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TD: Équations de la physique mathématique

Équations de la physique mathématique

 Ce  cours  est  sensé  fournir  les  outils  mathématiques  utilisés  dans  les  sciences  technique  (mécanique,  physique et  chimie…Ϳ.

Differential Equations


Differential Equations can be best described as "Higher-Level Integration Theory". The simplest Differential Equations have solutions that are simple Integrals. But very quickly the Differential Equations become more complicated, and so, too, are the solutions. Physicists think of Differential Equations as the equations that get spit out from their analysis of the various physics situations and thus need to be solved to understand the physics. Unfortunately, most Differential Equations cannot be solved algebraically, but the main focus of classroom/textbook courses is usually to just try to exhaust all of the Differential Equations that can be solved by hand.

Diffrential Geometry

Differential geometry is a branch of mathematics that deals with the geometry of objects that can be described by differentiable functions. It applies to the study of curves, surfaces, manifolds, and abstract spaces. Differential geometry uses mathematical tools such as topology, real analysis, linear algebra, projective geometry, and group theory to study the geometric properties of these objects. Differential geometry has important applications in fields such as robotics, fluid mechanics, cartography, and theoretical physics.
This course will allow the student to:
  1. Learn differential and integral calculus on abstract objects that are differentiable manifolds modeling real Euclidean spaces.
  1. Understand the basic concepts of differential geometry, such as the differential of a mapping, submanifolds, vector fields, differential forms, etc.
  1. Study the geometric properties of differentiable manifolds, such as curvatures and connections.
  1. Apply the tools of differential geometry to problems in physics and engineering, such as general relativity and fluid mechanics.
The learning objectives of this course include:
  1. State the definitions studied in the course.
  1. State the theorems and propositions studied in the course and prove them.
  1. Solve the problems given in the exercises.
  1. Develop skills in differential geometry calculations.
  1. Give examples of curves and surfaces and know how to parameterize them.