618-132 Applied Mathematics (Advanced)

Note:

1. Students may not gain credit for both 618-132 and 618-130.

2. Students who have obtained a result of H3 or better in 618-101 (1995 Handbook) or 618-121 may ask for permission to enter 618-132.

Credit Points:

Coordinator:

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Timetable:

Contact:

Objectives:

On completion of this subject, students should:

Comprehend:

• the classification and principles governing the solution of the basic first and second order differential equations;

• the range of calculus skills and techniques necessary for the solution of these differential equations, and the solution methods applicable to each type;

• the mathematical formulation of physical problems and their solution via the above techniques;

• the principles of Newtonian mechanics and its application in single particle and simple rigid body motions and in coupled vibrating systems.

Have developed:

• the ability to classify and solve the basic differential equations of first and second order; the integral and differential calculus skills to achieve these solutions with accuracy and confidence;

• a sound understanding of the action of forces in mechanical systems and the translation of that understanding into mathematical formulation of physical problems.

Appreciate:

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

Content:

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: