It will be done with open books and open notes, but calculators are NOT allowed.
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Though the course is mostly about the theory of ordinary differential equations ODEs , we may consider this theory in conjunction with some theoretical and practical aspects of numerical methods for ODEs. If you have a high interest in a specific topic related to ODEs, please let me know. Additional useful readings: Calculus of Variations by I. Gelfand and S.
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Second-Order Linear Equations. In Stock. An Introduction to Partial Differential Equations.
- A Short Course in Ordinary Differential Equations.
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An Introduction to Ordinary Differential Equations
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Compatibility conditions. Proof of Lemma 2. Example 2. Link between HJ equations and calculus variations problems.
toebooks45 - Download An Introduction to Ordinary Differential Equations (Universitext)
Legendre Transform. Value function and Hopf-Lax Formula. Proof of Theorem 2. It can be useful for knowledge: for link between Hopf-Lax Formula and solution given by method of characteristic, look for instance the book by Cannarsa and Sinestrari. A counter-example to the smoothness of the value function and to the uniqueness. Introduction to the Laplace equation. Invariance properties of the Laplace operator. Link between holomorphic functions and harmonic functions. Proof of Theorem 3.
For a repetition of divergence theorem and the conversion of a n-integral into integrals over spheres see e. Appendix C. Non validity of Maximum Principle in unbounded domains Remark 3. Mean Value Formulas.
It can be useful: : Exercise 3. Properties of Harmonic Functions. Regularity of harmonic functions. Proof of Theorems 3.