SOWISO - UvA | Doing mathematics with R

Introduction

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Goal

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Documentation

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Style guide

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Arithmetic with numbers

Control structures

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Conditional instruction

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Logical expressions

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Conditional repetition

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Restricted repetition

Functions

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Why use functions, anyway?

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The standard form of a function definition

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Multiple returns and returned values

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Default values for arguments of a function

Graphs of functions

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Plotting the graph of a function

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Combine graphs

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Graphs with ggplot2

Regression analysis in R

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Linear regression with a straight line

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Linear regression in general

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Multiple linear regression

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Nonlinear regression

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Nonlinear regression via the peeling-off method

Differential equations in R

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Solving a first order initial value problem

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Calculating and plotting multiple solution curves

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Solving systems of differential equations

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Parameter estimation in differential equations

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Differential equations with events

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Slope field and phase portait of an autonomous first-order differential equation

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Slope field and phase portrait of a nonautonomous first-order differential equation

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Stability analysis of an autonomous first-order differential equation

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Phase portrait of an autonomous system of two differential equations

Linear algebra in R

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Creation of vectors

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Selection of components of vectors, and assignment of values

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Computing with vectors

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Solving systems via solve and rref

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Basic properties and creation of matrices

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Selection of components of matrices and assignment of values

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Computing with matrices and vectors

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Row reduction and determinant

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Kernel and image of a linear mapping

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Similarity of matrices

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Eigenvalues and eigenvectors

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SVD and digital image compression