First order ODE (Existence and uniqueness, separable, exact equations), linear ODE (Existence and Uniqueness, constant coefficient homogenous, variable coefficient homogenous, constant coefficient nonhomogeneous), boundary value problems.
Vectors and the geometry of Space, dot and cross product, equations of lines and planes; Vector Functions, derivatives and integrals of vector functions, velocity and acceleration in space; Partial Derivatives, tangent planes and approximation, chain rule, directional derivatives, maximum and minimum values. Double and Triple Integrals. Vector Fields, Line integrals. Curl and Divergence, Stokes' Theorem. The Divergence Theorem.
This topic aims to equip students with the skills needed to solve engineering problems with several variables and differential equations. These provide the mathematical pre-requisites that the student needs for the second and higher year Engineering topics. The focus is on the application of the mathematical ideas to Engineering problems.