1. MAT 1235 Calculus II Section 9.1 Modeling with Differential Equations http://myhome.spu.edu/lauw

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

3. Preview Example of DE Basic ideas

4. (6.5) Two Common Ways… 2 ways to introduce a mathematical fact… 1. Verification 2. Show/Prove/Solve

5. (6.5) Definitions Differential Equation (D.E.): An equation involves derivatives Initial Value Problem (IVP): A D.E. with an initial condition

6. (6.5) Example 1 D.E. IVP

7. (6.5) Theorem The solution of is where c is some constant.

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

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

10. Example 1 (Chemistry) Reaction

11. Example 1 (Chemistry) Reaction

12. Example 2

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

15. Example 4 Coupled Spring/Mass System

16. Example 5 q = charge on the capacitor

17. Example 5 q = charge on the capacitor

18. Differential Equations

19. Example 6

20. Example 7

21. Example 8