Mathematics for Engineers I: Basic Calculus

The three books are part of a four-volume textbook on Engineering Mathematics for undergraduates. The organization of each of the volumes is done in a systematic way so that students will find an easy approach to mathematics. Students and lecturers will find more material in the volumes than a traditional lecture will be able to cover. Lecturers will select their own material for their needs and purposes to conduct their lecture to students. For students the volumes are helpful for their studies at home and for their preparation for exams. In addition the books may be also useful for private study and continuing education in mathematics. The large number of examples, applications, and comments should help the student to strengthen his knowledge. The volumes are organized as follows: Volume I treats basic calculus with differential- and integral calculus of single valued functions. We use a systematic approach following a bottom up strategy to introduce the different terms needed. Volume II covers series and sequences and first order differential equations as a calculus part. The second part of the volume is related to linear algebra. Volume III (prepared for July 2010) treats vector calculus and differential equations of higher order. In Volume IV we use the material of the previous volumes in numerical applications. The text uses Mathematica as a tool to discuss and to solve examples from mathematics. The basic use of this language is demonstrated by examples.