book

Learn Physics with Functional Programming

Name: Learn Physics with Functional Programming
Author: Scott N. Walck
ISBN: 9781718501669

by Scott N. Walck

January 2023

Intermediate to advanced

648 pages

17h 32m

English

No Starch Press

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Cover Page
Title Page
Copyright Page
Dedication
About the Author
About the Technical Reviewer
Brief Contents
Contents in Detail
ACKNOWLEDGMENTS
INTRODUCTION
Who This Book Is ForWhy Functional Programming, and Why Haskell?About This Book

PART I A HASKELL PRIMER FOR PHYSICISTS
1 CALCULATING WITH HASKELL
A Kinematics ProblemThe Interactive CompilerNumeric FunctionsOperatorsPrecedence and AssociativityThe Application OperatorFunctions with Two ArgumentsNumbers in HaskellNegative Numbers in HaskellDecimal Numbers in HaskellExponential NotationApproximate CalculationErrorsGetting Help and QuittingMore InformationSummaryExercises
2 WRITING BASIC FUNCTIONS
Constants, Functions, and TypesHow We Talk About FunctionsAnonymous FunctionsComposing FunctionsVariable Not in Scope ErrorSummaryExercises
3 TYPES AND ENTITIES
Basic TypesThe Boolean TypeThe Character TypeThe String TypeNumeric TypesFunction TypesSummaryExercises
4 DESCRIBING MOTION
Position and Velocity on an Air TrackTypes for Physical QuantitiesIntroducing DerivativesDerivatives in HaskellModeling the Car’s Position and VelocityModeling AccelerationApproximate Algorithms and Finite PrecisionSummaryExercises
5 WORKING WITH LISTS
List BasicsSelecting an Element from a ListConcatenating ListsArithmetic SequencesList TypesFunctions for Lists of NumbersWhen Not to Use a ListType VariablesType ConversionThe Length of ListsA String Is a List of CharactersList ComprehensionsInfinite ListsList Constructors and Pattern MatchingSummaryExercises
6 HIGHER-ORDER FUNCTIONS
How to Think About Functions with ParametersMapping a Function Over a ListIteration and RecursionAnonymous Higher-Order FunctionsOperators as Higher-Order FunctionsCombinatorsPredicate-Based Higher-Order FunctionsNumerical IntegrationIntroducing IntegratorsDigital IntegrationImplementing AntiderivativesSummaryExercises
7 GRAPHING FUNCTIONS
Using Library ModulesStandard Library ModulesOther Library ModulesPlottingFunction OnlyFunction and ModuleFunction, Module, and Plot DefinitionSummaryExercises
8 TYPE CLASSES
Type Classes and NumbersType Classes from the PreludeThe Eq Type ClassThe Show Type ClassThe Num Type ClassThe Integral Type ClassThe Ord Type ClassThe Fractional Type ClassThe Floating Type ClassExponentiation and Type ClassesSectionsExample of Type Classes and PlottingSummaryExercises
9 TUPLES AND TYPE CONSTRUCTORS
PairsCurrying a Function of Two VariablesTriplesComparing Lists and TuplesMaybe TypesLists of PairsTuples and List ComprehensionsType Constructors and KindsNumerical Integration ReduxSummaryExercises
10 DESCRIBING MOTION IN THREE DIMENSIONS
Three-Dimensional VectorsCoordinate-Free VectorsGeometric Definition of Vector AdditionGeometric Definition of Scaling a VectorGeometric Definition of Vector SubtractionGeometric Definition of Dot ProductGeometric Definition of Cross ProductDerivative of a Vector-Valued FunctionCoordinate SystemsVector Addition with Coordinate ComponentsVector Scaling with Coordinate ComponentsVector Subtraction with Coordinate ComponentsDot Product with Coordinate ComponentsCross Product with Coordinate ComponentsDerivative with Coordinate ComponentsKinematics in 3DDefining Position, Velocity, and AccelerationTwo Components of AccelerationProjectile MotionMaking Your Own Data TypeSingle Data ConstructorMultiple Data ConstructorsDefining a New Data Type for 3D VectorsPossible ImplementationsData Type Definition for VecVec FunctionsSummaryExercises
