The four methods to prove the statement (A implies B), with the geometric series as example. 1. Direct proof, 2. Contraposition, 3. Contradiction, 4. Mathematical Induction.
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Examples for dynamic optimization in continuous time / optimal control
More examples for optimization subject to inequality constraints, Kuhn-Tucker
Homogeneous Linear Systems of ODE: The Jordan case of non-diagonalizable matrices
Homogeneous Linear Systems of ODE: Diagonalizable matrices
Methods of Proof
Examples for optimization subject to inequality constraints, Kuhn-Tucker
Scalar first-order ODE: Separation of Variables
Scalar linear first-order ODE: Variation of Constants
Complex numbers
Examples for optimization subject to equality constraints, Lagrange
Determinants: The analytics
The geometry of determinants