Main Field of Study and progress level:
Mathematics: First cycle, has less than 60 credits in first-cycle course/s as entry requirements
Grading scale: Pass with distinction, Pass with merit, Pass, Pass with distinction, Pass, Fail
Responsible department: Department of Mathematics and Mathematical Statistics
Established by: Faculty Board of Science and Technology, 2024-09-19
Revised by: Faculty Board of Science and Technology, 2024-09-19
Contents
Module 1 (6.5 credits): Introduction to differential equations In the module, first-order ordinary differential equations (separable equations and integrating factor) and second-order ordinary differential equations (with constant coefficients and forcing functions) are dealt with. In addition, the phase plane, qualitative analyses, and the Laplace transform are included. Furthermore, the solution of linear systems of ordinary differential equations is studied using matrix methods and linearization with a focus on understanding system dynamics. Finally, an introduction to the solution of partial differential equations with separation of variables and Fourier series is given.
Module 2 (1 credit): Computer lab Lab that illustrates the concepts and demonstrates different numerical methods for solving ordinary differential equations of the types included in the course. In connection with the computer laboratory, an introduction to software for the numerical solution of differential equations is given.
Expected learning outcomes
For a passing grade, the student must be able to
Knowledge and understanding
account for the existence and uniqueness of solutions to ordinary differential equations
account for and apply variable separation to solve partial differential equations
calculate and account for properties of trigonometric Fourier series
Skills and abilities
apply the methods in the course to solve ordinary differential equations of order one and two
apply methods to solve and characterize the dynamics of linear systems of ordinary differential equations
solve nonhomogeneous differential equations using methods such as Laplace transforms and the method of undetermined coefficients
apply ordinary differential equations to model simpler biological and chemical situations and processes, for example predator-prey systems and systems of chemical reactions
use given computer programs to study and analyze numerical solutions of differential equations
write and modify given computer programs to solve tasks
give written accounts of solutions to given laboratory tasks
Form of instruction
The teaching on the course consists of lectures, exercise classes and supervision of computer labs.
Examination modes
Module 1 is assessed through written examination. Module 2 is assessed through written laboratory reports. On written tests, one of the following judgements is given: Fail (U), Pass (3), Pass without distinction (4) or Pass with distinction (5). On laboratory reports, only one of the judgements Fail (U) and Pass (G) is given. In order to be approved for the course, it is required that all tests and mandatory elements are approved. For the whole course one of the grades Fail (U), Pass (3), Pass without honors (4) or Pass with honors (5) is given, and the grade is determined by the assessment on part 1.
A student who has been awarded a passing grade for the course cannot be reassessed for a higher grade. Students who do not pass a test or examination on the original date are given another date to retake the examination. A student who has sat two examinations for a course or a part of a course, without passing either examination, has the right to have anotherexaminer appointed, provided there are no specific reasons for not doing so (Chapter 6, Section 22, HEO). The request fora new examiner is made to the Head of the Department of Mathematics and Mathematical Statistics. Examinations basedon this course syllabus are guaranteed to be offered for two years after the date of the student's first registration for the course.
Examiners may decide to deviate from the modes of assessment in the course syllabus. Individual adaption of modes of assessment must give due consideration to the student's needs. The adaption of modes of assessment must remain within the framework of the intended learning outcomes in the course syllabus. Students who require an adapted examination must submit a request to the department holding the course no later than 10 days before the examination. The examiner decides on the adaption of the examination, after which the student will be notified.
Credit transfer All students have the right to have their previous education or equivalent, and their working life experience evaluated for possible consideration in the corresponding education at Umeå university. Application forms should be addressed to Student services/Degree evaluation office. More information regarding credit transfer can be found on the student webpages of Umeå university, http://www.student.umu.se, and in the Higher Education Ordinance (chapter 6). If denied, the application can be appealed (as per the Higher Education Ordinance, chapter 12) to Överklagandenämnden förhögskolan. This includes partially denied applications
Other regulations
In a degree, this course may not be included together with another course with a similar content. If unsure, students should ask the Director of Studies in Mathematics and Mathematical Statistics
In the event that the syllabus ceases to apply or undergoes major changes, students are guaranteed at least three examinations (including the regular examination opportunity) according to the regulations in the syllabus that the student was originally registered on for a period of a maximum of two years from the time that the previous syllabus ceased to apply or that the course ended.
