Using a nonholonomic treatment to derive forces of constraint. Cyclic co- ordinates and constants of motion. Introduction to Phase Plane methods, isoclinal methods, family portraits. No mathematician can afford not to know group theory. Coding theory is an application of modern algebra.
Group structures occur in the theoretical study of most natural sciences.
Properties of integers and polynomials, division algorithms, primes, unique factorization, congruences. Group theory, Lagrange's theorem, quotient groups. Cauchy residue theorem, evaluation of some real value integrals using the Cauchy residue theorem. Inverse Laplace transform and Bromwich's contour integral formula. Continuity and convergence of processes are important considerations in our daily experiences.