Calculus 2 Archives | Every Step Calculus

Raw Transcript

Hello again, everyone, this is Tom from everystepcalculus.com and everystepphysics.com. I’m gonna do partial derivatives now in this video, generally with respect to calculus 2 or 3. Let’s do it. Index 8, get to my menu… Scroll up to get to the P’s quicker. It goes to the bottom of the alphabet, so we get to what we’re looking for, it’s partial derivatives. On the menu you can go second and the titanium second and then these cursers to go page by page. You do that here to get through the menu quicker, and we’re looking at, let’s see, partial fractions, here’s partial derivatives, and I programmed first order or second order; we’re going to do first order in this problem. Z= f (x,y) We’re going to enter our function, that the function given is. You have to press alpha before you enter anything into these entry lines in my programs, okay, so alpha, and then we’re going to press T here, which gives us the arc tangent for Y divided by X I always show you what you’ve entered so you can change it if you made a mistake. So it’s okay, and here’s the partial derivatives, with respect to x, is minus Y divided by X squared plus Y squared, this is a, if you go to my trig identities you’ll see that tangent to the minus 1 is 1 over the quantity of 1 plus x squared. In this case it would be 1 over the quantity 1 plus Y divided by X squared. To get the derivative with respect to X and with respect to Y, it’s this equation here. And then there’s a point A and B that they give you. Press the one for A, is alpha, minus 2. Make sure you know it’s interchanged the minus sign for the negative sign. And then for the B, alpha 7 is given. Again I’ll show you what you’ve entered, and we see that’s okay, and so the problem asks for fx(a,b), which is this right here, replacing the y’s and the x’s for whatever is given here for A and B. And I have to use quotation marks the way the calculator allows me to with programming, but you’re going to use parentheses here anytime you see a quotation here, because you’re substituting X and Y values for the X and Y values in the function. And the answer is -7 over 53. And now if they ask you for F of Y you’d go one step further, and that would be substituting this, you get -2 over 53. Pretty neat, huh? everystepcalculus.com, go to my site and subscribe to me so you can see other videos if you’re interested. Have a good one!

Programs Included in Calculus 2 & 3 App

Raw Transcript

Hello, everyone. This is Tom from everystepcalculus.com and everystepphysics.com. This video is on a menu of Calculus 2 and 3 if you purchased that. What you get. I’m going to go over each item and show you. Index 8 to get to the menu. The busy sign here means that it’s loading the programs. Sometimes it takes longer because of the size of the program but after it’s loaded once, it’s very quick. For instance like this F1 8 to clear, I’m going to press it now. Notice how quickly it comes up right away. I’m going to go up to the top here. And start name the things. Look at this part up here as I name them. A and B vectors, that comes in Calculus 3, generally. You’re doing all sorts of things with adding vectors and subtracting vectors and doing everything possible with them. So A and B vectors, Acceleration, Angle of Vector, Arc Length, that’s the f of x system and then the r t system, Area of a Parallelogram, Component of A Direction of B, Cosine of A and B, that’s the cosine of the A and B vectors. Cross Product, dealing with vectors. Curl computing it at a point, Curl conservative, whether it’s conservative or not, Curl whether it’s divergent, and then the systems of notation which is MNP and PQR for the curl. There’s a double integral, definite integral xy and there’s a definite integral xyz. One is area one is volume. Disk method, Divergence at a point, dot product, double integral, eliminate the parameter, equation of a tangent plane, an equation of a plane, Gradient, Green’s Theorem, Integration by Parts, Interval of Convergence, Line Integral f of xyz, linear approximation 2 variables, linear approximation 3 variables, linear equation, natural log of x the derivative of that, natural log of x the integral, natural log of x solving for x, and then log problems, those are to different bases. Mass and spring of a wire, money, p and q points, parametric equation, partial derivative, partial fractions, partial fraction decomposition, path of objects, polar to rectangle, conversion, position vectors, projection of a on b, projection of b on a, ratio test and series when you’re talking about Taylor and Maclaurin series, rectangular to polar, rectangular box, that’s a standard computation in calculus. Series Convergence, Shell Method, Simpson’s rule, Sine of x cubed, cosine of x squared times. Sketch the graph when you’re talking about p and q points, speed which is the same thing as volume. Sphere center midpoint, Sphere equation, sphere radius, Surface area of Revolution, Surface Integral xy, surface integral xz, surface integral yz. Tangent of log of x, the derivative of that. Natural log of x. Tangent of plane to surface. Taylor and Maclaurin series, Trig and half angled formulas, Trig derivatives and identities, trig integrals, triple integral xyz, triple integral zyx, U Substitution, Unit Tangent Vector, Unit Tangent PQ divided by the magnitude which is PQ. That’s those two lines there on each side of the PQ. Unit Vector Opposite, Vector length, vector between p and q, vector magnitude, Vector, unit, tangent, and Vectors. Which is taking 2 or 3 vectors and finding the angles of those vectors, etc. Quite a series of those. Vector Field Divergent, Velocity, Volume of a parallelpiped, the washer method, and that’s it. Have a good one.