Πρόκειται για ένα πλήρες και δωρεάν μάθημα για φοιτητές σε τμήματα Μαθηματικών, Φυσικής και Μηχανικών.

We are pleased to make this textbook available online. Published in 1991 and still in print from Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike.

This book is well organized, covers single variable and multivariable calculus in depth, and is rich with applications…

Περιεχόμενα

1. Εισαγωγή. Οι στοιχειώδης συναρτήσεις
2. Ολοκλήρωση
3. Προσεγγίσεις
4. Διανυσματική ανάλυση
5. Διαφορικές εξισώσεις
6. Εφαρμογές

Έκδοση 2008

The book gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations. These equations can number in the millions and are sparse in the sense that each involves only a small number of unknowns. The methods described are iterative, i.e., they provide sequences of approximations that will converge to the solution.

This book discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications.

This final text in the Zakon Series on Mathematics Analysis follows the release of the author’s Basic Concepts of Mathematics and Mathematical Analysis I and completes the material on Real Analysis that is the foundation for later courses in functional analysis, harmonic analysis, probability theory, etc.

Several Complex Variables is a central area of mathematics with strong interactions with partial differential equations, algebraic geometry and differential geometry. The 1995-96 MSRI program on Several Complex Variables emphasized these interactions and concentrated on developments and problems of current interest that capitalize on this interplay of ideas and techniques.

This collection provides a remarkably clear and complete picture of the status of research in these overlapping areas at the time of the conference, and will provide a basis for significant continued contributions from researchers as well as an introduction, for students, of the use of techniques from these other areas in several complex variables. Several of the articles are expository or have extensive expository sections, and are accessible to graduate students.

Σημειώσεις για το μάθημα Μαθηματικά II στο Χημικό Τμήμα Πατρών.

Περιέχει τα κεφάλαια:

• Διανυσματική Ανάλυση
• Διανυσματικές Συναρτήσεις
• Πίνακες, Ορίζουσες, Γραμμικά συστήματα
• Σειρές Φουριέ

Οι σημειώσεις αυτές διδάσκονται στο μάθημα Πραγματική Ανάλυση IV του Μαθηματικού Τμήματος Πατρών.

Είναι ασκήσεις που συμπληρώνουν το βιβλίο “Μαθηματική Ανάλυση” του L. Brand.

This book gives a treatment of exterior differential systems. It will include both the general theory and various applications.

An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. When all the forms are linear, it is called a pfaffian system. Our object is to study its integral manifolds, i.e., submanifolds satisfying all the equations of the system. A fundamental fact is that every equation implies the one obtained by exterior differentiation, so that the complete set of equations associated to an exterior differential system constitutes a differential ideal in the algebra of all smooth forms. Thus the theory is coordinate-free and computations typically have an algebraic character; however, even when coordinates are used in intermediate steps, the use of exterior algebra helps to efficiently guide the computations, and as a consequence the treatment adapts well to geometrical and physical problems.