Course syllabus for Real analysis

The course provides basic knowledge of the fundamental theories within mathematical physics. It also introduces the concept of diversity, equity, and inclusion (DEI) in both theory and practice.  

Understand the basic concepts and definitions in mathematical analysis

To be able to prove the basic theorems in mathematical analysis in one variable

To be able to formulate and solve linear/separable differential equations

To be able to expand analytic functions in Taylor series

To be able to analyze the asymptotics of certain sequences (for instance coming from linear difference equations and iterations schemes)

To be able to establish convergence/divergence of series using various tests/criteria.

To be able to establish convergence/divergence of power series.

To apply the notions of pointwise and uniform convergence for function series

To compute limits of functions in several variables

To be able to produce proofs independently.

To be able to solve problems which involve two or more of the above.

To understand the concepts of diversity, equity, and inclusion (DEI) in theory and in practice. 

Ordinary differential equations: linear equations of the first order, separable equations, linear differential equations of arbitrary order with constant coefficients, systems of equations, some special types such as Euler's differential equation. Mathematical models giving rise to differential equations. Numerical solution of differential equations. Taylor's formula, computation of limits, l'Hospital's rules. Difference equations. Sequences, series, power series, convergence criteria, solution of differential equations by means of power series. Uniform convergence of function sequences and function series. The vector space Rⁿ, polar and spherical coordinates, some topological concepts.  

The 1,5 credit part of the course consists of a  full day workshop with talks from mathematicians working in the industry explaining how they work with mathematics or statistics in their everyday work. During this workshop, guest lectures on DEI are also given, both from industry and academia.

Lectures and exercises, plus a one-day workshop. 

A. Persson, L.-C. Böiers: Analys i en variabel, Studentlitteratur, Lund. A. Persson, L.-C. Böiers: Analys i flera variabler, Studentlitteratur, Lund. Övningar till Analys i en variabel, Matematiska institutionen, Lunds tekniska högskola. Övningar till Analys i flera variabler, Matematiska institutionen, Lunds tekniska högskola. F. Eriksson, E. Larsson, G. Wahde: Matematisk analys med tillämpningar, del 3. OTHER LITERATURE L. Råde, B. Westergren: BETA - Mathematics Handbook, Studentlitteratur, Lund. 

A written examination.  Attendance and participation in the workshop and a brief text summarizing the experience.