March 2014
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	* [http://vipulnaik.com/teaching Vipul Naik's teaching]: Vipul Naik has put up quizzes for single-variable calculus courses he taught. These are focused on testing and improving conceptual understanding of specific topics, and they do require somewhat more advanced problem-solving skills than typical calculus classes, but not at the level needed for tournaments.		* [http://vipulnaik.com/teaching Vipul Naik's teaching]: Vipul Naik has put up quizzes for single-variable calculus courses he taught. These are focused on testing and improving conceptual understanding of specific topics, and they do require somewhat more advanced problem-solving skills than typical calculus classes, but not at the level needed for tournaments.
	* Many standard calculus texts, such as Stewart's text and the Salas-Hille-Etgen text, have a number of advanced problems in their exercises. Teachers often omit these problems when assigning homework, but if you have a calculus text, do consider looking for the advanced problems in the text.		* Many standard calculus texts, such as Stewart's text and the Salas-Hille-Etgen text, have a number of advanced problems in their exercises. Teachers often omit these problems when assigning homework, but if you have a calculus text, do consider looking for the advanced problems in the text.

			==Note on the Khan Academy==

			A number of people choose Khan Academy as a source of supplementary learning for all academic subjects, including calculus. We believe our recommended resources are generally better than Khan Academy, regardless of your goals. You might also be interested in reading our discussion of Khan Academy [[Khan Academy\|here]].

			If, however, our previous suggestions didn't fit your needs well, and you have found Khan Academy to generally work well for you, we recommend considering [[PatrickJMT]] ([http://patrickjmt.com patrickjmt.com]) as a free but somewhat superior alternative to Khan Academy that is very similar in style. Another alternative is [https://www.coursera.org/course/calc1 Calculus One from Coursera]. Both of these have the advantage over Khan Academy that the instructors have relevant mathematical background as well as teaching experience, so they are more likely to make accurate statements that are reflective of the deeper logic of the subject.

Vipul: /* First-time learning */

2014-03-02T03:18:18Z

First-time learning

← Older revision		Revision as of 03:18, 2 March 2014
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	\| You have an interest in solving challenging mathematical problems and discovering mathematical ideas through the problem-solving process. \|\| The AoPS calculus text: ''Calculus'' by David Patrick, ISBN 978-1-934124-24-6, [http://www.artofproblemsolving.com/Store/viewitem.php?item=calculus paperback]. You can also enroll in the [https://www.artofproblemsolving.com/School/courseinfo.php?course_id=calculus AoPS online calculus class], though that costs more money. \|\| ~$45 for the text, ~$10 for the solutions manual.<br>Current price for semester-long AoPS calculus class unavailable, but comparable precalculus class costs $425 ($478 with book).		\| You have an interest in solving challenging mathematical problems and discovering mathematical ideas through the problem-solving process. \|\| The AoPS calculus text: ''Calculus'' by David Patrick, ISBN 978-1-934124-24-6, [http://www.artofproblemsolving.com/Store/viewitem.php?item=calculus paperback]. You can also enroll in the [https://www.artofproblemsolving.com/School/courseinfo.php?course_id=calculus AoPS online calculus class], though that costs more money. \|\| ~$45 for the text, ~$10 for the solutions manual.<br>Current price for semester-long AoPS calculus class unavailable, but comparable precalculus class costs $425 ($478 with book).
	\|-		\|-
	\| You prefer to learn from videos that offer conceptual explanations of ideas, and you don't have an aversion to long videos. \|\| The Center of Math calculus videos ([http://centerofmath.org/videos/index.html here]) and their corresponding textbooks ([http://centerofmath.org/store/index.html store]). These introduce ideas in a concepts-first fashion. \|\| The Worldwide AP Calculus book (that covers all topics) costs $14.95 digital and $39.95 print.<br>Videos require a decent Internet connection, but we expect the Internet connections of most clients to be adequate.		\| You prefer to learn from videos that offer conceptual explanations of ideas, and you don't have an aversion to long videos. \|\| The [[Center of Math]] calculus videos ([http://centerofmath.org/videos/index.html here]) and their corresponding textbooks ([http://centerofmath.org/store/index.html store]). These introduce ideas in a concepts-first fashion. \|\| The Worldwide AP Calculus book (that covers all topics) costs $14.95 digital and $39.95 print.<br>Videos require a decent Internet connection, but we expect the Internet connections of most clients to be adequate.
	\|-		\|-
	\| You just want something cheap and basic to get started. \|\| Almost any book will do. Here's the [http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/ calculus online textbook] by Gilbert Strang that's reasonably good. \|\| Strang's book (digital version) is free.		\| You just want something cheap and basic to get started. \|\| Almost any book will do. Here's the [http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/ calculus online textbook] by Gilbert Strang that's reasonably good. \|\| Strang's book (digital version) is free.

