Difference between revisions of "MMS: Mathematical Foundations of M&S 2016 - I"
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+ | [[File:Logos-tadeo-central.png]] | ||
+ | == English version == | ||
+ | This is a course around basic mathematical concepts on Calculus, linear algebra and Differential equations. Emphasis is given to topics that will be useful in models and simulation for several disciplines. | ||
+ | |||
+ | === Goals === | ||
+ | * Enhance both mathematical skills and understanding of mathematical concepts. | ||
+ | * Acquire enough mathematical knowledge for modelling and simulation. | ||
+ | |||
+ | === Content === | ||
+ | |||
+ | <ul> | ||
+ | <li>Vectorial calculus. One variable calculus.</li> | ||
+ | <ol> | ||
+ | <li>Review of one variable calculus. Taller 1: [[file:Taller-CalcVec1.pdf]]</li> | ||
+ | <li>Function definition.</li> | ||
+ | <li>Derivatives.</li> | ||
+ | <li>Integrals.</li> | ||
+ | <li>Material: Presentación clase 1: [[file:FundMathMS-1dCalculus.pdf]], Apuntes sobre cálculo en una variable [[file:apuntesCalculoUnaVar.pdf]] Calculadora de raices de polinomios online: [http://www.mathportal.org/calculators/polynomials-solvers/polynomial-roots-calculator.php]</li> | ||
+ | </ol> | ||
+ | |||
+ | <li>Vectorial calculus. Several variable functions.</li> | ||
+ | <ol> | ||
+ | </li><li>Vectors in 2-Space and 3-Space. | ||
+ | </li><li>Inner Product (Dot Product). | ||
+ | </li><li>Vector Product (Cross Product). | ||
+ | </li><li>Vector and Scalar Functions and their Fields. | ||
+ | </li><li>Vector Calculus: Derivatives. | ||
+ | </li><li>Functions of Several Variables. | ||
+ | </li><li> Gradient of a Scalar Field. Presentación clase 2: [[file:Vectors-ScalarFields.pdf]] | ||
+ | </li><li>Directional Derivatives. | ||
+ | </li><li>Divergence of a Vector Field. | ||
+ | </li><li>Curl of a Vector Field. | ||
+ | </li><li>Lagrange multipliers. Lectura: [[file:LagrangeMult.pdf]] | ||
+ | </li><li>Taller 2: [[file:Taller-CalcVec2-V2.pdf]], Artículo: [[file:BIOS-83-97.pdf]], Datos: [[file:data.xls]], Salida zunzun: [[file:zunzunout.pdf]] Tutorial de cálculo vectorial con Matlab [http://www2.math.umd.edu/~jmr/241/MATLABmaterials.html] | ||
+ | </ol> | ||
+ | |||
+ | <li>Linear Algebra </li> | ||
+ | <ol> | ||
+ | <li>Spaces and subspaces.</li> | ||
+ | <li>Lineal combination and space generation.</li> | ||
+ | <li>lineal dependence and lineal independece.</li> | ||
+ | <li>Basis and dimension</li> | ||
+ | <li>Linear transformations.</li> | ||
+ | <li>Eigen-values and eigen-vectors</li> | ||
+ | </ol> | ||
+ | |||
+ | <ol> | ||
+ | <li>Matrix: Operations and properties.</li> | ||
+ | <li>Resolve linear systems by Gauss and Gauss-Jordan methods.</li> | ||
+ | <li>Resolve linear systems by inverse and Cramer's rule.</li> | ||
+ | <li>Applications: Leonlief product supplies analysis.</li> | ||
+ | </ol> | ||
+ | |||
+ | |||
+ | <li>First order differential equations.</li> | ||
+ | <ol> | ||
+ | <li>Basic Concepts. Modeling. | ||
+ | </li><li>Geometric Meaning of y r ϭ f (x, y). Direction Fields, Euler’s Method. | ||
+ | </li><li>Separable ODEs. Modeling. | ||
+ | </li><li>Exact ODEs. Integrating Factors. | ||
+ | </li><li>Linear ODEs. Bernoulli Equation. Population Dynamics. | ||
+ | </li><li>Orthogonal Trajectories. | ||
+ | </li><li>Existence and Uniqueness of Solutions for Initial Value Problem. | ||
+ | </ol> | ||
+ | |||
+ | <li>Second order differential equations.</li> | ||
+ | <ol> | ||
+ | </li><li>Homogeneous Linear ODEs of Second Order | ||
