The Riemann integral: Riemann sums, the fundamental theorem of calculus and the indefinite integral. Methods for computing integrals: integration by parts, substitution, partial fractions. Improper integrals and application to series. 2. Uniform and pointwise convergence. Cauchy criterion and the Weierstrass M-test. Power series. Taylor series. 3. First order ODE’s: initial value problem, local uniqueness and existence theorem. Explicit solutions: linear, separable and homogeneous equations, Bernoulli equations. 4. Systems of ODE’s. Uniqueness and existence (without proof). Homogeneous systems of linear ODE’s with constant coefficients. 5. Higher order ODE’s: uniqueness and existence theorem (without proof), basic theory. The method of undetermined coefficients for inhomogeneous second order linear equations with constant coefficients. The harmonic oscillator and/or RLC circuits. If time permits: variation of parameters, Wronskian theory.

Notes

Courses marked with (*) are required
for admission to the M.Sc. program in Mathematics.

The M.Sc. degree requires the successful completion of at least 2
courses marked (#). See the
graduate program for details

The graduate courses are open to strong undergraduate students who
have a grade average of 85 or above and who have obtained
permission from the instructors and the head of the teaching
committee.

Please see the detailed
undergraduate
and graduate programs for the
for details on the requirments and possibilities for complete the
degree.