Control Systems

  1. Mathematical Foundations
    1. Complex Variables and Functions
      1. Complex Numbers
        1. Complex Functions
          1. Poles and Zeros
            1. Residue Theory
            2. Differential Equations
              1. Linear Ordinary Differential Equations
                1. Initial Value Problems
                  1. Boundary Value Problems
                    1. Solution Methods
                    2. Laplace Transform
                      1. Definition and Properties
                        1. Linearity Property
                          1. Time Shifting Property
                            1. Frequency Shifting Property
                              1. Scaling Property
                                1. Differentiation Property
                                  1. Integration Property
                                    1. Convolution Property
                                    2. Common Transform Pairs
                                      1. Initial Value Theorem
                                        1. Final Value Theorem
                                          1. Inverse Laplace Transform
                                            1. Partial Fraction Expansion
                                              1. Residue Method
                                                1. Table Lookup
                                                2. Applications to Differential Equations
                                                3. Matrix Theory
                                                  1. Matrix Operations
                                                    1. Eigenvalues and Eigenvectors
                                                      1. Matrix Exponential
                                                        1. Similarity Transformations
                                                          1. Rank and Determinant

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                                                        1. Introduction to Control Systems

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                                                        3. Mathematical Modeling of Dynamic Systems