MAT 1235 Calculus II Section 9.1 Modeling with Differential Equations

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Presentation transcript:

MAT 1235 Calculus II Section 9.1 Modeling with Differential Equations

HW and … WebAssign 9.1 Exam is coming up, be sure to take time to review for your exam

Preview Example of DE Basic ideas

(6.5) Two Common Ways… 2 ways to introduce a mathematical fact… 1. Verification 2. Show/Prove/Solve

(6.5) Definitions Differential Equation (D.E.): An equation involves derivatives Initial Value Problem (IVP): A D.E. with an initial condition

(6.5) Example 1 D.E. IVP

(6.5) Theorem The solution of is where c is some constant.

Differential Equations Many “phenomenon” can be modeled /described by D.E.

Example 1 (Chemistry) Reaction X(t) = amount of C The rate of formation of C is given by

Example 1 (Chemistry) Reaction

Example 1 (Chemistry) Reaction

Example 2

Example 3 Pendulum When the angle is small, the motion can be modeled by

Example 4 Coupled Spring/Mass System

Example 5 q = charge on the capacitor

Example 5 q = charge on the capacitor

Differential Equations

Example 6

Example 7

Example 8