Mathematics 2

Teacher(s)

Ponce Augusto;

Language

French

Main themes

• Elements of matrix calculus (basic matrix operations and determinants).
• Functions of two or three real variables (graphs, cross-sections and contour lines, continuity and limits, partial and directional derivatives, gradient, tangent plane and differentiability, free and bound extrema, multiple integrals).
• Polynomial approximation (sequences, series, Taylor polynomials and entire series).

Learning outcomes

At the end of this learning unit, the student is able to :

Specific learning outcomes of the course: apply mathematical conventions and notation, explain one’s reasoning when carrying out a calculation, solve optimisation problems, calculate derivatives and integrals of two or three variables, manipulate a function using a polynomial approximation.

Content

The course will cover differential calculus in two and three variables :

• graphical representations
• limit and continuity
• partial derivatives and tangent plane
• free and constrained optimization problems
• multiple integral and change of variables
• sequences and series
• Taylor polynomials and power series

Teaching methods

The learning activities consist of lectures and practical sessions.
The lectures aim at introducing the fundamental concepts and motivating them with examples.
The supervised exercises will allow students to become familiar with the techniques and methods of differential and integral calculus in several variables, through the solution of problems and exercises.

Evaluation methods

The acquisition of skills will be assessed in a final exam. The questions will ask students to select and apply methods from the course to solve exercises.

The evaluation will focus on :

•     knowledge and understanding of the various mathematical objects and methods in the course,
•     the accuracy of the calculations,
•     the quality of the writing of the answers.

Online resources

Additional documents on Moodle.

Teaching materials

• W. L. Briggs, L. Cochran, B. Gillett, Calculus: Early Transcendentals, Global Edition, 2e édition, Pearson, 2016. ISBN-10: 1292062312

Faculty or entity

> SC