11 CREATING GRAPHS
Title and Axis LabelsOther LabelsPlotting DataMultiple Curves on One Set of AxesControlling the Plot RangesMaking a KeySummaryExercises
12 CREATING STAND-ALONE PROGRAMS
Using GHC to Make a Stand-Alone ProgramHello, World!A Program That Imports ModulesUsing Cabal to Make a Stand-Alone ProgramUsing Stack to Make a Stand-Alone ProgramSummaryExercises
13 CREATING 2D AND 3D ANIMATIONS
2D AnimationDisplaying a 2D PictureMaking a 2D AnimationMaking a 2D Simulation3D AnimationDisplaying a 3D PictureMaking a 3D AnimationMaking a 3D SimulationSummaryExercises
PART II EXPRESSING NEWTONIAN MECHANICS AND SOLVING PROBLEMS
14 NEWTON’S SECOND LAW AND DIFFERENTIAL EQUATIONS
Newton’s First LawNewton’s Second Law in One DimensionSecond Law with Constant ForcesSecond Law with Forces That Depend Only on TimeAir ResistanceSecond Law with Forces That Depend Only on VelocityEuler Method by HandEuler Method in HaskellThe State of a Physical SystemSecond Law with Forces That Depend on Time and VelocityMethod 1: Produce a List of StatesMethod 2: Produce a Velocity FunctionExample: Pedaling and Coasting with Air ResistanceEuler Method by HandMethod 1: Produce a List of StatesMethod 2: Produce a Velocity FunctionSummaryExercises
15 MECHANICS IN ONE DIMENSION
Introductory CodeForces That Depend on Time, Position, and VelocityA General Strategy for Solving Mechanics ProblemsSolving with Euler’s MethodProducing a List of StatesPosition and Velocity FunctionsA Damped Harmonic OscillatorEuler Method by HandMethod 1: Producing a List of StatesMethod 2: Producing Position and Velocity FunctionsEuler-Cromer MethodSolving Differential EquationsGeneralizing the State SpaceType Classes for State SpacesOne More Numerical MethodComparison of Numerical MethodsSummaryExercises
16 MECHANICS IN THREE DIMENSIONS
Introductory CodeNewton’s Second Law in Three DimensionsThe State of One ParticleSolving Newton’s Second LawOne-Body ForcesEarth Surface GravityGravity Produced by the SunAir ResistanceWind ForceForce from Uniform Electric and Magnetic FieldsState Update for One ParticlePreparing for AnimationTwo Helpful Animation FunctionsHow the Functions WorkSummaryExercises
17 SATELLITE, PROJECTILE, AND PROTON MOTION
Satellite MotionState-Update FunctionInitial StateTime-Scale FactorAnimation RateDisplay FunctionProjectile Motion with Air ResistanceCalculating a TrajectoryFinding the Angle for Maximum Range2D Animation3D AnimationProton in a Magnetic FieldSummaryExercises
18 A VERY SHORT PRIMER ON RELATIVITY
A Little TheoryA Replacement for Newton’s Second LawResponse to a Constant ForceProton in a Magnetic FieldSummaryExercises
19 INTERACTING PARTICLES
Newton’s Third LawTwo-Body ForcesUniversal GravityConstant Repulsive ForceLinear SpringCentral ForceElastic Billiard InteractionInternal and External ForcesThe State of a Multi-Particle SystemState Update for Multiple ParticlesImplementing Newton’s Second LawNumerical Methods for Multiple ParticlesComposite FunctionsSummaryExercises
20 SPRINGS, BILLIARD BALLS, AND A GUITAR STRING
Introductory CodeTwo Masses and Two SpringsForcesAnimation FunctionsStand-Alone Animation ProgramUsing Mechanical Energy as a Guide to Numerical AccuracyA CollisionData RepresentationsSpring Constant and Time StepMomentum and Energy ConservationNumerical IssuesAnimated ResultsWave on a Guitar StringForcesState-Update FunctionInitial StateStand-Alone ProgramAsynchronous AnimationSummaryExercises
PART III EXPRESSING ELECTROMAGNETIC THEORY AND SOLVING PROBLEMS
21 ELECTRICITY
Electric ChargeCoulomb’s LawTwo Charges InteractingLooking at ExtremesModeling the Situation in HaskellSummaryExercises
22 COORDINATE SYSTEMS AND FIELDS
