Author Archives: hangtime

Verifying Solutions of Differential Equations & Solving For C

Before you can solve differential equations, you have to know what the heck they are, what "specific" and "general" solutions are, how to verify your solution, and how to use "initial conditions" to solve for C. I bring this up because, obviously, all that stuff is covered in this video.

This video appears on the page: Differential Equations

Differential Equations
Verifying Solutions of Differential Equations & Solving For C
Solving Differential Equations Using Separation of Variables

This chapter covers solving differential equations using integration: separation of variables, initial conditions, general solutions, specific solutions.

Part of the course(s): ,Test Image Problem ,Calculus

Using Integrals to Calculate Pressure Force

Finally, what we've been building up to: using integration to calculate the force due to pressure and depth! These are tough to set up, but if you've already watched the non-calculus pressure videos they shouldn't completely blow your mind. They also bear a striking resemblance to area and centroid problems, so at least the integrals here should seem eerily familiar...

This video appears on the page: Fluid Pressure & Forces

Pressure & Force Due to Depth

This video explains why the pressure changes as we go up and down in the ocean or atmosphere, and it explains how to calculate the pressure at a given depth. It then gets into calculating the force on submerged windows and surfaces, and goes over some trick questions that teachers can try to burn you with. Example: If atmospheric pressure is 14 pounds per square inch, why isn't your kitchen table crushed?

This video appears on the page: Fluid Pressure & Forces

Intro to Pressure: Concepts, Formulas & Units

This video introduces the concept of pressure and its basic formula, P=F/A. It also explains what units to use with pressure, how to convert bad units into good units, and how to do basic calculations where a problem is asking for pressure or force due to a pressure.

This video appears on the page: Fluid Pressure & Forces

Fluid Pressure & Forces
Intro to Pressure: Concepts, Formulas & Units
Pressure & Force Due to Depth
Using Integrals to Calculate Pressure Force

This chapter covers the basics of pressure and the forces that pressure can exert on a surface, then it gets into using integrals to find the pressure on a vertical surface (plate, window, etc.).

Part of the course(s): ,Physics ,Test Image Problem ,Calculus

Centroids Using Integration

Ever wish you could use integration -- maybe even integration by parts -- to find the centroid of a 2-dimensional region in the x-y plane bounded by continuous functions of x? (crickets) That's what I thought! You're welcome!

This video appears on the page: Centroids & Center of Mass

Two-Dimensional Moments & Centroids

Whether your teacher just makes you find the centroid of a list of x-y coordinates and masses, or you have to find the centers of mass of strange shapes that require you to break them up into squares and rectangles, this video has you covered. Also explained are Moments, and why the heck you have to use M-x to find a y-coordinate M-y to find an X.

This video appears on the page: Centroids & Center of Mass

One-Dimensional Centroids

This video covers what to do when you're asked to find the centroid (a.k.a. center of mass) of a one-dimensional system. These questions can come in the form of a word problem about kids on a seesaw, or abstract lists of points and masses, or a diagram of masses on a number line.

This video appears on the page: Centroids & Center of Mass

Centroids & Center of Mass
One-Dimensional Centroids
Two-Dimensional Moments & Centroids
Centroids Using Integration

The first two videos in this chapter cover finding center of mass of one-dimensional and two-dimensional (2-D) systems without using calculus, then the final video covers using integrals.

Part of the course(s): ,Physics ,Test Image Problem ,Calculus

Work Done By A Variable Force (integrals)

This is what you've been waiting for: work problems with integrals. Work is a confusing topic, though, so it's highly recommended that you watch the prior two videos first. Examples: launching satellites, expanding gasses, springs, reeling up chains.

This video appears on the page: Work Done By A Force

What the heck is work?

This video is a bookend for the first one. Only this one is even better because it doesn't have numbers! Don't let that fool you, though, this video helps you figure out some of the peculiar vocabulary of work problems. Classic questions will be answered, such as "How can work be negative," and "what the heck is the difference between doing work and getting worked on, and why did I lose five points over it?"

This video appears on the page: Work Done By A Force ,Free Sample Videos ,physics free videos

Work Done By A Constant Force

Technically speaking, this video is a tad on the introductory side for Calculus, since it doesn't use any integrals. But that's kind of the point! Work is a confusing topic -- it's basically physics thrown into the middle of a math class -- so it's best if you learn how to do these more basic work problems first, before throwing crazy integrals into the mix.

This video appears on the page: Work Done By A Force

Work Done By A Force
Work Done By A Constant Force
What the heck is work?
Work Done By A Variable Force (integrals)

Work by a constant or variable force: gravity, expanding gas, friction, efficiency, power. Also fun explanations of what the heck work is, and how to figure out what these problems are even asking!

Part of the course(s): ,Physics ,Test Image Problem ,Calculus

Arc Length (using integrals)

The formula for these problems is simple, it's usually the algebra that gets you. But since there's only a few ways to contrive these problems so that the algebra (and ensuing u-sub integral) actually work out okay, once you've seen a few of these problems, you've really seen them all. These are those problems.

This video appears on the page: Arc Length & Surface Area

Area of Revolved Surfaces

The word "revolved" tends to give calc students unpleasant flashbacks to washer and shell methods, but these surface area problems aren't nearly as bad. So follow the few tricks in this video, and avoid the common mistakes I almost make, and you'll be okay.

This video appears on the page: Arc Length & Surface Area

Arc Length & Surface Area
Arc Length (using integrals)
Area of Revolved Surfaces

Using integration to find arc length of a function, or surface area of a revolved surface, on an interval.

Part of the course(s): ,Test Image Problem ,Calculus

Integration by Partial Fraction Decomposition

In this video we'll go through all the ins and outs (and rules) of using partial fractions to do integrals: linear factors, non-linear factors, repeating linear factors... All of it. If you're new to partial fractions, you might want to review the other two partial fractions videos below, but if you've seen them before this video should cover everything you need for calculus.

This video appears on the page: Integration by Partial Fraction Decomposition

Partial Fraction Decomposition
Integration by Partial Fraction Decomposition
Partial Fractions with "Non-Repeated Linear Factors"
Partial Fractions: Repeat & Non-Linear Factors

This chapter reviews partial fraction decomposition (in case you're rusty), then goes through how to use the technique to integrate some nasty rational functions.

Part of the course(s): ,Test Image Problem ,Calculus

Newton's Method of Approximating Zeros

Or roots. Or solutions. Or x-intercepts. Depending on your teacher, approximation can seem like a really confusing topic. Equations of lines, derivatives, crazy drawings and diagrams. But when it comes time to actually do the problems, it's basically just time to memorize this chart that you can plug-and-chug your way through every time.

This video appears on the page: Newton’s Method of Approximation