Part II of our book series Matematisk analys & linjär algebra (Mathematical analysis & linear algebra) is now available in book stores (and has been for some time). It’s great to finally see the book in the book store after long and hard work! The book is co-written with my colleagues Stig Larsson and Axel Målqvist.
The title of the book is Integralkalkyl och ordinära differentialekvationer and deals with integration (the fundamental theorem of calculus) and the closely related subject of integrating ordinary differential equations, including numerical methods for systems of nonlinear ODEs. The book also briefly discusses the finite element method for boundary value problems in 1D.
Here’s a peak at the table of contents:
Just as in the first book in the series, the book has 6 main chapters of theoretical content (including numerical methods which are a natural part of the construction of the mathematical theory), which is then followed by Chapter 7 focusing on applications of the mathematical methods to some interesting problems, including simulation of the solar system and the classic Lotka-Volterra predator-prey ODE system.
Work on the two remaining volumes, dealing with linear algebra (part III) and multivariate calculs & PDE (part IV) are progressing well and my Christmas project this year will be to write the final two chapters of book IV, dealing with discretization (of domains and functions) and the finite element method for solving initial and boundary value problems for PDE. Here’s a sneak peek on work in progress…