MATH 2082 - Linear Algebra and Differential Equations

1. Determinants
2. Ordinary Differential Equations
   1. Higher-order linear differential equations
   2. Reduction of order
   3. Characteristic polynomials
   4. Nonhomogenous case
   5. Undetermined coefficients
   6. Variation of parameters
   7. Numerical solution of differential equations
   8. Power Series solutions
   9. Applications
   10. Systems of linear differential equations
3. Systems of Linear Equations and Matrices
4. Vector Spaces and Linear Transformation
   1. Definition
   2. Subspaces
   3. Linear Independence, linear combination and span
   4. Bases and dimension
   5. Linear transformations
   6. Eigenvalues and Eigenvectors

1. Solve linear systems of equations by linear algebra and matrix methods.
2. Determine dimension, basis, dependence, or independence properties of given vector spaces.
3. Demonstrate critical and logical reasoning when solving problems.
4. Perform basic matrix algebra computations by hand and using technology.
5. Communicate clearly a problem¿s solution and its explanation for the intended audience in terms of the problem posed.
6. Determine kernel, range, nullity, and rank of a given linear transformation.
7. Solve a differential equation mostly by analytical methods and sometimes by graphical (slope field) and numerical (Euler’s or Runge-Kutta) methods.
8. Solve homogeneous and nonhomogeneous first-order (and higher-order) differential equations by symbolic methods, including techniques of linear algebra and vector spaces.
9. Solve physical problems using differential equations.
10. Solve systems of differential equations.

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