LINFO1111 Calculus, Fall 2023

Main themes

The course focuses on

understanding of mathematical tools and techniques based on a rigorous learning of concepts favored by highlighting their practical application,
careful handling of these tools and techniques in the framework of applications. For most concepts, applications are selected from the other courses of the computer science program (e.g., economy).

Sets and numbers

Sets (intersection, union, difference)
Order and equivalence
Interval, upper bounds, lower bounds, extremes
Absolute value, powers, roots

Real functions of one variable

Injective, surjective, bijective functions
Algebraic operations on functions (including graphic interpretation)
First-order functions
Exponential, logarithmic, trigonometric functions
Composition of functions and inverse functions

Limits

Conditions to ensure that a limit exists
Cimits to infinity

Continuous functions

Fundamental theorems of continuous functions

Differentiable functions

Derivative at a point (including graphical interpretation)
The Hospital’s theorem
Linear approximation of a function
Maximum and minimum
Increasing and decreasing function (sign study)
Concavity and convexity
Taylor’s development

Integrals

Primitive
Definite integrals (including graphic interpretation)
Indefinite integrals

Functions of two variables

Notion and calculation of partial derivative
Graphical interpretation of the gradient
Interpretation and computation of the Hessian matrix
Intuitive introduction to the use of the Hessian matrix and gradient for a two-variable function to determine critical points and their nature
Concept and computation of double integrals For this last part, a mainly “tool” approach will be favored.

Teaching material

Mathématiques pour l’économie (5ème édition) par Knut Sydsæter, Peter Hammond, Arne Strøm et Andrés Carvajal, Pearson, 2020
Exercises, old exams, summaries available on Moodle

Other resources

CC BY-SA 4.0 Guillaume Berger. Website built with Hugo.