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
