calc 3 - EICC - spring 2017
A selection of resources to accompany a calc 3 course using Thomas's Calculus 13ed. Some by me. Others borrowed / copied / modified by the kind people who are better at geogebra than I. Thanks.
Table of Contents
- ch. 12 - vectors & geometry of space
- 12.1 Three Dimensional Coordinate System
- calc 3 - 12.1 - 3d graphs
- calc 3 - ex 12.4.3
- 12.5.8 - find line of intersection of two planes
- ch. 13 - vector valued functions & motion in space
- calc 3 - openstax - parametric curves in space
- calc 3 - openstax - some helices
- 13.1 - ex 3 - discontinuous vector fu…
- calc 3 - openstax - derivatives of vector valued functions - tangent vector
- calc 3 - Tangent Velocity Vectors
- calc 3 - vector functions of constant length
- 13.4 - Normal Vector to Tangent Vector
- calc 3 - TNB Frame
- ch. 14 - Partial Derivatives
- Intro to Functions in Several Variables
- Domains of Functions in Two Variables
- Visualizing level curves
- Limits of Multivariable Functions
- Limits that Do Not Exist at Origin
- Directional Derivative
- ch. 15 - Multiple Integrals
- Riemann Sums of a Double Integral
- double integral as Volume
- Triple Integrals - an example to start
- Triple Integral in rectangula…
- Triple Integral Cylindrical C…
- Triple Integral Spherical Coo…
- ch. 16 - Integrals and Vector Fields
- Arc length & Area of fence
12.1 Three Dimensional Coordinate System
Introducing Three Dimensions!
Remember [i][math](x,y)[/math][/i]? We're great at working in the [math]xy[/math]-"[b]plane[/b]". But what about [math]\left(x,y,z\right)[/math]? We could think of this as working in an [math]xyz[/math]-"[b]space[/b]".[br][br]We're used to working with functions with one input and [i]only [/i]one output. Typically, we think of our [i][math]x[/math][/i]-value as our input ([math]x[/math]-axis), and our [i][math]y[/math][/i]-value as our output ([math]y=f\left(x\right)[/math]-axis).[br][br]We're entering into multi-variable calculus. Multi-variable can mean lots of things, which we'll get into later, but first we should develop a good grasp on the three-dimensional coordinate system. Enter:[br][center][i][math](x,y,z)[/math][/i][/center]Three variables can be thought of as a three dimensional [b][i]space[/i][/b], just like [math]\left(x,y\right)[/math] can be thought of as a [i][b]plane[/b][/i]. Where each of the coordinates tell us how far to move in the direction parallel to the respective axis. Which brings us to the right hand rule, and an explanation of the axes.[br][br]We will follow the generally accepted convention of thinking of the [math]z[/math]-axis as being vertical, with the [math]x[/math]- and [math]y[/math]-axes being parallel to the ground. [br][br]You might be wondering, how do we determine the orientation of the [math]x[/math]- and [math]y[/math]-axes? Good question: the right hand rule. (us left handed shmucks are out of luck). Draw an imaginary set of axes directly under your [i]right[/i] hand with its thumb up. Then think of wrapping your finders around a vertical [math]z[/math]-axis, keeping your thumb up. Your fingers will sweep across first the [i][b]positive[/b][/i] [math]x[/math]-axis, and then [math]y[/math]-axis in a counter clockwise rotation. (<----math's favorite direction! You may need to rotate the entire set of axes to align the positive [math]x[/math]- and [math]y[/math]-axes to directly in front of your view point)
calc 3 - openstax - parametric curves in space
Instructions
To explore the 4 different space curves defined:[br][br]First click the "play" icon on the t_tmax slider.[br][br]Then select the function (q,r,p, or h) you'd like to see, as well as the related vector that generates the points on the curve (v_p, v_r, v_p, or v_h).