Analysis III integration and differential equations element

  • ECTS

    6 credits

  • Component

    Faculty of Science

Description

This course will approach, in the continuity of the analysis course of S2, the notion of series with terms of any sign. The Riemann integral will be defined and applied to treat differential equations, especially linear ones. The integration part will be extended to generalized integrals.

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Objectives

Series with terms of any sign

  • Cauchy criterion, absolute convergence
  • other convergence criteria: Leibniz's (alternate series) and Abel's rules

- use of DLs to prove convergence.

- study of the remains, speed of convergence.

 Integration

- Integral of a step function

- Integrable Riemann functions

- Primitive and Integrals

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

- Riemann sums

 Differential equations

- Equations with separable variables

- Linear of order 1

- Linear of order 2 (with constant coefficients).

- Non-linear equations (Ricatti, Bernoulli)

Generalized integrals

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

- The Cauchy criterion.

- Comparisons of generalized integrals with positive terms.

- Criteria for absolute convergence.

- Semi-convergent integrals.

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Necessary pre-requisites

HAX201X - Analysis II Sequences, series, limited developments

 

Recommended prerequisites: L1 math

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Additional information

Hourly volumes:

            CM : 30

            TD : 30

            TP:

            Terrain:

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