nonhomogeneous linear systems undetermined coefficients
TRANSCRIPT
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?