Vipul: /* First-time learning */

2014-02-27T07:57:30Z

First-time learning

← Older revision		Revision as of 07:57, 27 February 2014
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	! If this description fits you ... !! ... this might be the best recommendation !! Cost		! If this description fits you ... !! ... this might be the best recommendation !! Cost
	\|-		\|-
	\| You have an interest in solving challenging mathematical problems and discovering mathematical ideas through the problem-solving process. \|\| The AoPS calculus text: ''Calculus'' by David Patrick, ISBN 978-1-934124-24-6, [http://www.artofproblemsolving.com/Store/viewitem.php?item=calculus paperback]. You can also enroll in the [https://www.artofproblemsolving.com/School/courseinfo.php?course_id=calculus AoPS online calculus class], though that costs more money. \|\| ~45 for the text, ~$10 for the solutions manual.<br>Current price for semester-long AoPS calculus class unavailable, but comparable precalculus class costs $425 ($478 with book).		\| You have an interest in solving challenging mathematical problems and discovering mathematical ideas through the problem-solving process. \|\| The AoPS calculus text: ''Calculus'' by David Patrick, ISBN 978-1-934124-24-6, [http://www.artofproblemsolving.com/Store/viewitem.php?item=calculus paperback]. You can also enroll in the [https://www.artofproblemsolving.com/School/courseinfo.php?course_id=calculus AoPS online calculus class], though that costs more money. \|\| ~$45 for the text, ~$10 for the solutions manual.<br>Current price for semester-long AoPS calculus class unavailable, but comparable precalculus class costs $425 ($478 with book).
	\|-		\|-
	\| You prefer to learn from videos that offer conceptual explanations of ideas, and you don't have an aversion to long videos. \|\| The Center of Math calculus videos ([http://centerofmath.org/videos/index.html here]) and their corresponding textbooks ([http://centerofmath.org/store/index.html store]). These introduce ideas in a concepts-first fashion. \|\| The Worldwide AP Calculus book (that covers all topics) costs $14.95 digital and $39.95 print.<br>Videos require a decent Internet connection, but we expect the Internet connections of most clients to be adequate.		\| You prefer to learn from videos that offer conceptual explanations of ideas, and you don't have an aversion to long videos. \|\| The Center of Math calculus videos ([http://centerofmath.org/videos/index.html here]) and their corresponding textbooks ([http://centerofmath.org/store/index.html store]). These introduce ideas in a concepts-first fashion. \|\| The Worldwide AP Calculus book (that covers all topics) costs $14.95 digital and $39.95 print.<br>Videos require a decent Internet connection, but we expect the Internet connections of most clients to be adequate.

Vipul: /* Practice at basic computation */

2014-02-13T18:29:29Z

Practice at basic computation

← Older revision		Revision as of 18:29, 13 February 2014
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	* You can use any calculus text. The [http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/ calculus online textbook] by Gilbert Strang, available online for free, is a good start. Answers are available to odd-numbered problems at the back of the text.		* You can use any calculus text. The [http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/ calculus online textbook] by Gilbert Strang, available online for free, is a good start. Answers are available to odd-numbered problems at the back of the text.
	* For practice with full-length exams, consider the [https://apstudent.collegeboard.org/apcourse/ap-calculus-ab/exam-practice AP exam practice] and [http://www.examswithsolutions.com/Subjects/math_exams.html this page] (many links within the latter page are broken).		* For practice with full-length exams, consider the [https://apstudent.collegeboard.org/apcourse/ap-calculus-ab/exam-practice AP exam practice] and [http://www.examswithsolutions.com/Subjects/math_exams.html this page] (many links within the latter page are broken).
	* If the problem lists in your calculus text are insufficient, you can also buy [http://www.amazon.com/The-Humongous-Book-Calculus-Problems/dp/1592575129/ The Humongous Book of Calculus Problems] and [http://www.amazon.com/Schaums-000-Solved-Problems-Calculus/dp/0071635343/ Schaum's 3000 Solved Problems in Calculus] to get a ''lot'' of practice with calculus problem-solving. These books cost some money but are not too expensive.		* If the problem lists in your calculus text are insufficient, you can also buy [http://www.amazon.com/The-Humongous-Book-Calculus-Problems/dp/1592575129/ The Humongous Book of Calculus Problems] (~$16 paperback) (and [http://www.amazon.com/Schaums-000-Solved-Problems-Calculus/dp/0071635343/ Schaum's 3000 Solved Problems in Calculus] (~$15 digital, ~$23 paperback) to get a ''lot'' of practice with calculus problem-solving. These books cost some money but are not too expensive.
	* Although existing problem lists in books are usually more than enough to give you practice and gauge your skill level, you can also in principle vary the numbers to create your own problem variants, then check your solutions against a calculator or [http://www.wolframalpha.com Wolfram Alpha].		* Although existing problem lists in books are usually more than enough to give you practice and gauge your skill level, you can also in principle vary the numbers to create your own problem variants, then check your solutions against a calculator or [http://www.wolframalpha.com Wolfram Alpha].
	* If you have Wolfram Pro, you can try the [http://www.wolframalpha.com/problem-generator/quiz/?category=Calculus Wolfram Problem Generator].		* If you have Wolfram Pro, you can try the [http://www.wolframalpha.com/problem-generator/quiz/?category=Calculus Wolfram Problem Generator].

