Roughly speaking, the book contains a synthesis of calculus and linear algebra including computational methods and a variety of applications. Emphasis is put on constructive/computational methods with the double aim of making the mathematics both understandable and useful.

Our ambition is to introduce the student early to both (from the perspective of traditional education) advanced mathematical concepts (such as Lipschitz continuity, Cauchy sequence, contraction mapping, initial-value problem for systems of differential equations), and advanced applications such as Lagrangian mechanics, n-body systems, population models, elasticity and electrical circuits, with an approach based on constructive/computational methods. The idea is thus that making the student comfortable with both advanced mathematical concepts and modern computational techniques, will open a wealth of possibilities of applying mathematics to problems of real interest.

This is in contrast to the traditional education where the emphasis is usually put on a set of analytical techniques within a conceptual framework of more limited scope. For example: we lead already in the second quarter the student to write (in Matlab) his/her own solver for general systems of ordinary differential equations based on mathematically sound principles (high conceptual and computational level), while traditional education at the same time often focuses on a training the student to master a bag of tricks for symbolic integration. We also teach the student some tricks to that purpose, but our over-all goal is different.

PDF | English | 64 MB

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