Emphasis is on analyzing the problem, constructing a suitable mathematical model, analyzing the model, transforming it into a form suitable for computation, and verifying the results. Applications are chosen from several different areas. An examination of methods of solving ordinary differential equations with emphasis on the existence and uniqueness of solutions of first order equations and second order linear equations. Topics may include Laplace transforms, systems of linear differential equations, power series solutions, successive approximations, linear differential equations, and oscillation theory with applications to chemistry and physics. An examination of numerical methods for the solution of algebraic and differential equations and systems of equations, interpolation and approximation, numerical integration, calculation of eigenvalues, and error estimation.
Emphasis is on methods suitable for implementation on a digital computer.
This course may be applied toward a major or minor field in Mathematics, or toward a major or minor in Computer Science, but not in both departments. The student must specify the department in which this course is to be counted. An introduction to the theories of finite-state machines, programmed computers, Turing machines, automata, and formal languages. This course may be applied toward a major or a minor in Mathematics, or toward a major or minor in Computer Science, but not in both departments. The student must specify the department in which this course is to be counted.