1. Nonhomogeneous Linear Systems Undetermined Coefficients

2. Homogeneous Linear Systems Find Eigenvalues and Eigenvectors and If Eigenvalues are distinct (real or complex) If Eigenvalue is repeated

3. Non-Homogeneous Linear Systems Remember, general solution takes the form General Solution To Homogeneous Equation Specific Solution to Nonhomogenous Equation Know how to find this

4. Non-Homogeneous Linear Systems Remember, general solution takes the form General Solution To Homogeneous Equation Specific Solution to Nonhomogenous Equation Today we will learn how to find this

5. Non-Homogeneous Linear Systems Several Different Methods We will focus on Undetermined Coefficients

6. Method of Undetermined Coefficients

7. Rewrite Homogeneous Term as sum of Constant Vectors times Functions

8. Method of Undetermined Coefficients General Solution

9. Method of Undetermined Coefficients (Homogeneous) General Solution Helps us Guess Form of Nonhomgeneous Solution

10. Method of Undetermined Coefficients (Homogeneous) General Solution Substituting in gives specific solution to Non-Homogeneous

11. Method of Undetermined Coefficients General Solution To Non- homogeneous

12. Method of Undetermined Coefficients Rewrite Homogeneous Term as sum of Constant Vectors times Functions

13. Method of Undetermined Coefficients Rewrite Homogeneous Term as sum of Constant Vectors times Functions

14. Method of Undetermined Coefficients

15. (Homogeneous) General Solution Helps us Guess Form of Nonhomgeneous Solution

16. Method of Undetermined Coefficients (Homogeneous) General Solution Helps us Guess Form of Nonhomgeneous Solution

17. Method of Undetermined Coefficients (Homogeneous) General Solution Helps us Guess Form of Nonhomgeneous Solution

18. Method of Undetermined Coefficients (Homogeneous) General Solution Helps us Guess Form of Nonhomgeneous Solution

19. Method of Undetermined Coefficients (Homogeneous) General Solution Helps us Guess Form of Nonhomgeneous Solution

20. Method of Undetermined Coefficients (Homogeneous) General Solution Helps us Guess Form of Nonhomgeneous Solution

21. Method of Undetermined Coefficients (Homogeneous) General Solution Guess Form of Nonhomgeneous Solution

22. Method of Undetermined Coefficients (Homogeneous) General Solution Guess Form of Nonhomgeneous Solution

23. Method of Undetermined Coefficients General solution

24. Questions?