Section 4.4: Additional Theory and Notes

This section has a more mathematical discussion of ordinary differential equations and is provided to complement the other notes in the section.

• 4.4.1 Steady State Model
• 4.4.2 The Richness of Dynamics
• 4.4.2.1 Analytic Solution of Gravity Outflow Problem with Constant Feed
• 4.4.3 Numerical Solution of an ODE
• 4.4.4 Time constant, Accuracy and Step Size
• 4.4.5 Numerical Instability
• 4.4.6 Systems of ODE's
• 4.4.6.1 Choosing a Step Size for More than One ODE
• 4.4.7 Other Methods: Euler is not the Only Method
• 4.4.7.1 Demonstration that Improved and Modified Euler are Second Order Methods
• 4.4.8 Applications of ODE's
• 4.4.8.1 Implicit Differentiation of Redlich-Kwong equation
• 4.4.9 DAE systems
• 4.4.9.1 DAE Formulation of Flow Controller problem
• 4.4.10 Towards Process Simulation
• 4.4.10.1 Material and energy balance for a tank

Next - Section 4.5: Case Study Section
Return to Section 4 Index