# Ordinary and Partial Differential Equations

University of the South Pacific

## Course Description

• ### Course Name

Ordinary and Partial Differential Equations

• ### Host University

University of the South Pacific

Suva, Fiji

Mathematics

• ### Language Level

Taught In English

MA211

• ### Course Level Recommendations

Upper

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• Credits

3 - 4
• Recommended U.S. Semester Credits
3 - 4
• Recommended U.S. Quarter Units
4 - 6
• ### Overview

The subject of differential equations can be described as the study of equations involving derivatives, or more commonly, as the study of change. There is an in-depth coverage of solutions to both the ordinary and the partial differential equations. Modelling real-life changes and then utilising various different techniques in solving these differential equations is the main flavour of this course. In general, the course has a strong emphasis on analytic methods, though qualitative techniques will also be briefly considered where the general properties of solutions are determined without concern for exact behaviour.
Topics
Ordinary Differential Equations: First order ODEs: separable, exact, linear, modelling; second order ODEs: homogeneous, differential operators, nonhomogeneous, modelling, solution by Laplace transforms. Higher order ODEs; systems of ODEs: linear and nonlinear, stability.
Partial Differential Equations: First order PDEs: characteristic curve method; classification of 2nd order PDEs; wave equation: Alanbert`s solution, Fourier series; heat equation: solution by Fourier series, Fourier integrals Dirichlet problem in a disk: Laplacian in polar coordinates. The Poisson`s integral; second order PDEs: separation of variables, Laplace and Fourier transforms.

### Course Disclaimer

Courses and course hours of instruction are subject to change.

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Please note that some courses with locals have recommended prerequisite courses. It is the student's responsibility to consult any recommended prerequisites prior to enrolling in their course.