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Physical Chemistry
United States
Registrace 28. 09. 2014
Micro lectures for learning physical chemistry.
Evaluating Indefinite Integrals
Integrals of common functions are introduced, and methods of integration are discussed, including integrals of sums of functions, substitution, and integration by parts. Examples are worked.
zhlédnutí: 11 042
Video
Evaluating Definite Integrals
zhlédnutí 6KPřed 9 lety
Indefinite, definite, and improper integrals are defined; properties of definite integrals are discussed; and the procedure for evaluating definite integrals from indefinite integrals is derived. Examples of evaluating definite and improper integrals are worked.
Products of Integrals
zhlédnutí 6KPřed 9 lety
Multivariable double and triple integrals that can be written as a product of single integrals are discussed. Area and volume elements are introduced.
Maxima and Minima
zhlédnutí 7KPřed 9 lety
The criteria for the existence of local extrema are introduced and used to locate the local minima, local maxima, and saddle points of an example function.
What Is an Integral?
zhlédnutí 984KPřed 9 lety
A Riemann sum is introduced as a way to estimate the area between a function and the x axis over an interval and then used to define a definite integral. The concept of net area is introduced, and the fundamental theorem of calculus is introduced as a way to evaluate indefinite integrals by treating integration and differentiation as inverses of each other.
Partial Derivatives
zhlédnutí 20KPřed 9 lety
First, second, and mixed partial derivatives of multi-variable functions are introduced, and geometric and physical interpretations are provided. Examples are worked.
Even and Odd Functions
zhlédnutí 3,4KPřed 9 lety
Even and odd functions are defined, properties of the integrals of even and odd functions are discussed, and examples are given of how to determine if a function is even or odd.
Concavity and Inflection Points
zhlédnutí 2,5KPřed 9 lety
Concavity is qualitatively described, and criteria are introduced for determining a function’s concavity from its first and second derivatives. Inflection points are introduced as points where concavity changes. Examples are provided.
Critical Points
zhlédnutí 3KPřed 9 lety
The sign of the derivative of a function at a value of x is related to whether the function is increasing or decreasing at that point. Critical points are introduced as locations where a function is neither increasing nor decreasing. Critical points are found for some example functions.
Rules for Finding Derivatives
zhlédnutí 10KPřed 9 lety
Rules are introduced for finding the derivative of constants, polynomials, trigonometric functions, other transcendental functions, sums of functions, and products of functions. The chain rule is introduced for evaluating the derivative of composite functions. Worked examples are provided.
Finding Derivatives Graphically
zhlédnutí 4,9KPřed 9 lety
The first and second derivatives of sin(x) are derived graphically by plotting the slope of the straight lines tangent to sin(x) and cos(x). Curvature is introduced quantitatively as the magnitude of the second derivative and qualitatively as the wiggliness of a function.
What Is a Derivative?
zhlédnutí 76KPřed 9 lety
The derivative of a function at an x coordinate is defined as the slope of the straight line tangent to the function at that point and as the instantaneous rate of change of the function at that point. A criterion for a function to be differentiable at a point is introduced. Some uses for derivatives are presented along with a selection of physical quantities that contain derivatives.
Relationship Between Force and Potential Energy
zhlédnutí 34KPřed 9 lety
The notion of conservative systems is introduced, and the relationship between the force and potential energy in conservative systems is discussed.
Harmonic Oscillator Equation of Motion
zhlédnutí 15KPřed 9 lety
The differential equation describing the motion of a classical harmonic oscillator is written and solved. The result is interpreted, and amplitude is introduced.
Introduction to Harmonic Motion
zhlédnutí 4,8KPřed 9 lety
The classical harmonic oscillator model is introduced, harmonic motion is described, and chemical applications of the model are discussed.
Im in 9th and am trying to learn a but more of calculus. I have learnt limits and derivations, integrals and sigma notation and am good in trignometry
czcams.com/video/nKv3IMhKlxk/video.html
Hmmmmmmmmmm 🤔 I will have to study to understand this
got complicated towards the end with the intro of sin and cos without explanation..perhaps this part best left to a more advanced vid
I got lost at 6:00 😅 I'm learning math from scratch and it seems it'll take me a while 😂
I am of grade 7, just curious to learn what an integral is
Nice animation and easy to understand. Thank you.
Just Awesome...it just became so clear to me finally
Eye opening. Thanks!
Im genuinely about to tear up because of how beautiful this is. The concept is so simple yet so genius. Math is beautiful. I still hate tests though.
That last chain rule example with nested chain rules didn't require nesting because sin^2(u) can use the product rule.
This 7 minute video masterfully summed up 2 hours of university lecture. Beautiful
Well if my calculus teacher would play this video to explain integrals she would have actually tought me smth :D. Thanks.
