Introducción al cálculo tensorial. by Machado, Luis M. Series: IRAM Edition statement:1a. ed. Physical details: p.: il.; 22 cm. Subject(s). ×. Cálculo tensorial — Problemas y ejercicios. More like this Add tags for “Teoría y problemas de análisis vectorial y una introducción al analisis tensorial”. Be the. Teoría y problemas de análisis vectorial y una introducción al análisis tensorial. [ Murray R Spiegel] vectorial — Problemas, ejercicios, etc. Cálculo de tensores.

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Curso de “Applied Topology” de Robert Ghirst. Historical comments about the tesnorial group, homology and cohomology. The idea is to mention analytical mechanics in the first part, electrodynamics in the second part and general relativity in the third part. Interpretation of Lorentz transformations. Local expression of a differential forms as a combination of determinants.

The final examination is scheduled for January 20th. Statement of the Stokes theorem. Some results relating curvature and topology.


The advisable length is pages double-spaced, 11pt or 12pt. Tensors on a mainfold. Note that neither the exam nor the composition is mandatory. Iintroduccion wrinkles make me stronger? E is max Final exam, Composition. The invariance of the exterior derivative by coordinate changes. Kinetic energy in generalized coordinates for the double pendulum. Calculations with the tangent map referred to the double pendulum. Differential forms as fields of alternating forms. Gauss intgoduccion of the curvature.

Proof of that cohomology is homotopy invariant.

Geometría Diferencial

The grading is as follows: Integral curves on manifolds. Properties of the exterior derivative. Motivation for Frobenius theorem.

Lagrangians invariant by transformations. A brief dictionary between geometry and mechanics through the double pendulum example. Motivation for the definition of connection.

Underlying ideas in Riemannian geometry. Transformation law for tensors. Conservation of the energy. Definition of manifold with boundary. The topics covered in each lecture are listed here. introduccipn

Introducción al cálculo tensorial

Ejercicios The following sheets are home assignments nitroduccion contribute to the grading. The lectures are scheduled on Tuesday and Thrusday I recommend to ask me for confirmation after choosing the topic.


Equivalence with the Newton’s second law for free introfuccion. The vector mechanics formulation of the planetary motion. Here you can find a brief approximate dictionary Mechanics-Geometry. Parallel transport “absolute parallelism”. The cotangent bundle as the phase space.

Definition of the de Rham cohomology. Cohomology ans differential topology: El teorema de Stokes en variedades. Geometric meaning of Ricci tensor.

Euclidean Tensors, Einstein summation convention. The problem introdjccion “avoidance of crossing” is proposed. No prior knowledge on Physics is assumed. Computation of a geodesic for the Schwarzschild metric. Maxwell equations and the Stokes theorem.

Content of the lectures Part 1 Date. Exponential map and Gauss Lemma.