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Functions & Calculus by Professor Calculish
United States
Приєднався 22 сер 2021
The ultimate Single Variable Calculus Hub! Everything necessary from A to Z to build the best Calculus foundation; primary focus is Calculus I and II.
I work out problems for the benefit of math students who are struggling with Calculus, and who don't have access to solutions manual (or solutions guidance).
For math education purposes and the enhancement of student success in Calculus. A strong foundation in basic Calculus sets the stage for everything else that follows.
I am not a professor by occupation. I appreciate your input and comments very much.
I work out problems for the benefit of math students who are struggling with Calculus, and who don't have access to solutions manual (or solutions guidance).
For math education purposes and the enhancement of student success in Calculus. A strong foundation in basic Calculus sets the stage for everything else that follows.
I am not a professor by occupation. I appreciate your input and comments very much.
Partial Derivative Application (slope of a "trace")
"A partial derivative represents the slope of a "trace" of a function, which is essentially the curve created when you slice the function's graph with a plane parallel to one of the coordinate planes, holding all other variables constant; meaning it captures the instantaneous rate of change of the function with respect to one variable while keeping the others fixed." (Google AI)
"The partial derivative at a specific point represents the slope of the tangent line to the trace at that point."
The purpose of the channel is to learn, familiarize, and review the necessary precalculus and trigonometry/geometry topics that form a basis for calculus (with a focus on functions). Calculus topics include limits, derivatives, integrals, formula derivations, derivations/proofs, area/volumes of curves and calculus applications.
Utilize simple and easy techniques to get the material across to you.
Disclaimer: I am not a professor by profession.
Thank you!
#partialderivatives #derivatives #differentialcalculus #multivariablecalculus #calculus #professorcalculish #functions #graphs #cartesian #parabolic #tangentline #slope #variables #constants #surfacegraphs #instantaneous
Content credit (all credit only to):Schaum's; Theory and Problems of Differential & Integral Calculus; Ayres, F. 1960.(solutions manual for questions from book)pg. 261 (inspired by Q # 13)not the exact Q
Other Credit: Desmos 3-D graphing (online software tool used in video); all credit for graphing to Desmos "Beautiful Free Math".
"The partial derivative at a specific point represents the slope of the tangent line to the trace at that point."
The purpose of the channel is to learn, familiarize, and review the necessary precalculus and trigonometry/geometry topics that form a basis for calculus (with a focus on functions). Calculus topics include limits, derivatives, integrals, formula derivations, derivations/proofs, area/volumes of curves and calculus applications.
Utilize simple and easy techniques to get the material across to you.
Disclaimer: I am not a professor by profession.
Thank you!
#partialderivatives #derivatives #differentialcalculus #multivariablecalculus #calculus #professorcalculish #functions #graphs #cartesian #parabolic #tangentline #slope #variables #constants #surfacegraphs #instantaneous
Content credit (all credit only to):Schaum's; Theory and Problems of Differential & Integral Calculus; Ayres, F. 1960.(solutions manual for questions from book)pg. 261 (inspired by Q # 13)not the exact Q
Other Credit: Desmos 3-D graphing (online software tool used in video); all credit for graphing to Desmos "Beautiful Free Math".
Переглядів: 29
Відео
Partial Derivatives (Application)
Переглядів 5021 годину тому
The purpose of the channel is to learn, familiarize, and review the necessary precalculus and trigonometry/geometry topics that form a basis for calculus (with a focus on functions). Calculus topics include limits, derivatives, integrals, formula derivations, derivations/proofs, area/volumes of curves and calculus applications. Utilize simple and easy techniques to get the material across to yo...
2nd Order Partial Derivatives
Переглядів 14714 днів тому
Regarding the name of the partial derivative symbol: (credit to Wikipedia); it is variously called: "partial", "curly d", "funky d", "rounded d", "curved d", "dabba", "number 6 mirrored", "Jacobi's delta", or as "del" (but this name is also used for the "nabla" symbol ∇). It may also be pronounced simply "dee", "partial dee", "doh", "dow" or "die". (from Wikipedia) relevant video: ua-cam.com/vi...
