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LINEAR ALGEBRA AND NUMERICAL METHODS

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Learning Outcomes

  • recognize matrices and employ matrix methods in the solution of various problems.
  • distinguishes matrix types and matrix elements.
  • calculate matrix determinants and inverses.
  • calculate matrix eigenvalues and eigenvectors.
  • realize matrix triangularization operations.
  • use matrices in the solution of linear algebraic equations.
  • Identify the areas of use of numerical methods, make comparisons with analytical methods and define the notion of error.
  • categorize numerical methods, lists areas of application.
  • explain the notion of error, categorizes and calculates errors.
  • Recognizes the Taylor series expansions and their use.
  • find roots of nonlinear equations.
  • Formulates graphical, interval halving, Newton-Raphson and secant methods and uses them for finding roots.
  • calculate the errors in the roots found.
  • employ curve fitting methods.
  • recognize interpolation methods and use them for generating polynomials; calculate the errors in the polynomialls found.
  • fit curves to data using the least squares method.
  • fit curves to linearized data after making the necessary transformations.
  • apply numerical integration methods.
  • formulate and use the Newton-Cotes integration formulas.
  • calculate the errors in the results.
  • apply methods of numerical differentiation.
  • calculate first and second derivatives using finite differences.
  • solve Ordinary Differential Equations.
  • solve ordinary differential equations using first and fourth order Runge-Kutta methods.
  • solve Partial Differential Equations.
  • categorize partial differential equations and list solution methods.
  • solve elliptical PDE’s.
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