160318

Differential Equations II

An advanced course in the analytical and numerical study of ordinary and partial differential equations, building on techniques developed in Differential Equations I. Ordinary differential equations: power series and Frobenius series solutions, special functions, Fourier series, Sturm-Liouville problems, qualitative analysis of nonlinear systems. Partial differential equations: classification of second-order equations, separation of variables, Fourier transforms, explicit and implicit numerical schemes.

Course code

Qualifications are made up of courses. Some universities call these papers. Each course is numbered using six digits.

160318

Level

The fourth number of the course code shows the level of the course. For example, in course 219206, the fourth number is a 2, so it is a 200-level course (usually studied in the second year of full-time study).

300-level

Credits

Each course is worth a number of credits. You combine courses (credits) to meet the total number of credits needed for your qualification.

15

Subject

Mathematics

Course planning information

Prerequisite courses

Complete first

You need to complete the above course or courses before moving onto this one.

General progression requirements

You must complete at least 45 credits from 200-level before enrolling in 300-level courses.

Learning outcomes

What you will learn. Knowledge, skills and attitudes you’ll be able to show as a result of successfully finishing this course.

  • 1 Construct power series and Frobenius series solutions to ordinary differential equations.
  • 2 Use solutions to Sturm-Liouville boundary value problems to construct series such as Fourier series.
  • 3 Analyse nonlinear dynamics of systems of ordinary differential equations.
  • 4 Use separation of variables to solve hyperbolic, elliptic, and parabolic partial differential equation boundary value problems.
  • 5 Construct Fourier transforms and use them to solve partial differential equations.
  • 6 Apply explicit and implicit schemes to numerically solve partial differential equations.

Learning outcomes can change before the start of the semester you are studying the course in.

Assessments

Assessment Learning outcomes assessed Weighting
Written Assignment 1 2 3 4 5 6 25%
Test 1 2 3 4 5 6 25%
Test 1 2 3 4 5 6 25%
Exam (centrally scheduled) 1 2 3 4 5 6 25%

Assessment weightings can change up to the start of the semester the course is delivered in.

You may need to take more assessments depending on where, how, and when you choose to take this course.

Explanation of assessment types

Computer programmes
Computer animation and screening, design, programming, models and other computer work.
Creative compositions
Animations, films, models, textiles, websites, and other compositions.
Exam College or GRS-based (not centrally scheduled)
An exam scheduled by a college or the Graduate Research School (GRS). The exam could be online, oral, field, practical skills, written exams or another format.
Exam (centrally scheduled)
An exam scheduled by Assessment Services (centrally) – you’ll usually be told when and where the exam is through the student portal.
Oral or performance or presentation
Debates, demonstrations, exhibitions, interviews, oral proposals, role play, speech and other performances or presentations.
Participation
You may be assessed on your participation in activities such as online fora, laboratories, debates, tutorials, exercises, seminars, and so on.
Portfolio
Creative, learning, online, narrative, photographic, written, and other portfolios.
Practical or placement
Field trips, field work, placements, seminars, workshops, voluntary work, and other activities.
Simulation
Technology-based or experience-based simulations.
Test
Laboratory, online, multi-choice, short answer, spoken, and other tests – arranged by the school.
Written assignment
Essays, group or individual projects, proposals, reports, reviews, writing exercises, and other written assignments.

Textbooks needed

Textbooks can change. We recommend you wait until at least seven weeks before the semester starts to buy your textbooks.

Recommended

DIFFERENTIAL EQUATIONS WITH BOUNDARY VALUE PROBLEMS

Author
D.G. ZILL, W.S.WRIGHT
ISBN
9781337559881
Edition
9TH (2017)
Publisher
BROOKS COLE

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