5 credits

30.0 h + 30.0 h

Q1

Teacher(s)

Glineur François; Jungers Raphaël; Remacle Jean-François coordinator; SOMEBODY; Wertz Vincent;

Language

French

Main themes

functions of a real variable, first order differential equations. Mathematical proof techniques. Modelling of simple problems, and problem solving.

Aims

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1 | At the end of the course the students will be able to - Manipulate functions of a single real variable ;
- Use first order differential equations, linear recurrence equations and simple discrete structures in order to model and solve problems ;
- Apprehend and visualize a scalar function of two real variables;
- Calculate partial derivatives and use them to form a first-order approximation.
- Understand the main mathematical proof techniques ;
- Make a critical reading and analysis of a problem statement;
- Find examples and counter-examples related to a mathematical statement;
- Write short mathematical proofs with rigor.
- Modelling of simple problems, and problem solving using the methods cited above.
Regarding the learning outcomes of the program of Bachelor in Engineering, this course contributes to the development and the acquisition of the following learning outcomes: LO1.1, 1.2, maybe 2.3, 2.6, 2.7, 3.2, 4.1. |

*The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.*

Content

- Real numbers, inequalities, sequences and series
- Real functions of one variable, limits and continuity, sequences of functions
- Derivation and applications, optimization
- Taylor polynomial
- Integration and applications
- Complex numbers
- Introduction to differential equations
- Introduction to multivariable calculus: continuity, limits and differentiability, gradient and tangent plane for scalar real functions of two variables

Teaching methods

Lectures in a large auditorium, supervised exercise (APE) and problem (APP) sessions in small groups, possibly supplemented with writing assignments and online exercises.

Evaluation methods

Students will be evaluated with an individual written exam, based on the above-mentioned objectives. Results from continuous assessment may also be taken into account for the final grade.

Online resources

Bibliography

- ' Calculus with Applications par Peter D. Lax et Maria Shea Terrell, Springer, 2014.
- ' Multivariable Calculus with Applications par Peter D. Lax et Maria Shea Terrell, Springer, 2017.

**Calculus with Applications**par Peter D. Lax et Maria Shea Terrell, Springer, 2014.

**Multivariable Calculus with Applications**par Peter D. Lax et Maria Shea Terrell, Springer, 2017.

Teaching materials

- Calculus with Applications par Peter D. Lax et Maria Shea Terrell, Springer, 2014.
- Multivariable Calculus with Applications par Peter D. Lax et Maria Shea Terrell, Springer, 2017.

Faculty or entity

**BTCI**