+ | </li><li>Homogeneous Linear ODEs with Constant Coefficients | ||
+ | </li><li>Modeling of Free Oscillations of a Mass–Spring System | ||
+ | </li><li>Differential Operators. | ||
+ | </li><li>Euler–Cauchy Equations | ||
+ | </li><li>Existence and Uniqueness of Solutions. | ||
+ | </li><li>Nonhomogeneous ODEs | ||
+ | </li><li>Modeling: Forced Oscillations. | ||
+ | </ol> | ||
+ | |||
+ | <li>Systems of ordinary differential equations.</li> | ||
+ | <ol> | ||
+ | <li> Homogeneous systems of ordinary differential equations.</li> | ||
+ | <li>Resolve linear systems of differential equations .</li> | ||
+ | <li>linearization of high order differential equations.</li> | ||
+ | </ol> | ||
+ | |||
+ | </ul> | ||
+ | |||
+ | |||
Volver a [[MMS:Courses]] | Volver a [[MMS:Courses]] |
Revision as of 11:53, 11 February 2016
English version
This is a course around basic mathematical concepts on Calculus, linear algebra and Differential equations. Emphasis is given to topics that will be useful in models and simulation for several disciplines.
Goals
- Enhance both mathematical skills and understanding of mathematical concepts.
- Acquire enough mathematical knowledge for modelling and simulation.
Content
- Vectorial calculus. One variable calculus.
- Review of one variable calculus. Taller 1: File:Taller-CalcVec1.pdf
- Function definition.
- Derivatives.
- Integrals.
- Material: Presentación clase 1: File:FundMathMS-1dCalculus.pdf, Apuntes sobre cálculo en una variable File:ApuntesCalculoUnaVar.pdf Calculadora de raices de polinomios online: [1]
- Vectorial calculus. Several variable functions.
- Vectors in 2-Space and 3-Space.
- Inner Product (Dot Product).
- Vector Product (Cross Product).
- Vector and Scalar Functions and their Fields.
- Vector Calculus: Derivatives.
- Functions of Several Variables.
- Gradient of a Scalar Field. Presentación clase 2: File:Vectors-ScalarFields.pdf
- Directional Derivatives.
- Divergence of a Vector Field.
- Curl of a Vector Field.
- Lagrange multipliers. Lectura: File:LagrangeMult.pdf
- Taller 2: File:Taller-CalcVec2-V2.pdf, Artículo: File:BIOS-83-97.pdf, Datos: File:Data.xls, Salida zunzun: File:Zunzunout.pdf Tutorial de cálculo vectorial con Matlab [2]
- Linear Algebra
- Spaces and subspaces.
- Lineal combination and space generation.
- lineal dependence and lineal independece.
- Basis and dimension
- Linear transformations.
- Eigen-values and eigen-vectors
- Matrix: Operations and properties.
- Resolve linear systems by Gauss and Gauss-Jordan methods.
- Resolve linear systems by inverse and Cramer's rule.
- Applications: Leonlief product supplies analysis.
- First order differential equations.
- Basic Concepts. Modeling.
- Geometric Meaning of y r ϭ f (x, y). Direction Fields, Euler’s Method.
- Separable ODEs. Modeling.
- Exact ODEs. Integrating Factors.
- Linear ODEs. Bernoulli Equation. Population Dynamics.
- Orthogonal Trajectories.
- Existence and Uniqueness of Solutions for Initial Value Problem.
- Second order differential equations.
- Homogeneous Linear ODEs of Second Order
- Homogeneous Linear ODEs with Constant Coefficients
- Modeling of Free Oscillations of a Mass–Spring System
- Differential Operators.
- Euler–Cauchy Equations
- Existence and Uniqueness of Solutions.
- Nonhomogeneous ODEs
- Modeling: Forced Oscillations.
- Systems of ordinary differential equations.
- Homogeneous systems of ordinary differential equations.
- Resolve linear systems of differential equations .
- linearization of high order differential equations.
Volver a MMS:Courses