Functions & Calculus by Professor Calculish
Functions & Calculus by Professor Calculish
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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".
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)
Indefinite Integration
Переглядів 7173 місяці тому
Indefinite Integration
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
Polar Forms of Folium of Descartes
Переглядів 774 місяці тому
Polar Forms of Folium of Descartes
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
Why is sqrt (-1) = i ?
Переглядів 5404 місяці тому
Why is sqrt (-1) = i ?
∞ / ∞ (why is it Indeterminate?)
Переглядів 595 місяців тому
∞ / ∞ (why is it Indeterminate?)
Parametric Equations for an Epicycloid
Переглядів 1335 місяців тому
Parametric Equations for an Epicycloid
The Fibonacci Sequence Algorithm
Переглядів 1585 місяців тому
The Fibonacci Sequence Algorithm
Try out these 2 Limits (squeeze theorem)
Переглядів 465 місяців тому
Try out these 2 Limits (squeeze theorem)

КОМЕНТАРІ

  • @Priyanka-er2mb
    @Priyanka-er2mb 2 дні тому

    Thank you Sir ❤

  • @bryansells4820
    @bryansells4820 9 днів тому

    How about if x approaches to 0?

    • @professorcalculish
      @professorcalculish 9 днів тому

      In that case you can simply apply l hopital rule and do cos(0) = 1

  • @0bush480
    @0bush480 12 днів тому

    Thank you so much, I have watched 2 of your videos so far and you explained the concepts extremely well!

  • @toffeetoe8939
    @toffeetoe8939 15 днів тому

    excellent topic

  • @arnabchowdhury4892
    @arnabchowdhury4892 17 днів тому

    @professorcalculish Please give the example in use of partial derivatives in solving real world problem?

    • @professorcalculish
      @professorcalculish 17 днів тому

      @@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...

  • @toffeetoe8939
    @toffeetoe8939 20 днів тому

    great

  • @wasimvillidad3000
    @wasimvillidad3000 27 днів тому

    No need for calculus. Area of kite - area of sector = 2 - arctan(2).

    • @professorcalculish
      @professorcalculish 27 днів тому

      @@wasimvillidad3000 true.but someone specifically wanted to see in calculus

  • @learningcomesfirst722
    @learningcomesfirst722 28 днів тому

    Great example

  • @toffeetoe8939
    @toffeetoe8939 28 днів тому

    excellent solution presentation

  • @toffeetoe8939
    @toffeetoe8939 Місяць тому

    great

  • @OsmanOnurBaşural
    @OsmanOnurBaşural Місяць тому

    Could you show how can we solve this by using calculus

  • @AviiPragvanshiii
    @AviiPragvanshiii Місяць тому

    Amazing 🤯🤯It Is called real chocolate Question 😳👏🏻🙌🏻 Great Work Sirrr❤👏🏻🙌🏻🙌🏻

    • @professorcalculish
      @professorcalculish Місяць тому

      @AviiPragvanshiii thank you

    • @AviiPragvanshiii
      @AviiPragvanshiii Місяць тому

      @professorcalculish which book you use sir fir that kind of questions calculation is really tough

    • @professorcalculish
      @professorcalculish Місяць тому

      @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

    • @AviiPragvanshiii
      @AviiPragvanshiii Місяць тому

      @professorcalculish Amazing Amazing 🔥🔥👏🏻 hats off to you sir 🙌🏻

    • @professorcalculish
      @professorcalculish Місяць тому

      @AviiPragvanshiii ✌️✌️

  • @learningcomesfirst722
    @learningcomesfirst722 Місяць тому

    Excellent question

  • @xfs4710
    @xfs4710 Місяць тому

    ϖ

  • @holyshit922
    @holyshit922 Місяць тому

    Homogeneous by putting y=e^{λx} Particular solution of non-homogeneous equation by undetermined coefficients y_{p}(x) = Axe^{x} + (Bx^2+Cx+D)

    • @professorcalculish
      @professorcalculish Місяць тому

      @@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!!

  • @toffeetoe8939
    @toffeetoe8939 Місяць тому

    Great video and question

  • @learningcomesfirst722
    @learningcomesfirst722 Місяць тому

    Excellent

  • @toffeetoe8939
    @toffeetoe8939 Місяць тому

    great Q!

  • @AviiPragvanshiii
    @AviiPragvanshiii Місяць тому

    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

  • @Melon_king_0772
    @Melon_king_0772 Місяць тому

    Why make it hard

    • @professorcalculish
      @professorcalculish Місяць тому

      @@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.....

  • @FoodeliciousKitchenbySabaish
    @FoodeliciousKitchenbySabaish Місяць тому

    excellent!

  • @MakeMeScientific
    @MakeMeScientific Місяць тому

    Great

  • @learningcomesfirst722
    @learningcomesfirst722 Місяць тому

    Great content.

