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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تولید کننده: PluralSight