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Professor Heather Pierce

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Module 2: Matrix Methods and Second Order

Linear Algebraic Equations

Video: Linear Systems
Video: Potential Problems

Matrices and Vectors

Video: Introduction to Matrices
Video: Arithmetic of Matrices
Video: Transpose and Identity
Video: The Matrix Inverse with MatLab
Video: Determinants
Video: Calculus of Matrices

Linear Systems in Normal Form

Video: Normal Form
Video: Linear Independence
Video: Fundamental Matrix

Homogeneous Systems

Video: Homogeneous Solutions
Video: Solving with Distinct Roots
Video: Solving with Repeated Roots

Complex Eigenvalues

Video: Euler’s Formula
Video: Complex Solutions
Video: Solving with Complex Roots

Homogeneous Linear Equations

Video: Second-Order Homogeneous Equations
Video: Second-Order with Distinct Roots
Video: Second-Order with Repeated Roots
Video: Third-Order Homogeneous Equations

Auxiliary Equations

Video: Second-Order with Complex Roots

Nonhomogeneous Equations

Video: Nonhomogeneous with Polynomial Functions
Video: Nonhomogeneous with Exponential Functions
Video: Nonhomogeneous with Trigonometric Functions
Video: Nonhomogeneous with Product Functions
Video: General Solutions

Superposition Principle

Video: Superposition Principle