System Dynamics Mathematical Background Introduction

System Dynamics (24.509)

II. Mathematical Background

Introduction

Three math-related topics that are required background material for this course are:

Solution of difference and differential equations,
Matrix notation and use/manipulation of matrix equations, and
Laplace transform techniques.

We will discuss items 1 and 2 in this section of notes and defer the review of Laplace transforms for the section on transform methods. The first two topics are detailed in the following subsections:

Differential Equations

Example 2.1

Example 2.2

Difference Equations

Example 2.3

Example 2.4

Review of Matrix Algebra and Matrix Calculus

Example 2.5

Example 2.6

Example 2.7

24.509 Lecture Notes by Dr. J. R. White, UMass-Lowell (Spring 1997).

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