First partial Derivatives (basic technique practice)
Переглядів 11121 день тому
The partial derivative symbol is called a "del". The purpose of the channel is to learn, familiarize, and review the necessary precalculus and trigonometry/geometry topics that form a basis for calculus (with a focus on functions). Calculus topics include limits, derivatives, integrals, formula derivations, derivations/proofs, area/volumes of curves and calculus applications. Utilize simple and...
Integral Calculus Exercise (area of shaded region)
Переглядів 11228 днів тому
Note, |2x| is same as 2|x| Relevant video link: ua-cam.com/video/vMsh2oPVDKY/v-deo.html The purpose of the channel is to learn, familiarize, and review the necessary precalculus and trigonometry/geometry topics that form a basis for calculus (with a focus on functions). Calculus topics include limits, derivatives, integrals, formula derivations, derivations/proofs, area/volumes of curves and ca...
2nd Order Nonhomogeneous (Find Current)
Переглядів 28Місяць тому
Continued focus on solving 2nd order Nonhomogeneous differential equations. Emphasis on technique for solving. Relevant videos: ua-cam.com/video/rNrX6IYFFV8/v-deo.html ua-cam.com/video/tWAB2TIhT-4/v-deo.html ua-cam.com/video/zqAFEbJoiyU/v-deo.html ua-cam.com/video/F8oQyviG1Jw/v-deo.html ua-cam.com/video/WKqF8gAFVjM/v-deo.html ua-cam.com/video/xN7Jf_u94HE/v-deo.html The purpose of the channel is...
Funnel Problem (rate of change)
Переглядів 49Місяць тому
Funnel problems are those where a liquid is draining from an inverted cone (funnel) and a variety of variable dimensions are being affected in terms of their change over time. The purpose of the channel is to learn, familiarize, and review the necessary precalculus and trigonometry/geometry topics that form a basis for calculus (with a focus on functions). Calculus topics include limits, deriva...
Solve this Nonhomogeneous Equation
Переглядів 93Місяць тому
Relevant videos: ua-cam.com/video/rNrX6IYFFV8/v-deo.html ua-cam.com/video/tWAB2TIhT-4/v-deo.html ua-cam.com/video/zqAFEbJoiyU/v-deo.html ua-cam.com/video/F8oQyviG1Jw/v-deo.html ua-cam.com/video/WYo19x2Tx9Y/v-deo.html ua-cam.com/video/WKqF8gAFVjM/v-deo.html The purpose of the channel is to learn, familiarize, and review the necessary precalculus and trigonometry/geometry topics that form a basis...
2nd Order Diff Eq Problem (Simple Harmonic Motion)
Переглядів 38Місяць тому
Relevant video: ua-cam.com/video/npJzJgA9m7E/v-deo.html The purpose of the channel is to learn, familiarize, and review the necessary precalculus and trigonometry/geometry topics that form a basis for calculus (with a focus on functions). Calculus topics include limits, derivatives, integrals, formula derivations, derivations/proofs, area/volumes of curves and calculus applications. Utilize sim...
Area of any Inscribed Regular Polygon (An) is Derived
Переглядів 79Місяць тому
Any regular polygon (having equal sides) inscribed in a circle has an Area (An) that has a formula derived and presented for you in this video. relevant video: ua-cam.com/video/2yjZQF-5Cnc/v-deo.html The purpose of the channel is to learn, familiarize, and review the necessary precalculus and trigonometry/geometry topics that form a basis for calculus (with a focus on functions). Calculus topic...
Solve this Nonhomogeneous Eq (trigonometric)
Переглядів 224Місяць тому
The purpose of the channel is to learn, familiarize, and review the necessary precalculus and trigonometry/geometry topics that form a basis for calculus (with a focus on functions). Calculus topics include limits, derivatives, integrals, formula derivations, derivations/proofs, area/volumes of curves and calculus applications. Utilize simple and easy techniques to get the material across to yo...
Derivative (rate of change) Problem
Переглядів 452 місяці тому
Very interesting derivative problem! The purpose of the channel is to learn, familiarize, and review the necessary precalculus and trigonometry/geometry topics that form a basis for calculus (with a focus on functions). Calculus topics include limits, derivatives, integrals, formula derivations, derivations/proofs, area/volumes of curves and calculus applications. Utilize simple and easy techni...
