Web course

In engineering mathematics for PhD-Students

Preface – A basic course in applied mathematics

These Lecture notes are mainly based on the following course book, where additional information can be found:

J. D. Logan, 1987. Applied Mathematics: A Contemporary Approach, John Wiley & Sons, New York.


IMPORTANT: These lecture notes should not be published in any format (even on other homepages, Department´s homepages, etc.) without permission  by me, Professor David Logan and the publishing company Wiley.

Remark:  There exists also a 3rd edition of the book of Professor Logan published in 2006. It has a new chapter on discrete models (with applications in biology) and a little more general approach.


I. Introduction to dimensional analysis and scaling.

II. Introduction to perturbation methods.

III. Introduction to the calculus of variations.

IV. Introduction to the theory of partial differential equations.

V. Introduction to Sturm-­Liouville theory, the theory for the corresponding generalized Fourier series and some further methods for solving PDE.

VI. Introduction to transform theory with applications.

VII. Introduction to Hamiltonian theory and isoperimetric problems.

VIII. Introduction to the theory of integral equations.

IX. Introduction to the theory of dynamical systems, chaos, stability and bifurcations.

X. Introduction to discrete mathematics.

Downloadable materials:

Lecture 1
Lecture 2
Lecture 3
Lecture 4
Lecture 5
Lecture 6
Lecture 7
Lecture 8
Lecture 9
Lecture 10