Mathematik

This four-color textbook provides a vivid picture of the entire mathematics for users in a single volume. Aspiring engineers and scientists will find the important concepts and terms explained in detail with many examples. The focus is on understanding the interconnections and mastering calculation techniques.

Outstanding features include:

• Consistently four-color layout with over 1500 illustrations
• Concisely formulated core ideas serve as section headings
• Self-tests at short intervals allow for learning control while reading
• Colored highlight boxes emphasize the most important points
• More than 100 application boxes explain topics such as geometry behind GPS, page ranking at Google, or harmonic oscillators
• Deepening boxes provide an outlook on advanced topics
• Summaries for each chapter as well as overview boxes
• Over 750 comprehension questions, calculation tasks, and application problems with numerous MATLAB® and R examples

The content spans from elementary foundations through the analysis of a single variable, linear algebra, the analysis of multiple variables, to advanced topics in analysis that are particularly important for application, such as partial differential equations, Fourier series, and Laplace transformations. Numerical concepts are an integral part of the chapters. Probability theory and statistics is one of the six parts of the book.

Notes, solution paths, and results for all exercises in the book are available as PDF files on the publisher's website. This book will be a long-term reliable companion for all users of mathematics, from the beginning of their studies through advanced semesters to professional practice. The present 5th edition includes more than 400 flashcards (Springer-Nature-Flashcards-App), which can help you improve both your understanding of the theory and your calculation skills in preparation for exams.