Solve Difficult Nonhomogeneous Diff Equation
Переглядів 1202 місяці тому
Relevant videos: ua-cam.com/video/rNrX6IYFFV8/v-deo.html ua-cam.com/video/tWAB2TIhT-4/v-deo.html ua-cam.com/video/zqAFEbJoiyU/v-deo.html ua-cam.com/video/F8oQyviG1Jw/v-deo.html The purpose of the channel is to learn, familiarize, and review the necessary precalculus and trigonometry/geometry topics that form a basis for calculus (with a focus on functions). Calculus topics include limits, deriv...
Triangular Pyramid Volume Exercise
Переглядів 732 місяці тому
The purpose of the channel is to learn, familiarize, and review the necessary precalculus and trigonometry/geometry topics that form a basis for calculus (with a focus on functions). Calculus topics include limits, derivatives, integrals, formula derivations, derivations/proofs, area/volumes of curves and calculus applications. Utilize simple and easy techniques to get the material across to yo...
Nonhomogeneous Diff Eqs 2nd order (part 3, solving)
Переглядів 302 місяці тому
Nonhomogeneous Diff Eqs 2nd order (part 3, solving)
Nonhomogeneous Solving "issue" (exponential variety)
Переглядів 302 місяці тому
Nonhomogeneous Solving "issue" (exponential variety)
Nonhomogeneous Diff Eqs 2nd order (part 2, solving)
Переглядів 312 місяці тому
Nonhomogeneous Diff Eqs 2nd order (part 2, solving)
Practice Question (Nonhomogeneous, Quadratic)
Переглядів 522 місяці тому
Practice Question (Nonhomogeneous, Quadratic)
Nonhomogeneous Diff Eqs 2nd order (part 1, solving)
Переглядів 513 місяці тому
Nonhomogeneous Diff Eqs 2nd order (part 1, solving)
Converting between Polar and Cartesian Equations
Переглядів 503 місяці тому
Converting between Polar and Cartesian Equations
Develop Parametric Equations for Hyperbola
Переглядів 564 місяці тому
Develop Parametric Equations for Hyperbola
Trochoid and its Parametric Equations
Переглядів 2374 місяці тому
Trochoid and its Parametric Equations
Area of a Loop of Folium of Descartes
Переглядів 1754 місяці тому
Area of a Loop of Folium of Descartes
Parametric Equations for an Epicycloid
Переглядів 1335 місяців тому
Parametric Equations for an Epicycloid
Try out these 2 Limits (squeeze theorem)
Переглядів 465 місяців тому
Try out these 2 Limits (squeeze theorem)
Thank you Sir ❤
@@Priyanka-er2mb very welcome 🙏
How about if x approaches to 0?
In that case you can simply apply l hopital rule and do cos(0) = 1
Thank you so much, I have watched 2 of your videos so far and you explained the concepts extremely well!
@@0bush480 thank you very much!
excellent topic
@@toffeetoe8939 thank you
@professorcalculish Please give the example in use of partial derivatives in solving real world problem?
@@arnabchowdhury4892 real world applications would be engineering or science related, perhaps out-of my own scope, as it is multivariate....if I can, I'll send you a link, else youtube search and you may find something...
great
@@toffeetoe8939 thank you
No need for calculus. Area of kite - area of sector = 2 - arctan(2).
@@wasimvillidad3000 true.but someone specifically wanted to see in calculus
Great example
@@learningcomesfirst722 thank you
excellent solution presentation
@@toffeetoe8939 thank you
great
@@toffeetoe8939 thank you
Could you show how can we solve this by using calculus
@@OsmanOnurBaşural sure I can, send you video link soon
ua-cam.com/video/pD0Uq4Q96Dc/v-deo.html
Amazing 🤯🤯It Is called real chocolate Question 😳👏🏻🙌🏻 Great Work Sirrr❤👏🏻🙌🏻🙌🏻
@AviiPragvanshiii thank you
@professorcalculish which book you use sir fir that kind of questions calculation is really tough
@AviiPragvanshiii some questions are provided to me by viewers others come from, but are slightly modified, from Stewart's single variable calculus...and Strouds Differential equations (British book); other questions I make up myself
@professorcalculish Amazing Amazing 🔥🔥👏🏻 hats off to you sir 🙌🏻
@AviiPragvanshiii ✌️✌️
Excellent question
@@learningcomesfirst722 thank you
ϖ
@@xfs4710 kindly translate
Homogeneous by putting y=e^{λx} Particular solution of non-homogeneous equation by undetermined coefficients y_{p}(x) = Axe^{x} + (Bx^2+Cx+D)
@@holyshit922 inhomogeneous when introduced to students new to this topic and the general basis is made by means of function after equal sign. I appreciate your comment!!