WTF! This dude is so out of touch that he thinks human beings can process information like robots do and he also speaks to us like he's a robot, only faster. I imagine he's one of those individuals that thinks he's smarter than all of us and thus behaves like a robot to prove it, to himself of course, or maybe he's trying to behave like an AI but even AI's want to learn how to speak like we do if only to fools us. Anyhow, the only thing that really stands out in this video is how hard he works to make sure we don't understand a things he's saying. If only he thought of us as human beings and treated us like such this could be an interesting video, but I've seen his kind before and at this juncture it sounds like he's all fired up and hell bent to be one of those quantum crazies.
are you autistic ? its the best video on this topic for revision
Can someone explain Why at the delta Xj the -1 is added? 3:00
It represents the width of the rectangle. For example, the width of the second rectangle is X2 - X1. This can be re-written as X2 - Xsub(2-1) since Xsub(2-1) is just X1.
@@m0onshyne970Can you help explain why did he took delta x of j?
Each smallest rectangle area is y (height or length of rectangle) times the width, say the width is ‘(x1-x0)’ = y times (x1-x0), i.e., what is y is nothing but y = f(x) at all times, y varies based on x coordinate value. So Area of the smallest rectangle is substituting y=f(x) in the product above becomes f(x) times (x1-x0). This is proof for Area S = f(x)(x1-x0) in the 1st step. / not obvious for first timers who may assume it is so as teacher said as a statement. But simple substitution.Cheers!
You are incredible please continue your work on this channel it is invaluable
hey, great video. though is there a good explanation out there of how we got from the limit of the riemann-sum to the basic integration rules (for example polynomial rule, or trigonometric)? how did people find out that for polynomials such as a^n the integral is a^(n+1) * 1/(n+1)?
Why J is equal to 1?
,
Tysm for this lovely vid ❤
we still can't solve the integral of some basic mathematical functions For example, although we can calculate the result of the integral e^sin(x) dx numerically, we cannot express it symbolically. Mathematics is not a science, it is a language. #math #mathematics #integral #sinus #cosinus
#sinus is funny
#sinusinfection
constants are not constants, variables do not want to work, . Murphy's law
hai sir my name danial do you has a telegram i want to pm you..tq sir
Your explanations are absolute fantastic, God bless
The missile knows where it is at at all times because it knows where it isn’t.
You have explain my 1h30min session without understanding in 10 min... Thank..now I can see the light
I wasn't tired before watching this..
This video was worth half of my college semester. Thank you so much for the great explanation! Please make more videos on this topic!😃
so this is what people calling "crystal clear"
Salute to your clarity 👍 Your six minutes are superior than my 16 years education
Not a word wasted. Pause. Rewatch. Nice.
I love you no homo
BRO THANK YOU SO MUCH!!!!
II'm in the 8th grade and I wanted to get a little ahead of the concepts of my classes. This video was ideal for understanding the integrals.
What 8th grader is doing integrals on class
Guess he wants to be a mathematician@@yaboyyoob7531
"Heighth"
The visuals in this was absolutely horrible starting at 3:00. Why dont you SHOW people what and WHERE it is instead of zooming through it like you’re late during a lecture and having nothing but the equations written on a whiteboard? You’re on youtube, so you can make it more beneficial with specifically visuals and you just choose not to do it with an unchanging picture. Your job is clearly to speed through a video and make money, not to teach people anything. Selfish people like you make this world suck, honestly. Greed will never end.
Oh, it's so cool explanation, very simple to understand what integrals are and how do they work under the hood. Thank you.
Well explained, organized writing and explanation. Thank you.
Holy poop. You're the bomb.
Ive been watching like 10 videos and i finally now understnad integrals, at least a little bit. Thank you so much
Man this is just next level of godly explaination
But how the area under curve is linked to increment the power then divide bla bla, and height if the rectangles are not fixed as the curve goes up down
Woah woah woah... hold on..... . . How do I draw that little worm guy?
My Pre-Calc teacher has been calling them "Relative Maximums" instead. I assume it's just a change in curriculum. Although we haven't learned about 'Absolute Maximums" yet. Anyway, this was a very cool video to see the practical applications of derivatives. I still don't understand what the point of integrals are, but if they're inverses of derivatives, I assume they're just as useful.
ahhh constants of integration exist because of Sum Rule. The derivative of the sum of two functions is the same as their derivatives added, and the derivative of a constant is always 0. So the derivative of any function is the same as the derivative of that function plus any constant since that constant becomes 0 when differentiated.
A super video ❤️
So it is just for loop?????
this is cool as shit
Element of the dual of the continuous functions endowed with the supremum distance
Great