To demonstrate the usefulness of the Inverse Function Theorem Describe the most interesting curvilinear coordinates in the two-and three-dimensional Euclidean space Consideration of vector spaces, of the same dimension of the object coordinate, in each of its points. Construction of the bases of vector spaces as tangent vectors to the coordinate curves

Specific Objectives

Understand the concept of change of variables respecting the regularity properties Learn to make the most usual change of variable Describe vector fields related to coordinate objects Understanding the Jacobian of curvilinear coordinates as the change of variable matrix for vector fields

Dedication

Change of parameter and tangent to curves Qualitative understanding of regular curves

Specific Objectives

Know the different kinematic concepts related to the trajectory of a point in geometric terms Construct the minimum information necessary to distinguish the curves parameterized except for rigid motion

Dedication

Understanding the structure of surfaces and the control of their regularity Determine the surfaces and their aspect by the way of to describe Diffeomorphisms on surfaces and the First Fundamental Form The gaussian curvature and other curvatures in coordinates

Specific Objectives

Distinguish why an application is a surface and evaluate when it has a tangent plane Knowing ruled surfaces, surfaces of revolution and level surfaces Consider the composition with the parametrizations to extend the differential calculus on the surfaces and introduce the ability to measure on surfaces Get the curvatures of any parameterized surface and understand the major characteristics of the surfaces most used

Dedication

Surface extension of the concept of regular and metric dimension n objects in a space of dimension s environment Consider parameterizations of closed intervals and closed pseudo-intervals, and characterize the orientation induced on the boundary of the parameterization

Specific Objectives

Provide a common language to curves, surfaces, and open two-and three-dimensional Know the description of a variety of objects such as finite union of pseudo-intervals or for the parameterization of these

Dedication

Obtaining the StokesTheorem on parameterized intervals, by applying the Barrow Rule in each variable Getting the divergence theorem, Stokes-Ampère and Green in the plane, as elementary application of general Stokes theorem Solving exercises in which they appear most distinctive resources that facilitate the resolution of a wide range of problems

Specific Objectives

Understanding the scope of integration of functions and the correspondence between the implementation of integration within the objects or on their boundary Understanding the relationship between divergence, flow and circulation of vector fields on tri and bidimensional objects and their boundaries Learning to solve problems of integration on complex objects, but whose pieces are described by simple expressions that facilitate the realization of calculations on them

Dedication

Dedication

Knowledge of the variation of integrals with respect to the time when both subintegral function as the domain of integration depend of the time Getting some conservation laws, as pure application of the results of integration and basic mechanical concepts in elementary media

Specific Objectives

Using elementary techniques of integration and implementation of the classic theorems, connect with key elements in the description of continuous media Spending on basic physical laws from a simplified perspective emphasizing techniques of vector calculus

Dedication

Formulation of the problem, necessary condition for extrema, Euler and Euler-Lagrange equations and natural boundary conditions Systematically explore the problems posed by the necessary condition for extrema, identifying the characteristics of the different types of equations obtained, self-adjoint problems, problems of one or more variables, eigenvalues, natural boundary conditions or enforced

Specific Objectives

It is intended to provide a systematic way of expose problems, covering the most relevant part of the problems that arise in the context of differential equations in both one variable as in several variables It is intended to come into contact with a number of problems that will gradually expand the horizon of action, from the classic problem of brachistochrone to the equations from the minimization of elastic strain energy

Dedication

From the minimization of quadratic functionals and considering isoperimetric conditions, with functions of one variable, we obtain linear boundary problems and eigenvalues problems for ODE's Will be posed classification criteria and the prototypes of elliptic equations, parabolic equations and hyperbolic equations

Specific Objectives

Aims to provide tools to solve these problems of great interest in applications, the tools previously known consist only in rudiments to address basic problems of initial value We present families of problems that can be tackle, heat equations, wave equation, Laplace equation, types of domains and the initial and boundary conditions

Dedication

Estimation and analysis of eigenvalues of Sturm-Liouville problems, and solving boundary value problems including the use of Green's functions

Specific Objectives

Gain experience in using methods of solving such problems, these techniques remain in force when dealing with problems of partial differential equations by separation of variables

Dedication

We introduce the Fourier method for the one-dimensional diffusion problems, and we extend this method of resolution to any problem that fits with it. This allows us to resolve many issues previously raised whose solutions will be represent in orthonormal bases

Specific Objectives

Have a tool to obtain effective analytical solutions of problems of interest in many applied areas and also understand its scope, on the other hand it allows to assess the need for other techniques to address problems that can not solve the method

Dedication

The direct methods consist in considering Minimizing sequences and are not easy to systematize, the weak form is to write the equations in integral form and with less regularity requirements and are easy to systematize Expose a method to control the coefficients of the existing problems, to obtain the approximate solution in finite dimensional spaces. Evolution problems.

Specific Objectives

Consider alternative methods to the separation of variables for the solution of problems of great interest and expose the rudiments to the weak form as the way for implementation the approximation methods for many problems. Access the basic rudiments so that, throughout their studies, they can know the methods of numerical solution of many problems of interest including evolution problems.

Dedication

Dedication