Math 221 Final Exam Review Topics
Spring 08 Math 221 Final Exam Review Topics
Analytical Methods: Separation of variables; first order linear equations; homogeneous and linear equations with constant coefficients; method of undetermined coefficients; method of variation of parameters; method of Laplace transform; homogeneous and linear systems of equations; eigenvalues, eigenvectors, and eigensolutions;
Geometrical and Numerical Methods: phase line method; classify the stability of equilibrium points; vector fields/solution curves; Euler’s method.
Applications: compartment modeling: mixing problem;
Complementary Techniques: Elementary trig identities, e.g. half/double angle formula; elementary integrals for polynomial, exponential, trig, logarithmic functions; integration technique by substitutions, integration technique by parts; partial fractions; definition of Laplace transforms, transformations of elementary functions, the first and second translation formulas their inverse transforms, transformation of derivatives, transformation of impulse delta function, complete squaring, add/subtract, multiply/divide techniques.
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