Nonhomogeneous Linear Systems Undetermined Coefficients.

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Presentation transcript:

Nonhomogeneous Linear Systems Undetermined Coefficients

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

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

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

Non-Homogeneous Linear Systems Several Different Methods We will focus on 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

(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?