### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Calculus III MATH 113

GPA 3.7

### View Full Document

## 20

## 0

## Popular in Course

## Popular in Mathematics (M)

This 6 page Class Notes was uploaded by Maximilian Turcotte on Monday October 5, 2015. The Class Notes belongs to MATH 113 at Colgate University taught by Staff in Fall. Since its upload, it has received 20 views. For similar materials see /class/219592/math-113-colgate-university in Mathematics (M) at Colgate University.

## Reviews for Calculus III

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/05/15

Contour Plots Math 113 7 This Maple session gives some examples of creating contour plots i First load the quotplotsquot library gt withplots De ne an expression to hold fxy We39ll do a contour plot for fxy x 22yA2 gt f x 2 2y 2 f x2 2 y2 The contourplot command creates a contour plot The first argument is the function the second and third arguments are the x and y ranges respectively 7 gt contourplotfxl lyl After the first three arguments you can include many optional arguments The following are just a small sample You can specify the exact number of contours to draw with quotcontoursNquot replace N with the number The default is 8 OR you can specify the actual contour values to be used to create the contour lines with quotcontoursz122znquot For example the option c0nt0urs005115225 would create a contour plot with the six given contour values You can change the color of the contour lines for example quotcolorgreenquot You can force the plot to use the same scaling on the x and y axes so a circle really looks like a circle with quotscalingconstrainedquot Ifthe curves in the contour plot look jagged you can increase the resolution with the option quotgridNxNy quot where you replace Nx and Ny with integers that give the x and y resolutions The default is 2525 7 Here are some examples that use these options 7 gt contourplot fx l ly l l contours21 colorblue scalingconst rained gt g xA2yA2yA3 2 2 3 g3x y y contourplot gxl lyl lcontours 04 0200204 grid 4141 scalingconstrained V Maw m 52 6mm 9nltlcc mums Salu b ws Fau oJ 3 ke 39gkej f Plotting Surfaces with Grapher Warren Weekesser September 9 2005 These brief notes explain how to plot surfaces with Grapher an application that is avail able on the computers in the Computer Lab Plotting the graph of z ay H F 9 4 U 03 Start Grapher by clicking on the Grapher icon A window with the title New Graph will appear Click on 3D Graph7 then click on Open A larger window with the title Untitled will appear There will be an empty set of yellow axes visible Above the axes is an area where you can de ne your equation It will initially contain 2 You can type your function here After 2 enter7 for example7 x 7 2y x 2yz When you hit Enter7 the graph will be drawn with a light and dark green checkerboard pattern Note When you type the rst opening parenthesis7 the program automatically adds the closing parenthesis7 and puts the cursor inside them You can use the right arrow key to move out of the parentheses The surface will looked stretched out77 vertically A quick way to see a nicer view is to click on Zoom In two or three times Note This plot is an example of a monkey saddle Move the mouse into the plotting region7 and click and drag on the plot to change the point of view Optional but possibly useful We can control the view more precisely by changing the Frame Limits In the menu bar at the top of the screen7 select View7 and then Frame Limits In the small window that pops up7 you can set the L y and z limits of the plot Change the z and y lower and upper limits to be7 say7 71 and 17 respectively7 and change the z limits to be 72 and 2 Click on OK or just hit Enter 7 00 Plotting implicitly de ned surfaces Grapher can show the contour lines of this function In the menu bar at the top of the screen7 select Window7 and then Show Inspector The small window that appears allows you to change several aspects of the plot In particular7 click on the check box next to Contours This will add contour lines in the surface These are the curves where horizontal planes intersect the surface If you then rotate the surface so that you are looking straight down the z axis7 you will see the contour diagram Click on the small left most circle in the title bar of the Inspector window to close it Experiment with other functions For example7 try the function from the quiz 2 xyz While you are at it7 experiment with other options in the Inspector window Explore other features of the program Have fun Grapher can handle surfaces de ned implicitly For example7 the equation of a sphere of radius 2 centered at the origin is 1 E0 00 x2y2224 Enter the equation of the sphere in the eld above the plot You can rst delete anything that is already there7 including 2 Note Depending on your current Frame Limits7 you may rst have to click on Zoom Out a few times to see the sphere The sphere that you see is not perfectly smooth It is faceted7 and looks a bit like a golf ball The plot generated by the computer is only an approximation7 in which the smooth surface is approximated with many small at surfaces You can control resolution of the approximation Select Window and Show Inspector ifthe Inspector window is not already visible7 and in the section labeled Implicit Graph7 move the blue sliders next to Abscissa Ordinate and Height to the right Then click on the black circular arrow to regenerate the plot It may take a few seconds7 but eventually the surface will be redrawn7 and the facets will be smaller Experiment with other implicitly de ned surfaces For example7 try this one xz37222xy71 Use L y and 2 frame limits of 73 and 3 Then change 722 to 22 and observe how the surface changes Make up your own formulas Go nuts

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "I bought an awesome study guide, which helped me get an A in my Math 34B class this quarter!"

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.