Lecture 19

26 Novembro 2019, 21:30 • José Pedro Gaivão

Examples. 

General solution of planar linear ODE and exponential matrix. 

Classification of the trivial equilibrium. Phase portraits.

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Lecture 18

22 Novembro 2019, 18:00 • José Pedro Gaivão

Introduction to planar linear ODEs.

Transforming a scalar 2nd order linear ODE to a planar linear ODE. 

Examples. 

Solution of the IVP. 

Linear change of variables. Eigenvectors and eigenvalues and canonical forms.

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Lecture 17

19 Novembro 2019, 21:30 • José Pedro Gaivão

Qualitative theory of scalar ODEs:

- Existence and uniqueness of solutions; maximal interval of existence.

- Equilibrium points; stability

- Phase portrait; examples.

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Lecture 16

15 Novembro 2019, 18:00 • José Pedro Gaivão

Integrating factor for solving 1st order linear scalar ODEs.

Method of separation of variables.

Examples.

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Lecture 15

12 Novembro 2019, 21:30 • José Pedro Gaivão

Mixed constraints.

Necessary conditions and sufficient conditions for optimal points under convexity.

Examples.

Introduction to scalar ODEs. Classification and examples.

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