Great video and question
@@toffeetoe8939 thank you
Excellent
@@learningcomesfirst722 thank you
great Q!
@@toffeetoe8939 thank you
Thank You Sir 😊😊❤ Please continue that type of questions series it helps me alot when I open UA-cam I watch your videos instead of any other video
@AviiPragvanshiii sure I will!
@AviiPragvanshiii and thanks you very much
Kindly give this a try: ua-cam.com/video/EAauPoi3Lh0/v-deo.html
Why make it hard
@@Melon_king_0772 if I make it easy and too quick, some will say I jumped right through it and they did not get it.....
excellent!
@@FoodeliciousKitchenbySabaish thank you
Great
@@MakeMeScientific thank you!
Great content.
@@learningcomesfirst722 thank you
This was the most helpful video ever! So simple and effective. Thanks
@@isabella.underscore you are most welcome! Thanks 😉
why do you hold the marker like that
@@Sid_itsme because I have a pinched nerve in the thumb that shoots signals when I hold it the normal way...
@@professorcalculish I'm sorry if i sounded rude
@Sid_itsme trust me you did nor! It's all goood✌️✌️
Excellent
thank you
সেই
@@professorcalculish In Bengali,It means Very good
@horek_01 ok thank you much!
But why would gravity do positive work in this case, if gravitational energy is increasing? Shouldn't it have done negative work?
@@professorcalculish I fail to see where the minus got dropped / added.
@@NPK13look specifically at time 2:45 and 3:10.....
omg always a random Indian guy on youtube who can save me from hell, really really appreciate this video :3
@@DungNguyen-fd9px most welcome. Technically from Pakistan but it's by no means an insult, in all sincerity, to be called Indian 😉 😉
Difficult q!
@@learningcomesfirst722 if done in steps or parts it's not as bad
Excellent!
@@toffeetoe8939 thank you
Yes, thank You sir. My 7th grade Twins and I REALLY appreciate your help🎉
@@sakinnahwebster701 alhamdolillah. Jazak'Allah
So how do you find the volume if you only have the values for S and length?
Having on the values for "s" (side) and "length"....by "length" did you mean height?
This video will help you: ua-cam.com/video/_XVeVIfJJIU/v-deo.html
Thank you so much, professor. Earlier, you mentioned that we can informally refer to a and b as the radii. Could you please clarify how to formally define the concept of "radius" in this context?
@@quandaledingle1231 welcome. The formal definition would require one to see that if they were standing in the center of an Ellipsoid, and looking towards the surface, on an x y z coordinate system one would see that a radius is really an interplay of the major and minor axis, unlike in a sphere where the radius is equivalent any way around. For Ellipsoid we would be entering realm of geometric calculus to best appreciate the radius concept.
great explanation of process
@@musicbytahaanddad thanks 😊
Excellent example question!
I'm beginning to get these finally!
@@learningcomesfirst722 excellent. Keep at it
Thank you this is what I was looking for 👍
@@nastudios915 most welcome. Something slightly more comprehensive: ua-cam.com/video/xj13Ry8w7uk/v-deo.htmlfeature=shared
Great example
@@learningcomesfirst722 thank you
Great… Very fast … To the point explanation….
@@KUDIYARASAN- thank you sir
Awesome I may need you for a project to calculate some volumes 🤩🤔😜🥳🥳
@@damianalbanis9403 👍👍👍👍
Thnx sir
@@AbdullahKarim-e6v Jazak'Allah!
Thnx Sir😊
@@AbdullahKarim-e6v most welcome!
Thank you
@@BradyLauria most welcome!!!
Wow!
Excellent topic, but difficult
@@learningcomesfirst722 thank you
like this
@@matemaniaindonesia3635 thanks much!
Excellent video question
excellent video
@@foodelicioussaba5749 thank you
Well-explained, I always found these hard!
@@toffeetoe8939 thank you, keep at it, it gets easier