This course provides an in depth exposition of the theory of differential equations and vector calculus. Applications will be related to problems mainly from the Physical Sciences.

Topics to be covered include:

Ordinary Differential Equations - Linear and non-linear first order differential equations; second order linear equations; initial and boundary value problems; Green's functions; power series solutions and special functions; systems of first and second order equations; normal modes of oscillation; nonlinear differential equations; stability of solutions; existence and uniqueness of solutions;

Advanced Vector Calculus - Curves and surfaces in three dimensions; parametric representations; curvilinear coordinate systems; Surface and volume integrals; use of Jacobians; gradient, divergence and curl; identities involving vector differential operators; the Laplacian; Green’s and Stokes’ theorems.

Note: This is an HPC, taught at a level requiring greater conceptual understanding than MATH2305.

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Explain the fundamental concepts of differential equations and vector calculus and their role in modern mathematics and applied contexts.
2. Demonstrate accurate and efficient use of techniques involved in solving differential equations and applying vector differential operators.
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from the theory of differential equations.
4. Apply problem-solving using techniques in differential equations and vector calculus in diverse situations in physics, engineering and other mathematical contexts.

Assessment will be based on:

• Eight assignments (25% in total; LO 1-4)
• Mid-semester test (25%; LO 1-4)
• Final examination (50%; LO 1-4)

48 lectures and 10 tutorials

MATH1116; or a mark of 70 or more in MATH1014.

MATH2014, MATH2114, MATH3109, MATH3209, MATH2305 and ENGN2212.