Unit

School Of Computing And Mathematics

Engineering Mathematics 2Western Sydney University Unit Code: 14506.1

Discipline: MATHEMATICAL SCIENCES

Student Contribution Band: 2

Level: 1

Credit Points: 10

Prerequisite
14505 Engineering Mathematics 1

About this Unit
Students will not gain credit for this unit and 14504 Mathematics 4. This unit covers the following: firstly, partial derivatives: functions of two or more variables; level curves and level surfaces; limits and continuity; partial differentiation; the chain rule; gradients and directional derivatives; tangent planes and normal lines; higher order derivatives; maxima, minima and saddle points; linear approximations and increment estimates; Lagrange multipliers. Secondly, multiple integrals: double integrals; areas, moment and centres of mass; double integrals, polar form; substitution in double integrals, Jacobians; triple integrals, rectangular coordinates; masses and moments in three dimensions; triple integrals, cylindrical and spherical coordinates; applications. Thirdly, differential equations: first order, first degree separable variables; exact differential equations; linear first order equation; applications of first order differential equations to orthogonal trajectories, electrical circuits; homogeneous linear second order equations; reducible equations; linear second order homogeneous with constant coefficients; differential operators; linear second order, non-homogeneous, constant coefficients, method of undetermined coefficients; application to electrical circuits; equations with variable coefficients; Euler equation; power series solutions; solutions around ordinary points; solutions around singular points, the method of Frobenius; solution of Bessel's and Legendre's equations; the Laplace Transform and the Inverse Laplace Transform; translation theorems; derivatives of a Transform; transforms of derivatives and integrals; the convolution theorem; transforms of periodic functions; applications to solving differential equations.