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LINEAR ALGEBRA AND DIFFERENTIAL EQUATIONS

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Learning Outcomes

  • Express the basic concepts about arbitrary finite-dimensional vector space.
  • Define the concepts of vector space and subspace of a vector space.
  • Use vector space properties to examine the properties of R^n and subspaces of R^n.
  • Determine whether a subset of a vector space is linear dependent.
  • Describe the concept of a basis for a vector space.
  • Investigate properties of vector spaces and subspaces by using linear transformations.
  • Express linear transformation between vector spaces.
  • Represent linear transformations by matrices.
  • Explain the relation between vector space basis by matrices.
  • Describe the concepts of eigenvalue, eigenvector and characteristc polynomial.
  • Determine whether a linear transformation is diagonalizable or not.
  • Generalize the concept of a real inner product space to an arbitrary inner product space.
  • Express the concepts of an inner product space and an orthonormal basis.
  • Apply the gram-schmidt process to construct an orthonormal basis for a space.
  • Analyze the solution set of a system of linear equations.
  • Do basic matrix operations.
  • Express a system of linear equations in matrix form.
  • Do the elementary row operations for the matrices and systems of linear equations.
  • Apply Cramer's rule to solve a system of linear equations if the determinant of the matrix of coefficients of the system is not zero.
  • Understand solution character of homogeneous and nonhomogeneous linear DE's, the relation between them, and solve linear DE's with constant coefficients by two methods
  • Apply the method of undetermined coefficients.
  • Apply variation of parameters.
  • Express solution methods of the first and second order linear differential equations.
  • Express solution methods of higher-order linear differential equations.
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