Handbook

This course builds upon students’ studies on first-order ordinary and second order ordinary differential equations with constant coefficients from their first-year mathematics courses. In this course, students explore second-order ordinary differential equations with variable coefficients and, in addition, are introduced to partial differential equations. An investigation of boundary value problems is conducted, and these problems are contrasted with the initial value problems. Not all differential equations can be solved in terms of known functions such as polynomials and exponentials and the like. At the completion of the course, students will understand how to get information about the solution in these cases using power series methods and the Frobenius method. They will also understand how to find solutions to boundary value problems in 1D using Sturm-Liouville methods and Fourier series methods, and find solutions to boundary value problems in 2D using Elliptic differential operators, Green identities, Elliptic eigenproblems and Wave and diffusion equations.

This course is a prerequisite for the third year courses MATH3121 Mathematical Methods and Partial Differential Equations, MATH3120 Dynamical Systems and Chaos, and MATH3261 Fluids, Oceans and Climates.

All content of MATH2121 is common to MATH2221, but presented in greater depth, and with some additional topics. Instruction consists of four hours of lecture per week together with one hour of tutorial per week. Both lecture and tutorial instruction are delivered face-to-face.