SUPPLEMENTRY NOTES FOR L3 Differential E.pptx

Lecture Notes

1. Supplementary Notes for Lecture 3 Differential Equations (DE) 1.0 Linear, Homogeneous Equations with Constant Coefficients 8/23/2025 COMPILED BY: ALEX W JOHN 1

2. Linear, Homogeneous Equations with Constant Coefficients Key Idea DE and its Characteristics Equation Characteristics Roots and General Solution * Distinct Real Roots *Complex Roots * Repeated Roots Worked out Examples 8/23/2025 COMPILED BY: ALEX W JOHN 2

3. Key Idea Linear , Homogeneous Equations with Constant Coefficients 8/23/2025 COMPILED BY: ALEX W JOHN 3

4. Characteristic Root DE and its Characteristic Equation Characteristic Root 8/23/2025 COMPILED BY: ALEX W JOHN 4

5. A. Distinct Real Roots Proposition The particular solution for an initial value problem can be found by evaluating the constants C 1 and C 2 using the initial conditions. 8/23/2025 COMPILED BY: ALEX W JOHN 5

6. EXAMPLE 1 8/23/2025 COMPILED BY: ALEX W JOHN 6

7. B. COMPLEX ROOTS Proposition 8/23/2025 COMPILED BY: ALEX W JOHN 7

8. Complex Roots.Cont.. 8/23/2025 COMPILED BY: ALEX W JOHN 8 Proposition ..cont.

9. Example 2 8/23/2025 COMPILED BY: ALEX W JOHN 9

10. c. Repeated Roots Proposition 8/23/2025 COMPILED BY: ALEX W JOHN 10

11. Example 3 8/23/2025 COMPILED BY: ALEX W JOHN 11

12. Announcement… New Google Classroom code Tutorials Solutions will be uploaded, only the selected ones Assignment One will be Uploaded, after Mr. Gibson’s Approval We’ll start unit two on Monday 8/23/2025 COMPILED BY: ALEX W JOHN 12

13. 8/23/2025 COMPILED BY: ALEX W JOHN 13 THE END……………