Mathematics: Linear Analysis

Education facts

Code: MATB34

<p>The course introduces fundamental concepts, results, and methods in Fourier analysis and aims for students to develop an understanding of and ability to apply these to describe, analyze, and solve relevant problems related to linear analysis. Furthermore, the course aims to prepare students for further studies in mathematics, natural sciences, and engineering.</p><p>The course treats:</p> <ul> <li>Basic properties of Fourier series of functions in one variable. Exponential form and trigonometric form. Riemann-Lebesgue lemma. Elementary conditions for pointwise and uniform convergence. Gibbs phenomenon.</li> <li>Basic properties of convolutions of periodic functions in one variable. Interaction with Fourier series. Convolution kernels and their applications in summing Fourier series. Fejér’s theorem and Weierstrass approximation theorem.</li> <li>Linear spaces and examples of linear operators. Vector norm, inner product, and Cauchy-Schwarz inequality. Hilbert space, minimum distance to closed convex sets, projection theorem. Orthonormal systems, Bessel’s inequality, and Parseval’s identity. Completeness of the Fourier system.</li> <li>Basic properties of Fourier transforms of functions in one variable. Interaction with translation, modulation, scaling, differentiation and convolution. Laplace transforms. Elementary conditions for pointwise convergence of the inverse Fourier transform. Some information on Schwartz functions and Plancherel’s identity.</li> <li>Applications towards classical partial differential equations such as the heat equation, wave equation, and Dirichlet problem in simple domains. Method of separation of variables.</li> </ul><p>https://maths.lu.se/english/education/</p>

Entry requirements

The course requires basic knowledge in analysis in one and several variables and linear algebra, corresponding to, for example: MATA31Analysis in One Variable, 15 credits MATA32 Algebra and Vector Geometry, 7,5 credits MATB21 Analysis in Several Variables, 7,5 credits MATB32 Linear Algebra, 7,5 credits Additionally, knowledge equivalent to MATB33 Mathematics: Introduction to Higher Analysis, 7.5 credits, or FYSB21 : Mathematical Methods for Vibrations, Waves and Diffusion, 7.5 credits, is required.

Education offerings

Each offering has its own dates and conditions. Closed offerings are retained as history and do not mean that a new application is open.

• Mathematics: Linear Analysis

  Lund University

  Start date: 19 January 2026

  End date: 22 March 2026

  Pace of study: 50 %