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Mathematics 1

1MAB1 Mathematics 1 Materials and Mechanics - Apprenticeship S5
Lessons : 12 h TD : 12 h TP : 0 h Project : 0 h Total : 24 h
Co-ordinator : Patricia Jouannot-Chesney
Prerequisite
Basic knowledge of matrices, classical functions and their derivatives and simple integral calculations.
Course Objectives
To consolidate or acquire some of the basic mathematical knowledge essential to the comprehension of the courses of mechanics and materials.
Syllabus
I. Linear transformations, Euclidean space : dot product, norm
II. Matrices: determinant, rank, trace, diagonalization
III. Integral calculation (change of variables, integration by parts ...)
IV. Ordinary Differential Equations with constant coefficients (1st, 2nd order and order n). Ordinary Differential Equations of 1st order
V. Maclaurin series
Practical work (TD or TP)
Vector calculations to compute stress fields and solid deformations
Acquired skills
At the end of this course, the students will be able to follow courses dealing with mechanics or materials without being hampered by difficulties in elementary mathematics.
Bibliography
R. BRONSON. Equations différentielles. Méthodes et applications. Série Schaum, Mc Graw-Hill, 1994.
C. CARCHEREUX, F. LUSSIER, G. DE MONICAULT, S. NICOLAS, B. CAMINADE, dirigé par C. GAUTIER, A. WARUSFEL. Mathématiques tout-en-un BCPST 1ère année, Cours et exercices corrigés. Dunod, 2008.
F. LIRET, M. ZISMAN. Maths, Tome 2. Dunod, 1984.
F. LUSSIER, G. DE MONICAULT, S. NICOLAS, M. RAMIS, B. CAMINADE, dirigé par C. GAUTIER, A. WARUSFEL. Mathématiques tout-en-un BCPST 2e année, le cours de référence. Dunod, 2007.
J. PICHON. Primitives, équations différentielles. Ellipses, 1989.
http://mathworld.wolfram.com/
http://fr.wikipedia.org/wiki/Portail:Mathématiques

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