  • @isabella.underscore
    @isabella.underscore Місяць тому

    This was the most helpful video ever! So simple and effective. Thanks

    • @professorcalculish
      @professorcalculish Місяць тому

      @@isabella.underscore you are most welcome! Thanks 😉

  • @Sid_itsme
    @Sid_itsme Місяць тому

    why do you hold the marker like that

    • @professorcalculish
      @professorcalculish Місяць тому

      @@Sid_itsme because I have a pinched nerve in the thumb that shoots signals when I hold it the normal way...

    • @Sid_itsme
      @Sid_itsme Місяць тому

      @@professorcalculish I'm sorry if i sounded rude

    • @professorcalculish
      @professorcalculish Місяць тому

      @Sid_itsme trust me you did nor! It's all goood✌️✌️

  • @learningcomesfirst722
    @learningcomesfirst722 Місяць тому

    Excellent

  • @horek_01
    @horek_01 Місяць тому

    সেই

    • @horek_01
      @horek_01 Місяць тому

      @@professorcalculish In Bengali,It means Very good

    • @professorcalculish
      @professorcalculish Місяць тому

      @horek_01 ok thank you much!

  • @NPK13
    @NPK13 Місяць тому

    But why would gravity do positive work in this case, if gravitational energy is increasing? Shouldn't it have done negative work?

    • @NPK13
      @NPK13 Місяць тому

      @@professorcalculish I fail to see where the minus got dropped / added.

    • @professorcalculish
      @professorcalculish Місяць тому

      ​@@NPK13look specifically at time 2:45 and 3:10.....

  • @DungNguyen-fd9px
    @DungNguyen-fd9px 2 місяці тому

    omg always a random Indian guy on youtube who can save me from hell, really really appreciate this video :3

    • @professorcalculish
      @professorcalculish 2 місяці тому

      @@DungNguyen-fd9px most welcome. Technically from Pakistan but it's by no means an insult, in all sincerity, to be called Indian 😉 😉

  • @learningcomesfirst722
    @learningcomesfirst722 2 місяці тому

    Difficult q!

    • @professorcalculish
      @professorcalculish 2 місяці тому

      @@learningcomesfirst722 if done in steps or parts it's not as bad

  • @toffeetoe8939
    @toffeetoe8939 2 місяці тому

    Excellent!

  • @sakinnahwebster701
    @sakinnahwebster701 2 місяці тому

    Yes, thank You sir. My 7th grade Twins and I REALLY appreciate your help🎉

  • @sakinnahwebster701
    @sakinnahwebster701 2 місяці тому

    So how do you find the volume if you only have the values for S and length?

    • @professorcalculish
      @professorcalculish 2 місяці тому

      Having on the values for "s" (side) and "length"....by "length" did you mean height?

    • @professorcalculish
      @professorcalculish 2 місяці тому

      This video will help you: ua-cam.com/video/_XVeVIfJJIU/v-deo.html

  • @quandaledingle1231
    @quandaledingle1231 2 місяці тому

    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?

    • @professorcalculish
      @professorcalculish 2 місяці тому

      @@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.

  • @musicbytahaanddad
    @musicbytahaanddad 2 місяці тому

    great explanation of process

  • @toffeetoe8939
    @toffeetoe8939 2 місяці тому

    Excellent example question!

  • @learningcomesfirst722
    @learningcomesfirst722 2 місяці тому

    I'm beginning to get these finally!

  • @nastudios915
    @nastudios915 2 місяці тому

    Thank you this is what I was looking for 👍

    • @professorcalculish
      @professorcalculish 2 місяці тому

      @@nastudios915 most welcome. Something slightly more comprehensive: ua-cam.com/video/xj13Ry8w7uk/v-deo.htmlfeature=shared

  • @learningcomesfirst722
    @learningcomesfirst722 2 місяці тому

    Great example

  • @KUDIYARASAN-
    @KUDIYARASAN- 2 місяці тому

    Great… Very fast … To the point explanation….

  • @damianalbanis9403
    @damianalbanis9403 2 місяці тому

    Awesome I may need you for a project to calculate some volumes 🤩🤔😜🥳🥳

  • @AbdullahKarim-e6v
    @AbdullahKarim-e6v 2 місяці тому

    Thnx sir

  • @AbdullahKarim-e6v
    @AbdullahKarim-e6v 2 місяці тому

    Thnx Sir😊

  • @BradyLauria
    @BradyLauria 2 місяці тому

    Thank you

  • @Local.idiotic
    @Local.idiotic 2 місяці тому

    Wow!

  • @learningcomesfirst722
    @learningcomesfirst722 2 місяці тому

    Excellent topic, but difficult

  • @matemaniaindonesia3635
    @matemaniaindonesia3635 2 місяці тому

    like this

  • @professorcalculish
    @professorcalculish 2 місяці тому

    Excellent video question

  • @foodelicioussaba5749
    @foodelicioussaba5749 2 місяці тому

    excellent video

  • @toffeetoe8939
    @toffeetoe8939 3 місяці тому

    Well-explained, I always found these hard!

    • @professorcalculish
      @professorcalculish 3 місяці тому

      @@toffeetoe8939 thank you, keep at it, it gets easier