CS123 Engineering Computation Lab Lab 1 Bruce Char Department of Computer Science Drexel University Spring 2013

Welcome Back to CS123 Goals and objectives for this term – by the end of this term, students should be able to : Use Maple’s Optimization feature to solve differential calculus problems involving maximum and minimum (optimal) solutions Use Maple’s piecewise function feature to define functions that vary across the range of the independent variable Develop data fitting correlations using Maple’s Spline curve fitting algorithm More fully develop code scripts and programs using Maple’s “procedure” (proc) feature, including additional creation of time step simulations Develop user interfaces from Maple’s Components palette

CS123 – Basic Schedule 4 labs in even numbered weeks (2, 4, 6 and 8) 4 quizzes in odd numbered weeks (3, 5, 7 and 9) 4 pre-lab quizlets in weeks (1, 3, 5 and 7) Proficiency Exam in week 10 Flow of course similar to cs121 and cs122 Be sure to review contents of course web site for details

What’s Included in CS123? Extra consultation activity Intended for students who struggled with the quizzes and proficiency exam in cs122 Goal of 1or 2 sections 4 sessions to be held on Tuesday evenings following lab week (weeks 3, 5, 7 and 9) 6 to 7:50 PM *** Monday session will be added if attendance warrants Focus on problem solving and Maple exercises to enable enhanced performance in quizzes A 3 point bonus will be awarded to all students who attend all 4 sessions To enroll, please contact Dave Augenblick at 1 st session  Tuesday, April 16 th (+ perhaps Monday, 4/15)

Administrative Notes Please contact your individual instructors with questions and problems CLC (room 147 UC) will be staffed at same times as for cs122 in Winter (odd weeks – starting week 3) Note that CLC is staffed on Monday through Friday (9 AM to 5 PM) Missed work policies – same as in cs121 and cs122 Makeup labs to be held on Monday at 6 PM (odd weeks). Must receive explicit approval from your instructor in order to attend! Makeup quiz offered (30% penalty) – Friday through Sunday after completion of regular quiz No excused quizzes due to MapleTA login issues – please resolve any such issues immediately All MapleTA login accounts have been (re) set to your Drexel id (ID) and 8 digit student number (password) No makeup quizlets No bbLearn Discussion Board monitoring this term

Lab 1 Overview Based on materials from Chapters 16 and 17 Chapter 16 – Calculus and Optimization Develop an objective function for the minimum surface area of a can and find optimal dimensions (radius and height) using Maple’s Optimization feature Chapter 17 – more Maple support for mathematical modeling Solving integration problems – finding the surface area of an irregularly shaped object Piecewise expressions – irregularly shaped curve consisting of a series of “piecewise” expressions Curve fitting using Splines – generating spline curves of various degrees to connect a series of data points

Lab 1 Overview Lab 1 outline Part 0 – practice with Maple mechanics for Optimization, piecewise expressions, integration and differentiation, Spline curve fitting Part 1 – Find the minimum dimensions of a can that holds a specified volume of liquid using Maple’s Optimization function Create an expression for the can’s surface area (objective function) to hold a constant volume of liquid Use the Maple Optimization function to find the minimum dimensions (radius and height) for the surface area Part 2 – finding the surface area of an irregularly shaped machine part Define top of object in terms of a series of piecewise expressions Bottom = a single expression Plot top, bottom expressions  shape of object Integrate (top – bottom)  area between curves

Lab 1 Overview Lab 1 outline Part 3 – Spline curve fitting to analyze the power of a baseball bat swing Given a table of times (seconds) versus power (hp), create and plot spline curves of degrees 1 through 4 Answer questions using the results of the spline plots Notes: B. total energy transferred is the integral of the power curve C. point of maximum power increase – take derivative of power curve and then find maximum (optimization)

Lab 1 Overview New lab description format for Lab 1 –Basic lab description document in form of a shell, directing you to starter scripts for each of 4 parts (Part 0, 1, 2 and 3) –Each starter script consists of text directions for completing that part –Maple statements and results to be generated at various points within starter scripts Mix of text and math modes

Lab 1 Maple Concepts: Discussion and Demo Part 1 – Maple’s Optimization feature Creating the Objective function (surface area of a can) Surface area = lateral area + top and bottom SA = 2*Pi*r*h + 2*Pi*r^2 Since the surface area needs to be a function of a single variable (eg. radius=r), we need to find an function relating h (height) to r and substitute. Since the volume is constant at 1000: 1000 = Pi*r^2*h  h = 1000 / (pi*r^2) Substitute this equation for h into the SA equation above to obtain the objective function SA(r).

Lab 1 Maple Concepts: Discussion and Demo Part 1 – Maple’s Optimization feature - continued Now use this objective expression SA(r) to find the minimum surface area over a range of radii that holds a volume = 1000 minRslt:=Optimization[ Minimize](objexpression,r=1..10) You will obtain 2 results minRslt[1]  minimum surface area minRslt[2]  radius that produces this minimum SA Substitute minRslt[2] into the equation for h to obtain the associated height Note Optimize[Minimize](objexp,x=a..b) → produces set of approximate results Minimize(objexp,a=a..b, location) → produces set of exact results

Lab 1 Maple Concepts: Discussion and Demo Part 2 – Area between 2 curves Piecewise expressions Use clickable interface as opposed to textual I/F To add more than 2 piecewise expressions Ctrl-Shift-R (PC) (Command=Shift-R for Mac) Be sure to highlight each area and type over it (not as “free-form” as you would like) – see demo “otherwise” condition – can use to denote all other values not defined in piecewise expressions Be sure to assign the piecewise expression a name → top := “piecewise expression” Integration Indefinite integral  int(f(x),x)  generates function in terms of x Definite integral  int(f(x),x=a..b)  numeric result Differentiation → result := diff(somefunction, x);

Lab 1 Maple Concepts: Discussion and Demo Problem 3 – analysis of batter’s swing Plot_structure:=CurveFitting[Spline](x values, y values, name for independent variable, degree=degree of Spline fit) Or, can use with(CurveFitting); Spline( ); Ex. CurveFitting[Spline](T,P,t,degree=3) Will produce a Spline curve fit using cubic piecewise expressions Some Spline details Curve passes through all points (note that linear least squares curve fit produces a “best straight line estimate” for all points, and may possibly not pass through any point) A piecewise expression will be generated to connect each pair of adjacent points

Lab 1 – Maple Part 0 Exercises 1. Maple optimization logistics 2. Piecewise expression and integration 3. More on integration and differentiation 4. Curve fitting with Splines

Quiz Week (3) Activities Quiz 1 will be released on Friday (4/13) at 6 PM Deadline: Thursday (4/19) at 4:30 PM Makeup quiz – from Friday (4/20) at 9 AM through Sunday (4/22) at 11:00 PM 30% penalty Pre-lab 2 quizlet From Thursday (4/19 – noon) through Monday (4/23 – 8 AM) Be sure to visit the CLC for quiz or general Maple assistance Be sure to register for extra consultation initiative if interested