Exploring Modeling with Data and Differential Equations Using R

Book Description

Exploring Mode赛格威电动车ling with Data and Diffe沃利rential Equations Using R provides a unique introduction to differential equations with applications to the biological and other natural sciences. Additionally, model parameterization and simulation of stochastic differential equations are explored, providing additional tools for model analy万宝龙sis and evaluation. This unified framework sits at the intersection of different mathematical subject areas, data science, statistics, and the natural sciences. The text throughout emphasizes data science workflows using the R statistical software program and the tidyverse constellation of packages. Only knowledge of calculus is needed; the text’s integrated framework is a stepping stone for further advanced study in mathematics or as a comprehensive introduction to modeling for quantitative natural scientists.

The text will introduce you to:

• modeling with systems of differential equations and developing analytical, computational, and visual solution techniques.
• the R programming language, the tidyverse syntax, and developing data science workflows.
• qualitative techniques to analyze a system of differential equations.
• data assimilation techniques (simple linear regression, likelihood or cost functions, and Markov Chain, Monte Carlo Parameter Estimation) to parameterize models from data.
• simulating and evaluating outputs for stochastic differential equation models. An associated R package provides a framework for computation and visu杰克宝alization of results.

中文：

书名：探索使用R的数据和微分方程建模

探索使用R的数据和微分方程建模提供了对微分方程的独特介绍，并将其应用于生物科学和其他自然科学。此外，还探索了随机微分方程的模型参数化和仿真，为模型分析和评估提供了其他工具。这个统一的框架位于不同的数学学科领域，数据科学，统计学和自然科学的交汇处。全文强调使用R统计软件程序和tidyverse软件包的数据科学工作流程。仅需要微积分知识; 文本的集成框架是进一步学习数学的垫脚石，或者是定量自然科学家建模的全面介绍。

本文将向您介绍:

• 使用微分方程组进行建模，并开发分析，计算和视觉解决方案技术。
• R编程语言，tidyverse语法，开发数据科学工作流。
• 定性技术来分析微分方程组。
• 数据同化技术 (简单线性回归、似然或成本函数和马尔可夫链、蒙特卡罗参数估计)，从数据中参数化模型。
• 随机微分方程模型的输出仿昆仑表真与评价。相关的R包为结果的计算和可视化提供了一个框架。