Table Of Content

Maple A primer Maple A primer Bernard V Liengme St Francis Xavier University, Antigonish, Canada Morgan & Claypool Publishers Copyrightª2019Morgan&ClaypoolPublishers Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem ortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recording orotherwise,withoutthepriorpermissionofthepublisher,orasexpresslypermittedbylawor undertermsagreedwiththeappropriaterightsorganization.Multiplecopyingispermittedin accordancewiththetermsoflicencesissuedbytheCopyrightLicensingAgency,theCopyright ClearanceCentreandotherreproductionrightsorganizations. Rights&Permissions Toobtainpermissiontore-usecopyrightedmaterialfromMorgan&ClaypoolPublishers,please [email protected]. Supplementarymaterialtoaccompanythisbookisavailableathttp://iopscience.iop.org/book/ 978-1-64327-488-1. ISBN 978-1-64327-488-1(ebook) ISBN 978-1-64327-485-0(print) ISBN 978-1-64327-486-7(mobi) DOI 10.1088/2053-2571/ab0bb3 Version:20190501 IOPConcisePhysics ISSN2053-2571(online) ISSN2054-7307(print) AMorgan&ClaypoolpublicationaspartofIOPConcisePhysics PublishedbyMorgan&ClaypoolPublishers,1210FifthAvenue,Suite250,SanRafael,CA, 94901,USA IOPPublishing,TempleCircus,TempleWay,BristolBS16HG,UK To Pauline, my wonderful wife, friend and critic. Contents Preface xi Author biography xiii 1 Starting Maple 1-1 1.1 What is Maple? 1-1 1.2 The Maple interface 1-1 1.3 Entering simple expressions 1-3 1.4 The use of evalf[d](term) 1-7 1.5 Some handy algebraic commands 1-8 1.6 Context menus 1-10 1.7 Formatted output with printf 1-12 1.8 Data structures 1-13 1.9 Defining a function 1-17 1.10 Debugging a worksheet 1-18 2 Introductory examples 2-1 2.1 Ammonia 2-1 2.2 Water pump 2-1 2.3 Telescope resolution 2-1 2.4 Velocity of a bullet 2-3 2.5 Solve puzzle 2-3 2.6 Vertex form 2-4 2.7 Classic inclined plane problem 2-7 2.8 Baseball problem 2-8 2.9 Center of mass 2-9 2.10 Trough problem 2-13 3 Plotting with Maple 3-1 3.1 Starting with plot 3-1 3.2 Plot tools 3-1 3.3 Customizing with the context menu 3-3 3.4 Customizing a plot with parameters 3-4 3.5 A logarithmic plot 3-7 3.6 Using display for multifunction plots 3-7 3.7 Two plots side by side 3-8 vii Maple 3.8 Plotting a family of curves 3-9 3.9 Plotting digitalized data 3-9 3.10 Parametric plots 3-9 3.11 Using the coords = polar option 3-12 3.12 Implicit plots 3-14 3.13 Animated plots 3-18 3.14 Exploring with the Explore command 3-18 3.15 Plot with two axes 3-20 3.16 Three-dimensional plots 3-20 4 Solving equations and systems of equations 4-1 4.1 The solve command 4-1 4.2 Solving inequalities 4-3 4.3 Stress analysis 4-4 4.4 The assign command 4-5 4.5 The fsolve command 4-6 4.6 Systems of equations with fsolve 4-8 4.7 Finding complex roots 4-8 4.8 Restricting the root to a range 4-11 4.9 Example of using isolve 4-14 4.10 Off to Mars 4-15 5 Using units and physical constants 5-1 5.1 Some basic examples 5-1 5.2 Examples of usage 5-1 5.3 Using the Units command 5-3 5.4 Temperature conversions 5-4 5.5 Physical constants 5-7 5.6 Gravity constants G and g 5-7 5.7 Pump problem revisited 5-8 6 Linear algebra 6-1 6.1 Matrices and vectors 6-1 6.2 Simple matrix and vector math 6-2 6.3 Linear algebra 6-2 6.4 Solving a system of equations 6-2 viii Maple 6.5 Introduction to eigenvectors and eigenvalues 6-8 6.6 Notes on Maple vector commands 6-13 6.7 Some vector calculations 6-14 7 Introduction to calculus 7-1 7.1 Looking for the limit 7-1 7.2 Some differentiation examples 7-1 7.3 The D operator 7-5 7.4 Implicit differentiation 7-5 7.5 Examples of critical points 7-5 7.6 Some integration examples 7-6 7.7 Definite integrals 7-7 7.8 The assume command 7-8 7.9 Finding the area between two curves 7-9 7.10 Introduction to ODEs 7-10 8 Differential equations 8-1 8.1 Initial value problems (IVPs) 8-1 8.2 Entering ODEs and initial/boundary conditions 8-1 8.3 Boundary value problems (BVPs) 8-2 8.4 Family of solutions 8-4 8.5 Numerical integration 8-4 8.6 The simple pendulum 8-7 8.7 Coupled ODEs 8-10 8.8 Singular and general solutions 8-12 8.9 Direction fields 8-13 9 Procedures 9-1 9.1 Programming structures 9-1 9.2 Simple examples 9-2 9.3 Procedures 9-2 9.4 Several ways to find the GCD 9-4 9.5 Further procedure examples 9-5 9.6 Fourier expansion 9-10 9.7 Common errors in procedures 9-10 ix