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Calculus
CE1.00

Description
1. Real functions of one real variable: differential calculus, definition of the derivative, geometric meaning of the derivative, properties
2. Real functions of several real variables: definition and properties of partial derivatives of order one and higher order, Schwarz theorem, differential of a function 
3. Differentiation of composite functions: exposure of various cases, deduction of the formulas for derivatives of order one and two 
4. Local extrema: Taylor’s formula for functions of several real variables, definition of local extrema, critical points, algorithms to determine the local extrema 
5. Implicit functions: definition, existence theorem, derivatives of the implicit functions 
6. Differential operators: gradient, divergence, laplacian, curl operator, jacobian 
7. Changes of variables in differential expressions 
8. Definite integrals: definition, geometric meaning, integration by parts, changes of variables 
9. Line integrals concerning arc length: definition, method of calculus, applications 
10. Line integrals concerning coordinates: definition, method of calculus, applications, path independence 
11. Double integrals: definition, calculus by iteration, examples 
12. Changes of variables in double integrals: general formula, the particular case of polar coordinates 
13. Applications of double integrals: calculus of area, mass, mass center, inertia momentum 
14. Triple integrals: definition, calculus by iteration, change of variables, applications

Crédits ECTS
5

Langue d'enseignement
English

Langue d'examen
English

Langue des supports pédagogiques
English

Acquis d'apprentissage fondamentaux

Entité de gestion (faculté)
Faculty of Civil Engineering (UTCN)