TCPS 04 Calculus Applied Mathematics Projects Math Fest

TCPS 04 – Calculus Applied Mathematics Projects Math. Fest 2016 Columbus OH Franklin A - 1: 40 -1: 50 PM - 4 August 2016 Complex Technology-Based Problems in Calculus www. rose-hulman. edu/Class/Calculus. Probs/ Brian Winkel, Emeritus Math. Sci US Military Academy, West Point NY USA Director SIMIODE and Founding Editor of PRIMUS

An aside MAA Mini. Course Math. Fest 2016 Columbus OH Begins Later today! 3: 30 – 5: 30 PM - 4 August 2016 Taft D 1: 00 – 3: 00 PM - 6 August 2016 Taft D Teaching Modeling First Differential Equations Building Community in SIMIODE Walk in. . . not too late to join us.

www. SIMIODE. org

www. SIMIODE. org

Back to calculus. . . What we're all about: Source for complex, technology-based problems in calculus with applications in science and engineering. These problems have a higher level of complexity than traditional text book problems and foster use of a computer algebra system. Each problem set includes discussions of related teaching issues and solutions worked in Mathematica.

Each problem is provided in three formats: Mathematica notebook in HTML format with figures translated to GIF files. This is readable by any standard WWW viewer. Mathematica notebook. Text as ASCII. This contains all the text of statement of problem, comments and solutions.

How to search: By category: Choose from categories that best describe the problem type desired. Full text word search: All problems with the string you enter will be listed. Keyword search: All problems come with a list of key words provided by the author(s). Alphabetically: If you know the file name for a problem set, you can find it in alphabetical order

The production of this material was supported by the National Science Foundation under Division of Undergraduate Education grant DUE 9352849. Thank you Liz Teles of NSF. 1993 -1994 Co-directed by Aaron Klebanoff and Brian Winkel, Math. Sci, and Jerry Fine, Mechanical Engineering, Rose-Hulman Institute of Technology, Terre Haute IN Assisted by many creative high school mathematics teachers in Indiana.

Anti-Differentiation ANTDIG Model for the time it takes an ant to build a tunnel. We employ the derivative and antiderivative to model the time T(x) it takes an ant to dig a tunnel of length x. This is a paper and pencil activity and does not need technology.

Data Fitting POPRANK Population Rank Modelling. Fitting a function to the population vs. rank data for major cities in a region and conjecturing (1) how this function changes over time and (2) how plots for different societies, e. g. rural, industrial, compare. Urban and Agrarian Few or many large cities

Data Fitting ROCKRAMA Data analysis through mathematical model of data collected from a "rock" experiment. An experiment in data collection and analysis is described in which collective groups of subjects are analyzed as to their abilities to differentiate masses of rocks. A reasonable sigmoidal function is needed to sit the data and comparisons between groups of subjects leads to fun discussion as to which group is better. Students determine criterion for best, e. g. , steepest slope at inflection point. Perfect knowledge Random guessing

Data Fitting SOUNDBITE Sound Bite length for Presidential Election - Predictions. Over time the average length of uninterrupted speech offered by a Presidential candidate on the evening news has decreased. Where is the average length of these sound bites headed? We take data from a New York Times article and see if politicians are doomed to a "Yup!" "Nope!" soundbite in the future and if so when?

Data Fitting OILSLICK Modeling an Oil Slick Growth. Can we use differenced data taken at unknown starting times to ascertain the size of a growing oil slick? Either difference or differential equation models will permit discovery if student are willing to plot and do some differencing. Argh!!!! What can we plot?

Data Fitting OILSLICK Modeling an Oil Slick Growth. Can we use differenced data taken at unknown starting times to ascertain the size of a growing oil slick? Either difference or differential equation models will permit discovery if student are willing to plot and do some differencing.

Data Fitting OILSLICK Modeling an Oil Slick Growth. Can we use differenced data taken at unknown starting times to ascertain the size of a growing oil slick? Either difference or differential equation models will permit discovery if student are willing to plot and do some differencing.

Data Fitting OILSLICK Modeling an Oil Slick Growth. Can we use differenced data taken at unknown starting times to ascertain the size of a growing oil slick? Either difference or differential equation models will permit discovery if student are willing to plot and do some differencing.

Integration BREADCUT How to cut a hemispherical loaf of French bread so that each of 8 guests gets the same amount of crust. The claim is that by slicing parallel sections of equal altitudes from a sphere we get identical surface areas of these sections. The problem is posed in terms of equity of crust distribution for French bread.

Motion BALLPARK Designing a Fair Ballpark. Some ball parks favor right hand hitters over left (and possibly vice versa. ) This problem is concerned with the how to build the outfield fence (height) so that the ball park isn't biased for any directions. This is an involved problem accessible to students of projectile motion.

Motion CANNON Shooting a Cannonball Over a Wall. We present problems related to shooting a cannonball over a mountain to hit a target with a minimum velocity. Two dimensional projectile motion is appropriate Motion DEEPWELL How deep is a well -- using sound of falling body striking the bottom of the well? We drop a small stone in a deep well. Given the time elapsed from release until we hear the splash determine the depth of the well.

Motion RODYOKE Relative Motion of Rod and Yoke. We seek to render parametric equations which describe the tip of a rod sitting astride a moving, circular-headed, piston, given the rules of motion of the piston.

Optimization CAMPFIRE Put out the Camp Fire. This Oldie is a nice introductory calculus problem: find the shortest path from your car to a camp fire if you have to stop at the river bank to get water on the way. Next, find the shortest travel time (and corresponding route) possible given that you can walk faster without water than with it. NOTE USAFA Approach! ALWAYS minimize the time over enemy territory, not total time!

Optimization GEOTIME Using Sound to Determine Subsurface Geological Structure. We determine the flow of soundwaves in an underground sonic boom through various media and we attempt to determine the shape of the underlying region given timings on soundwave propagation.

Optimization MALLED Getting Malled - Determining the geographical region for which travel to a mall is one hour or less given a road configuration. Determine the one hour driving neighborhood about a shopping mall when a high speed highway is put in place. Optimization of a function of one variable will help.

Optimization RAMPOUT Maximum Horizontal Bounce Distance of Ball Bouncing On Inclined Ramp. Drop a ball on an inclined ramp from a fixed height. Of all the angles you can incline the ramp which permits the ball to bounce OUT the farthest.

Parameter Estimation CHEMOPT Reaction chemistry, parameter estimation, and optimization. After modeling a chemical reaction A->B->C with a set of linear, first-order differential equations we estimate kinetic parameters through a number of methods and determine the run time for the reaction which will optimize a financial return on the reaction.

Visualization OVERVIEW What we can see on one hill from a nearby hill. We ask readers to place their eye on one mountain and (1) describe what they can see, (2) how much surface area they can see, and (3) nearest point - all relative to a nearby mountain. Invent partial derivatives, tangent plane, gradient, and later elements of surface area.

Guiding Philosophy Teach mathematics in context. Relate the mathematics to areas of interest and other fields students study. Motivate, develop curiosity, empower students to invent. Use technology regularly as part of problem solving toolkit. Increase the complexity and draw them in – gives confidence. Practice transferability of the mathematics they learn.

Complex Technology-Based Problems in Calculus www. rose-hulman. edu/Class/Calculus. Probs/ Brian Winkel, Emeritus Math. Sci US Military Academy, West Point NY USA Brian@simiode. org Director SIMIODE www. simiode. org

Thank you for your time and attention. Questions? Comments?