Vipul: /* Acquiring greater depth in calculus topics you already learned */

2014-02-13T18:25:28Z

Acquiring greater depth in calculus topics you already learned

← Older revision		Revision as of 18:25, 13 February 2014
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	{\| class="sortable" border="1"		{\| class="sortable" border="1"
	! If this description fits you ... !! ... this might be the best recommendation		! If this description fits you ... !! ... this might be the best recommendation !! Cost
	\|-		\|-
	\| You are considering studying higher math and want to relearn calculus in a way that prepares you for higher math. \|\| [http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ Calculus, 4th Edition, by Michael Spivak] ~~('''expensive, ~$75-100''')~~ is a good choice. This text is used in Honors Calculus classes in many universities.		\| You are considering studying higher math and want to relearn calculus in a way that prepares you for higher math. \|\| [http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ Calculus, 4th Edition, by Michael Spivak] is a good choice. This text is used in Honors Calculus classes in many universities. \|\| Expensive, ~$75-100
	\|-		\|-
	\| You like a nice integrated course experience with professionally done videos, quizzes, and lecture materials. \|\| [https://www.coursera.org/course/calcsing Calculus: Single Variable by Robert Ghrist (University of Pennsylvania) on Coursera]		\| You like a nice integrated course experience with professionally done videos, quizzes, and lecture materials. \|\| [https://www.coursera.org/course/calcsing Calculus: Single Variable by Robert Ghrist (University of Pennsylvania) on Coursera] \|\| Free
	\|-		\|-
	\| You are looking for detailed explanations of a few important topics in single-variable calculus, without necessarily getting comprehensive coverage of all topics \|\| [http://www.youtube.com/user/vipulsclassroom Vipul's Classroom] has video playlists on some calculus-related topics, including limits, many subtopics of integration, differential equations, some subtopics of sequences and series.		\| You are looking for detailed explanations of a few important topics in single-variable calculus, without necessarily getting comprehensive coverage of all topics \|\| [http://www.youtube.com/user/vipulsclassroom Vipul's Classroom] has video playlists on some calculus-related topics, including limits, many subtopics of integration, differential equations, some subtopics of sequences and series. \|\| Free
	\|}		\|}

Vipul: /* First-time learning */

2014-02-13T18:24:45Z

First-time learning

← Older revision		Revision as of 18:24, 13 February 2014
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	\| You have an interest in solving challenging mathematical problems and discovering mathematical ideas through the problem-solving process. \|\| The AoPS calculus text: ''Calculus'' by David Patrick, ISBN 978-1-934124-24-6, [http://www.artofproblemsolving.com/Store/viewitem.php?item=calculus paperback]. You can also enroll in the [https://www.artofproblemsolving.com/School/courseinfo.php?course_id=calculus AoPS online calculus class], though that costs more money. \|\| ~45 for the text, ~$10 for the solutions manual.<br>Current price for semester-long AoPS calculus class unavailable, but comparable precalculus class costs $425 ($478 with book).		\| You have an interest in solving challenging mathematical problems and discovering mathematical ideas through the problem-solving process. \|\| The AoPS calculus text: ''Calculus'' by David Patrick, ISBN 978-1-934124-24-6, [http://www.artofproblemsolving.com/Store/viewitem.php?item=calculus paperback]. You can also enroll in the [https://www.artofproblemsolving.com/School/courseinfo.php?course_id=calculus AoPS online calculus class], though that costs more money. \|\| ~45 for the text, ~$10 for the solutions manual.<br>Current price for semester-long AoPS calculus class unavailable, but comparable precalculus class costs $425 ($478 with book).
	\|-		\|-
	\| You prefer to learn from videos that offer conceptual explanations of ideas, and you don't have an aversion to long videos. \|\| The Center of Math calculus videos ([http://centerofmath.org/videos/index.html here]) and their corresponding textbooks ([http://centerofmath.org/store/index.html store]). These introduce ideas in a concepts-first fashion. \|\| The Worldwide AP Calculus book (that covers all topics) costs $14.95 digital and $39.95 print.		\| You prefer to learn from videos that offer conceptual explanations of ideas, and you don't have an aversion to long videos. \|\| The Center of Math calculus videos ([http://centerofmath.org/videos/index.html here]) and their corresponding textbooks ([http://centerofmath.org/store/index.html store]). These introduce ideas in a concepts-first fashion. \|\| The Worldwide AP Calculus book (that covers all topics) costs $14.95 digital and $39.95 print.<br>Videos require a decent Internet connection, but we expect the Internet connections of most clients to be adequate.
	\|-		\|-
	\| You just want something cheap and basic to get started. \|\| Almost any book will do. Here's the [http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/ calculus online textbook] by Gilbert Strang that's reasonably good. \|\| Strang's book (digital version) is free.		\| You just want something cheap and basic to get started. \|\| Almost any book will do. Here's the [http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/ calculus online textbook] by Gilbert Strang that's reasonably good. \|\| Strang's book (digital version) is free.