الخطوط العريضة للقسم

  • Preface

    طي الكل توسيع الكل

    This course is intended for 2nd year students of Material Sciences (MS). It has nine (09)
    main chapters, which expose the methods for calculating in…nite sums such as numer-
    ical sequences, sequences of functions, series of functions, integer series, and di¤ equations,...etc.
    The aim of this course is to generalize the notion of …nite sum of terms by studying how the
    latter behaves when we consider an in…nite succession of terms. The key will be to consider these
    in…nite sums, also called series, as the limit of sequences. In other words, when we remember
    the course on sequences, it will be easier to assimilate the course on the series This is why the
    …rst two chapters concerning reminders should not be neglected.
    One of the key points of this course will be the study of Fourier series whose applications are quite
    numerous in other areas of mathematics (notably di¤erential equations and partial di¤erential
    equations). To reach the chapter concerning Fourier series, however, it will be necessary to
    take a short path which will take us there in a less abrupt way. As we wrote above, we will
    recall the structure of R, then the notion of sequences in R or C. We will then consider the
    series in their generality, then the sequences and series of functions, to then move on to integer
    series, to functions developable in integer series and …nally Fourier series. We can then solve
    some di¤erential equations using this theory. The objective of the other chapters of the course
    will be to solve di¤erential equations using Laplace transforms. This mathematical tool cannot
    be applied rigorously without a little preliminary work on integrals depending on a parameter.

  • chapter1 SINGLE DOUBLE AND TRIPLE INTEGRALS

  • Chapter 2. IMPROPER INTEGRALS

  • Chapter 3 DIFFERENTIAL EQUATIONS

  • Chapter 4 SERIES

  • Chapter 5 LAPLACE & FOURIER TRANSFORMATION

  • Bibliography

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    [5] Benseghir, A., Séries et équations di¤érentielles pour la deuxième année, Poplycopie de cours, Université Ferhat Abbas Setif1, (2018).
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