620-130 Applied Mathematics

Note

Students may only gain credit for one of 620-130, 620-132 (1997 Handbook 618-130, 618-132).

Credit Points

Coordinator

Prerequisites

One of 620-111, 620-121, 620-142, 620-200 or 620-211 (1997 Handbook one of 618-111, 618-121, 618-142, 618-200, 618-211); or one of 620-141, 620-162 (1997 Handbook 618-141 or 618-162) with 620-142 as corequisite; or concurrent enrolment in one of 620-200, 620-211.

Semester

Contact

Subject Description

This subject introduces the terminology of ordinary differential equations; the principles of first and second ordinary differential equations; linear systems of first and second order ordinary differential equations and their application primarily in the field of mechanics;

Students completing the subject develop the ability to solve analytically first order ordinary differential equations (ODEs), second order linear ODEs, and systems of two or three linear first order ODEs using eigenvalue/eigenvector techniques; and to apply the above techniques to simple problems in particle dynamics, including projectile motion. The subject demonstrates the role of differential equations in applied mathematics and their use in modelling the dynamics of single particles and small systems of particles.

Differential equations: first-order differential equations (separable, linear via integrating factor, homogeneous) and applications; second-order differential equations (reducible to first-order, linearly independent solutions), second-order linear differential equations (particular integrals, complementary functions) and applications; numerical solution of first-order equations. Mechanics: Straight-line motion; motion of a projectile; motion in a circle; simple harmonic motion; momentum; impulse; work and energy; pendulum; friction; connected bodies; springs. Systems of differential equations: Eigenvalues and eigenvectors; systems of first-order differential equations and applications; phase portraits; systems of second-order linear differential equations and applications.

Assessment

Up to 24 pages of written assignments, a three-hour end-of-semester written examination and class tests totalling not more than 1.5 hours.