Nonhomogeneous Linear Systems Undetermined Coefficients.

NonhomogeneousLinear Systems

Undetermined Coefficients

Homogeneous Linear Systems

Find Eigenvalues and Eigenvectorsan

dandIf Eigenvalues are distinct (real or

complex)

If Eigenvalue is repeated

Non-Homogeneous Linear Systems

Remember, general solution takes the form

General SolutionTo

HomogeneousEquation

Specific Solutionto

NonhomogenousEquation

Know how to find this

Non-Homogeneous Linear Systems

Remember, general solution takes the form

General SolutionTo

HomogeneousEquation

Specific Solutionto

NonhomogenousEquation

Today we will learn how to find this

Non-Homogeneous Linear Systems

Several Different Methods

We will focus on Undetermined Coefficients

Method of Undetermined Coefficients

Method of Undetermined Coefficients

Rewrite Homogeneous Term as sum of

Constant Vectors times Functions

Method of Undetermined Coefficients

General Solution

Method of Undetermined Coefficients

(Homogeneous) General Solution

Helps us Guess Form of Nonhomgeneous Solution

Method of Undetermined Coefficients

(Homogeneous) General Solution

Substituting in gives specific solution

to Non-Homogeneous

Method of Undetermined Coefficients

General Solution To Non-homogeneous

Method of Undetermined Coefficients

Rewrite Homogeneous Term as sum of

Constant Vectors times Functions

Method of Undetermined Coefficients

Rewrite Homogeneous Term as sum of

Constant Vectors times Functions

Method of Undetermined Coefficients

Method of Undetermined Coefficients

(Homogeneous) General Solution

Helps us Guess Form of Nonhomgeneous Solution

Method of Undetermined Coefficients

(Homogeneous) General Solution

Helps us Guess Form of Nonhomgeneous Solution

Method of Undetermined Coefficients

(Homogeneous) General Solution

Helps us Guess Form of Nonhomgeneous Solution

Method of Undetermined Coefficients

(Homogeneous) General Solution

Helps us Guess Form of Nonhomgeneous Solution

Method of Undetermined Coefficients

(Homogeneous) General Solution

Helps us Guess Form of Nonhomgeneous Solution

Method of Undetermined Coefficients

(Homogeneous) General Solution

Helps us Guess Form of Nonhomgeneous Solution

Method of Undetermined Coefficients

(Homogeneous) General Solution

Guess Form of Nonhomgeneous Solution

Method of Undetermined Coefficients

(Homogeneous) General Solution

Guess Form of Nonhomgeneous Solution

Method of Undetermined Coefficients

General solution

Questions?