L1 - CUPGE Mechanical Engineering

The purpose of this unit is to clarify the concepts of limits of sequences and functions, to explore sequences and functions in greater depth, to examine the concepts of continuity and differentiability of functions, and to introduce the main “common” functions.

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This course is an introduction to linear algebra (formalized in S2) based on intuition drawn from plane and solid geometry. It includes an introduction to matrix algebra.

The EU is also introducing the basic language of polynomials.

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This unit aims to explore plane geometry, its objects, and proofs. The unit also aims to introduce complex numbers. The sections on geometry and complex numbers each make up half of the unit.

- objects in plane geometry: points, lines, vectors, angles, circles, triangles, etc.

- Geometric transformations of the plane: symmetries, homotheties, rotations, translations.

- work on mathematical proofs

- Introduction to complex numbers, geometric interpretation, calculations with complex numbers

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The purpose of this unit is to revisit certain analytical concepts covered in high school, explore them in greater depth, and develop students’ computational skills and their ability to interpret calculations.

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The main objective of this course is to teach you how to formulate and solve simple physics problems. The areas of application are the mechanics of a point particle and geometric optics.

Mechanics of the Material Point:

• Statics: Analysis of Mechanical Systems in Equilibrium.
• Kinematics: the study of the motion of bodies, independent of the causes that produce it.
• Dynamics: the relationships between the causes of motion and motion itself.
• Work and Energy: Work Done by Forces (Conservative and Non-Conservative), the Kinetic Energy Theorem, the Mechanical Energy Theorem, and Their Applications.

Geometric Optics:

• Light Propagation (Fermat's Principle, Snell-Descartes' Laws, refractive index),
• Image Formation and Optical Systems (stigmatism, Gaussian approximation, mirrors, thin lenses, dispersive systems, centered systems, optical instruments).

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4 assessment tests during the semester in mathematics and physics.

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This course follows on from the S1 course (Analysis I), in which we were introduced to the continuity and differentiability of real-valued functions, common functions, and the study of real sequences.

The goal is to continue and expand on the work on sequences and functions, and to introduce the study of numerical series.

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This course follows S1 (Algebra I), in which linear algebra in R², R³, and^{R^n}, matrix algebra, and polynomials with real coefficients were introduced.

The goal is to introduce some basic concepts of algebraic structure and to delve deeper into vector spaces and linear mappings, as well as polynomials.

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After reviewing classical mechanics, we will discuss the fundamental quantities of thermodynamics: elementary work, macroscopic work...
The distinction between heat and temperature will be explained in detail.
The concept of pressure will be explained from a macroscopic perspective, while also providing its microscopic interpretation.
Next, using a historical approach, we will show how the first and second laws of thermodynamics came to be formulated.

From there, we will look at various applications: cycles, ideal and real gases, etc.

With the introduction of phase changes, examples (critical point) will be discussed.
We will conclude with thermal phenomena: primarily diffusion. Depending on the time remaining, concepts related to radiation will be discussed.

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This course unit introduces the basic concepts of Newtonian dynamics by building on the concepts of point-particle dynamics covered in the General Physics course unit and extending them to non-inertial reference frames, collision theory, and systems with variable mass. The basic concepts of hydrostatics and the dynamics of ideal fluids will also be covered.

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The purpose of this Solid Mechanics course is to study articulated systems composed of rigid solids by examining their motions and equilibrium positions. Topics covered include velocity fields in solids, the classification of joints, and internal forces. Graphical methods of kinematics and statics are also used.

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This module provides an introduction to using Python for students pursuing a degree in the sciences. It covers concepts in algorithms and the Python language, but the focus is primarily on practical applications in the sciences. The examples will therefore address issues related to other first-year courses.

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This is a laboratory course intended for students in the CUPGE Physics and Mathematics program and the CUPGE Mechanics program; it is shared with part of the PCSI portal’s lab course. These lab sessions will enable students to acquire fundamental concepts from the three disciplines (physics, mechanics, and electrical engineering), which are essential for continuing their studies in their chosen specialty or for transitioning to other disciplines.

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4 assessment tests during the semester in mathematics and physics/mechanics.

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