620-132 Applied Mathematics (Advanced)

Note

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

Credit Points

Coordinator

Prerequisites

620-111 with a grade of H3 or better, or one of 620-121, 620-142 with a grade of H2A or better, or 620-211 (1997 Handbook 618-111 with a grade of H3 or better, or one of 618-121, 618-142 with a grade of H2A or better, or 618-211), or invitation by the Head of Department.

Corequisites

If none of 620-112, 620-122, 620-200, 620-211 (1997 Handbook 618-112, 618-122, 618-200, 618-211) has yet been passed, one of 620-112, 620-122, 620-200 or 620-211 must be taken simultaneously.

Semester

Contact

Subject Description

This subject introduces the classification and principles governing the solution of the basic first and second order differential equations; and the principles of Newtonian mechanics and its application in single particle and simple rigid body motions and in coupled vibrating systems.

Students completing the subject develop the ability to classify and solve with accuracy and confidence the basic differential equations of first and second order and to understand the action of forces in mechanical systems and translate that understanding into mathematical formulation of physical problems.

This subject demonstrates the power of differential equation modelling in advancing an understanding of complex physical processes from a wide variety of real world phenomena.

Differential equations: first-order differential equations (linear via integrating factors, separable and homogeneous) and applications; linear differential equations with constant coefficients, particular integrals and complementary functions. Mechanics: kinematics; Newton's laws, projectiles, constrained motion of a particle; systems of particles; motion of a rigid body; impulse problems. Systems of differential equations: systems of linear differential equations with constant coefficients, applications of matrix methods, stability; equilibrium and stability of conservative systems, small oscillations; first-order autonomous nonlinear systems and the phase plane.

Assessment

Up to 24 pages of written assignments and a three-hour end-of-semester written examination.