Analysis III: Integration and Elementary Differential Equations

This course will build on the S2 analysis course by covering the concepts of series with terms of any sign. Riemann integrals will be defined and applied to solve differential equations, particularly linear ones. The integration section will be expanded to include generalized integrals.

Series with arbitrary signs

• Cauchy criterion, absolute convergence
• other convergence criteria: Leibniz's rule (for alternating series) and Abel's rule

- use of DLs to prove convergence.

- study of remains, convergence speed.

 Integration

- Integral of a step function

- Riemann integrable functions

- Primitives and Integrals

- Some calculation methods (IPP, change of variables, mean formulas)

- Riemann sums

 Differential equations

- Separable variable equations

- Linear Order 1

- Linear equations of order 2 (with constant coefficients).

- Nonlinear equations (Ricatti, Bernoulli)

Generalized integrals

- Definitions: generalized integrals that are convergent, absolutely convergent, semi-convergent, divergent.

- Cauchy's criterion.

- Comparisons of generalized integrals with positive terms.

- Absolute convergence criteria.

- Semi-convergent integrals.

HAX201X – Analysis II Sequences, series, limited developments

Recommended prerequisites: L1 math

Hourly volumes:

            CM: 30

            TD: 30

            TP:

            Land: