MAT332 - Series and integration - GBX3MT92

Syllabus:

• Numerical series: convergent series and absolutely convergent series. Example of geometric series and Riemann series. Series with positive terms, comparison theorem, d'Alembert and Cauchy rules. Alternate series and series of terms of any sign (Abel's theorem, summation by parts). Complements: increase of the remainders, change of the order of the terms

• Riemann integral of a continuous or piecewise continuous function over a closed bounded interval and link with the notion of primitive. Some integration techniques: integration by parts, change of variables, decomposition into simple elements, linearisation of trigonometric polynomials, etc. 

• Integration over noncompact intervals: notion of improper integral. Absolutely convergent integrals, comparison theorems and their use. Study of a few cases of convergent but not absolutely convergent integrals.