Polar CoordinatesCylindrical CoordinatesSpherical CoordinatesIntroductory CodeA Type for PositionDefining the New TypeMaking a PositionUsing a PositionDisplacementThe Scalar FieldThe Vector FieldFunctions for Visualizing Scalar Fields3D Visualization2D VisualizationFunctions for Visualizing Vector Fields3D Visualization2D VisualizationGradient VisualizationSummaryExercises
23 CURVES, SURFACES, AND VOLUMES
Introductory CodeCurvesParameterizing CurvesExamples of CurvesSurfacesParameterizing SurfacesExamples of SurfacesOrientationVolumesSummaryExercises
24 ELECTRIC CHARGE
Charge DistributionsIntroductory CodeA Type for Charge DistributionExamples of Charge DistributionsTotal ChargeTotal Charge of a Line ChargeTotal Charge of a Surface ChargeTotal Charge of a Volume ChargeCalculating Total Charge in HaskellElectric Dipole MomentSummaryExercises
25 ELECTRIC FIELD
What Is an Electric Field?Introductory CodeCharge Creates an Electric FieldElectric Field Created by a Point ChargeElectric Field Created by Multiple ChargesElectric Field Created by a Line ChargeElectric Field Created by a Surface ChargeElectric Field Created by a Volume ChargeScalar IntegralsScalar Line IntegralScalar Surface IntegralScalar Volume IntegralApproximating Curves, Surfaces, and VolumesApproximating a CurveApproximating a SurfaceApproximating a VolumeSummaryExercises
26 ELECTRIC CURRENT
Current DistributionsIntroductory CodeA Type for Current DistributionExamples of Current DistributionsConservation of Charge and Constraints on Steady Current DistributionsMagnetic Dipole MomentSummaryExercises
27 MAGNETIC FIELD
A Simple Magnetic EffectIntroductory CodeCurrent Creates Magnetic FieldMagnetic Field Created by a Line CurrentMagnetic Field Created by a Surface CurrentMagnetic Field Created by a Volume CurrentSummaryExercises
28 THE LORENTZ FORCE LAW
Introductory CodeStatics and DynamicsState of One Particle and FieldsLorentz Force LawDo We Really Need an Electric Field?State UpdateAnimating a Particle in Electric and Magnetic FieldsUniform FieldsClassical HydrogenSummaryExercises
29 THE MAXWELL EQUATIONS
Introductory CodeThe Maxwell EquationsRelationships Between Electricity and MagnetismConnection to Coulomb’s Law and Biot-Savart LawState UpdateSpatial Derivatives and the CurlA Naive MethodThe FDTD MethodThe Yee CellA Type for StateFDTD and the CurlState UpdateAnimationCurrent DensityGrid BoundaryDisplay FunctionTwo Helping FunctionsMain ProgramSummaryExercises
APPENDIX: INSTALLING HASKELL
Installing GHCInstalling a Text EditorInstalling GnuplotInstalling Haskell Library PackagesUsing CabalUsing StackInstalling GlossInstalling DiagramsSetting Up Your Coding EnvironmentWhat We Want in a Coding EnvironmentAll Code in One DirectoryOne Way to Use StackSummary
BIBLIOGRAPHY
INDEX

Content preview from Learn Physics with Functional Programming

15MECHANICS IN ONE DIMENSION

In this chapter, we’ll complete the story of mechanics in one dimension by developing tools for situations in which the forces on an object can depend on position as well as on time and velocity. This will require thinking about second-order differential equations, which we’ll convert into systems of first-order differential equations.

As before, we’ll transform information about the physical situation through several different forms, beginning with the object’s mass and the forces that act on it, and ending with functions that give the position and velocity of the object with time. A functional language like Haskell ...

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Learn Physics with Functional Programming

by Scott N. Walck

15MECHANICS IN ONE DIMENSION

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.