book

Applying Math with Python

Name: Applying Math with Python
Author: Sam Morley
ISBN: 9781838989750

by Sam Morley

July 2020

Intermediate to advanced

358 pages

8h 23m

English

Packt Publishing

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Title Page
Copyright and Credits
Applying Math with Python
Dedication
About Packt
Why subscribe?
Contributors
About the authorAbout the reviewersPackt is searching for authors like you
Preface
Who this book is forWhat this book coversTo get the most out of this bookDownload the example code filesCode in ActionConventions usedSectionsGetting readyHow to do it…How it works…There's more…See alsoGet in touchReviews
Basic Packages, Functions, and Concepts
Technical requirementsPython numerical typesDecimal typeFraction typeComplex typeBasic mathematical functionsNumPy arraysElement accessArray arithmetic and functionsUseful array creation routinesHigher dimensional arraysMatricesBasic methods and propertiesMatrix multiplicationDeterminants and inversesSystems of equationsEigenvalues and eigenvectorsSparse matricesSummary Further reading
Mathematical Plotting with Matplotlib
Technical requirementsBasic plotting with MatplotlibGetting readyHow to do it...How it works...There's more...Changing the plotting styleGetting readyHow to do it...How it works...There's more...Adding labels and legends to plotsHow to do it...How it works...Adding subplotsGetting readyHow to do it...How it works...There's more...See alsoSaving Matplotlib figuresGetting readyHow to do it...How it works...There's more...See alsoSurface and contour plotsGetting readyHow to do it...How it works...There's more...Customizing three-dimensional plotsGetting readyHow to do it...How it works...There's more...Further reading
Calculus and Differential Equations
Technical requirementsWorking with polynomials and calculusGetting readyHow to do it...How it works...There's more...See alsoDifferentiating and integrating symbolically using SymPyGetting readyHow to do it...How it works...There's more...Solving equationsGetting readyHow to do it...How it works...There's more...Integrating functions numerically using SciPyGetting readyHow to do it...How it works...There's more...Solving simple differential equations numericallyGetting readyHow to do it...How it works...There's more...See alsoSolving systems of differential equationsGetting readyHow to do it...How it works...There's more...Solving partial differential equations numericallyGetting readyHow to do it...How it works...There's more...See alsoUsing discrete Fourier transforms for signal processingGetting readyHow to do it...How it works...There's more...See alsoFurther reading
Working with Randomness and Probability
Technical requirementsSelecting items at randomGetting readyHow to do it...How it works...There's more...Generating random dataGetting readyHow to do it...How it works...There's more...Changing the random number generatorGetting readyHow to do it...How it works...There's more...Generating normally distributed random numbersGetting readyHow to do it...How it works...There's more...Working with random processesGetting readyHow to do it...How it works...There's more...Analyzing conversion rates with Bayesian techniquesGetting readyHow to do it...How it works...There's more...Estimating parameters with Monte Carlo simulationsGetting readyHow to do it...How it works...There's more...See alsoFurther reading

Working with Trees and Networks
Technical requirementsCreating networks in PythonGetting readyHow to do it...How it works...There's more...Visualizing networksGetting readyHow to do it...How it works...There's more...Getting the basic characteristics of networksGetting readyHow to do it...How it works...There's more...Generating the adjacency matrix for a networkGetting readyHow to do it...How it works...There's more...Creating directed and weighted networksGetting readyHow to do it...How it works...There's more...Finding the shortest paths in a networkGetting readyHow to do it...How it works...There's more...Quantifying clustering in a networkGetting readyHow to do it...How it works...There's more...Coloring a networkGetting readyHow to do it...How it works...There's more...Finding minimal spanning trees and dominating setsGetting readyHow to do it...How it works...Further reading
Working with Data and Statistics
Technical requirementsCreating Series and DataFrame objectsGetting readyHow to do it...How it works...There's more...See alsoLoading and storing data from a DataFrameGetting readyHow to do it...How it works...See alsoManipulating data in DataFramesGetting readyHow to do it...How it works...There's more...Plotting data from a DataFrameGetting readyHow to do it...How it works...There's more...Getting descriptive statistics from a DataFrameGetting readyHow to do it...How it works...There's more...Understanding a population using samplingGetting readyHow to do it...How it works...See alsoTesting hypotheses using t-testsGetting readyHow to do it...How it works...There's more...Testing hypotheses using ANOVAGetting readyHow to do it...How it works...There's more...Testing hypotheses for non-parametric dataGetting readyHow to do it...How it works...Creating interactive plots with BokehGetting readyHow to do it...How it works...There's more...Further reading
Regression and Forecasting
Technical requirementsUsing basic linear regressionGetting readyHow to do it...How it works...There's more...Using multilinear regressionGetting readyHow to do it...How it works...Classifying using logarithmic regressionGetting readyHow to do it...How it works...There's more...Modeling time series data with ARMAGetting readyHow to do it...How it works...There's more...Forecasting from time series data using ARIMAGetting readyHow to do it...How it works...Forecasting seasonal data using ARIMAGetting readyHow to do it...How it works...There's more...Using Prophet to model time series data Getting readyHow to do it...How it works...There's more...Further reading
Geometric Problems
Technical requirementsVisualizing two-dimensional geometric shapesGetting readyHow to do it...How it works...There's more...See alsoFinding interior pointsGetting readyHow to do it...How it works...Finding edges in an imageGetting readyHow to do it...How it works...Triangulating planar figuresGetting readyHow to do it...How it works...There's more...See alsoComputing convex hullsGetting readyHow to do it...How it works...Constructing Bezier curvesGetting readyHow to do it...How it works...There's more...Further reading
Finding Optimal Solutions
Technical requirementsMinimizing a simple linear functionGetting readyHow to do it...How it works...There's more...Minimizing a non-linear functionGetting readyHow to do it...How it works...There's more...Using gradient descent methods in optimizationGetting readyHow to do it...How it works...There's more...Using least squares to fit a curve to dataGetting readyHow to do it...How it works...There's more...Analyzing simple two-player gamesGetting readyHow to do it...How it works...There's more...Computing Nash equilibriaGetting readyHow to do it...How it works...There's more...See alsoFurther reading
Miscellaneous Topics
Technical requirementsKeeping track of units with PintGetting readyHow to do it...How it works...There's more...Accounting for uncertainty in calculationsGetting readyHow to do it...How it works...There's more...Loading and storing data from NetCDF filesGetting readyHow to do it...How it works...There's more...Working with geographical dataGetting readyHow to do it...How it works...Executing a Jupyter notebook as a scriptGetting readyHow to do it...How it works...There's more...Validating dataGetting readyHow to do it...How it works...Working with data streamsGetting readyHow to do it...How it works...See alsoAccelerating code with CythonGetting readyHow to do it...How it works...There's more...Distributing computing with DaskGetting readyHow to do it...How it works...There's more...
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Content preview from Applying Math with Python

Calculus and Differential Equations

In this chapter, we will discuss various topics related to calculus. Calculus is the branch of mathematics that concerns the processes of differentiation and integration. Geometrically, the derivative of a function represents the gradient of the curve of the function, and the integral of a function represents the area below the curve of the function. Of course, these characterizations only hold in certain circumstances, but they provide a reasonable foundation for this chapter.

We start by looking at calculus for a simple class of functions: the polynomials. In the first recipe, we create a class that represents a polynomial and define methods that differentiate and integrate the polynomial. Polynomials ...

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Applying Math with Python

by Sam Morley

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.