Lecture 11

16 Fevereiro 2023, 17:30 • Rita Sousa

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Ordinary Differential Equations: Linear, second order, scalar ODEs, with constant coefficients; characteristic polynomial and solutions of the associated homogeneous equations; method of undetermined coefficients to obtain a particular solution.

Lecture 10

14 Fevereiro 2023, 19:00 • Rita Sousa

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Ordinary Differential Equations: general solution of a linear, first order, scalar ODE; Application: present discounted value; Application: continuous vs. discrete compound interest rates; Qualitative methods for first order autonomous ODEs.

Lecture 9

14 Fevereiro 2023, 17:30 • Rita Sousa

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Ordinary Differential Equations: classification; separable ODEs; notable examples; Picard's theorem (existence and uniqueness); a priori estimate for time of existence of a solution.

Lecture 8

9 Fevereiro 2023, 19:00 • Rita Sousa

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Difference equations: solution of 2nd order linear difference equations with constant coefficients; characteristic equation (and it's generalization to higher order linear difference equations with constant coefficients); example: the Fibonacci sequence; appliation: Gambler's ruin.

Lecture 7

9 Fevereiro 2023, 17:30 • Rita Sousa

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Difference equations: backward and forward solutions of 1-st order, non-autonomous, linear difference equations with constant coefficients; equilibrium points and stability criteria; cobweb diagrams; cycles.