This textbook places particular emphasis on a motivating and well-founded presentation, as well as on a reader-guided development of a field that is especially important for applications in physics. Clear and concise formulations facilitate optimal understanding of the material, even for self-study and exams. The text focuses on what is truly essential for the study. This widely read and proven book, now presented in its 5th completely revised edition, is based on the author's many years of practical experience in teaching this application-rich mathematical content to students. Only minimal physics knowledge is required, as this textbook is intended specifically to train for use in physics. Concrete suggestions are often provided on how the topics being studied can be applied.