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Student Learning Outcomes

Course Name: Linear Algebra and Differential Equations
Course Number: Math 285
Course Objectives:
  • Students can solve non-homogeneous linear differential equations of any order using a variety of methods
  • Students can formulate and solve differential equations which model real-world phenomena
  • Students can diagonalize square matrices and apply these results to the solutions of linear systems of differential equations.
  • Students can solve linear differential equations using power series
  • Students can prove and apply facts regarding vector spaces, subspaces, linear independence, bases, and orthogonality.
  • Math students feel they have the resources necessary for their success.
  • Students will feel that mathematics is a beneficial part of their education
  • Identify and solve the following ordinary differential equations (ODEs): separable, 1st order linear. Set up and solve differential equations for the following applications: simple and logistic population growth model, simple electric circuits, mixing, orthogonal trajectories. Plot slope fields and numerically solve 1st order differential equations using Euler's and Runga Kutta methods.
  • Demonstrate the operations of matrix algebra, row operations for linear systems, and the methods of Gaussian Elimination and matrix inversion for solving linear systems.
  • Evaluate determinants using cofactors and row operations. Demonstrate the properties of determinants and matrix inversion using cofactors.
  • Solve problems pertaining to the definitions of vector space, subspace, span, linear dependence and independence, basis and dimension, row and column space and inner product space. Demonstrate the use of the Gram-Schmidt process for orthogonalization.
  • Solve problems pertaining to the definitions of linear transformation, kernel and range. Compute eigenvalues and eigenvectors. Diagonalize a square matrix, with the special case of orthogonal diagonalization of symmetric matrices. Demonstrate matrix representation of a linear transformation, change of bases. 6. Solve linear differential equations of order n with constant coefficients (homogeneous or non-homogeneous,) the methods of undetermined coefficients and variation of parameters with applications to RLC circuits or mass spring systems.
  • Express a linear system of differential equations in vector form, and then solve the system using eigenvalues and eigenvectors. Analyze non-linear systems numerically, including phase-plane analysis, using a computer algebra system.
  • Apply the Laplace Transform and its inverse, using the rules of the Laplace Transform, along with the 1st Shifting Theorem. Solve linear differential equations with constant coefficients using the Laplace Transform.
  • Solve ODEs using power series.