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دسته بندی دوره ها

Applying Differential Equations and Inverse Models with R

سرفصل های دوره

This course focuses on conceptually understanding and implementing numerical techniques to solve differential equations, including ordinary/partial/delay differential equations, and systems of equations known as Differential Algebraic Equations.


1. Course Overview
  • 1. Course Overview

  • 2. Getting Started with Differential Equations
  • 01. Version Check
  • 02. Prerequisites and Course Outline
  • 03. Introducing Differentiation
  • 04. Interpreting Derivatives
  • 05. Verhulsts Equation of Population Growth
  • 06. Introducing Integration to Solve Differential Equations
  • 07. Types of Differential Equations
  • 08. Initial and Boundary Value Problems
  • 09. Analytical and Numerical Solvers
  • 10. Modeling Technology Adoption Using an S-curve
  • 11. Modeling Financial Assets Using PDEs

  • 3. Understanding Types of Differential Equations
  • 1. Ordinary Differential Equations
  • 2. Differential Algebraic Equations
  • 3. Partial Differential Equations
  • 4. Solving Partial Differential Equations
  • 5. The Diffusion Equation
  • 6. Delay Differential Equations
  • 7. Infectious Disease Modeling

  • 4. Solving Differential Equations
  • 1. Demo - Solving ODEs - The Population Growth Model
  • 2. Demo - Solving ODEs - Van Der Pols Equation
  • 3. Demo - Solving ODEs - Chaotic Solutions to Lorenzs Equation
  • 4. Demo - Solving DAEs - An Auto-catalytic Chemical Reaction
  • 5. Demo - Solving DAEs - The Pendulum Equation
  • 6. Demo - Solving PDEs - The Diffusion Equation for Heat Transfer
  • 7. Demo - Solving DDEs - Infectious Disease Modeling

  • 5. Understanding and Applying Linear Inverse Models
  • 01. Framing the Optimization Problem
  • 02. Forward Models and Inverse Models
  • 03. The Wyndor Glass Case Study
  • 04. Primal and Dual Problems
  • 05. Underdetermined and Overdetermined Systems
  • 06. Demo - Solving Even Determined Systems
  • 07. Demo - Solving Overdetermined Systems
  • 08. Demo - Solving Underdetermined Systems
  • 09. Demo - Applying Linear Inverse Models
  • 10. Summary and Further Study
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    مدت زمان: 144 دقیقه
    تاریخ انتشار: 8 فروردین 1402
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