Integral Transforms

Cod y Modiwl
MA33310
Teitl y Modiwl
Integral Transforms
Blwyddyn Academaidd
2026/2027
Semester
Semester 1
Cyd-gysylltydd y Modiwl
Dr Daniel Peck
Rhestr Ddarllen
Gweld ar Aspire
Rhagofynion
MA21510 neu MT21510
Anghymharus (Unrhyw Flwyddyn Acad)
MAM3320
Staff Eraill sy'n Cyfrannu
Dr Daniel Peck

Dulliau Asesu

Math o Asesiad

Manylion Asesiad

Cyfran
Arholiad Semester Written Examination: 2 Awr 100%
Arholiad Ailsefyll Written Examination: 2 Awr 100%

Canlyniadau Dysgu

Wedi cwblhau'r modiwl dylai'r myfyrwyr fedru:

  1. Construct various integral transforms and be able to define Fourier, Laplace and Mellin transforms
  2. State the main properties of these three transforms and evaluate their inverses
  3. Make use of the transforms to solve linear ODEs and PDEs

Disgrifiad cryno

In their original formulation, many problems in mathematics appear intractable. The application of an integral transform to an equation often acts to simplify its solution. This module will explain the basic ideas behind integral transforms, generalizing the idea of Fourier transforms to include Laplace and Mellin transforms. Their use will be demonstrated in the solution of both ordinary and partial differential equations. The idea of generalized functions will be introduced, and their properties and applications described.

Cynnwys

• Brief description of complex integration: Cauchy's theorem, the residue theorem. Principal value integrals. Computations of standard integrals using contour integrals.
• Distributions and the Dirac delta function.
• The Fourier transform. Linearity, dilation, translation, convolution, derivatives, the inversion formula.
• The Laplace transform. Linearity, dilation, convolution, derivatives, the inversion formula.
• The Mellin transform. Linearity, dilation, convolution, derivatives, the inversion formula.
• Applications of integral transforms to (partial) differential equations, integral equations, difference equations, solid and fluid mechanics.

Sgiliau Modiwl

Math o Sgiliau

Manylion Sgiliau
Cyfathrebu Written answers to questions must be clear and well-structured, and should communicate students’ understanding
Datrys Problemau Throughout
Gwaith Tim Students will be encouraged to work together on questions in workshops and on Example sheets.
Gwella dysgu a pherfformiad ei hun Students are expected to develop their own approach to time-management regarding the completion of Example sheets on time, assimilation of feedback, and preparation between lectures.
Rhifedd Throughout
Sgiliau pwnc penodol Students will be encouraged to independently find and assimilate useful resources.
Technoleg Gwybodaeth Use of blackboard

Nodau

Mae'r modiwl hwn yn cydymffurfio a FfCChC Lefel 6