This textbook takes physics and engineering undergraduates through the mathematics they need in the first years of study. It offers an accessible approach which is characterized by the combination of the textbook with a detailed study guide. This study guide, supplied as freely accessible downloads for each chapter, divides the whole learning task into small units. You will read and study a limited section of the textbook and then return to the study guide afterwards. Learning results are controlled, monitored and deepened by graded questions, exercises, repetitions and finally by problems and applications of the content studied. The degree of difficulty slowly rises, which will let you gain confidence and experience your own progress, thus fostering motivation. The sequence of studies can be individualized according to performance and can be regarded as a full tutorial course. This combination of a textbook with a detailed study guide is a powerful means to meet the rising importance of learning outside of lectures at home and will be of great benefit, especially to students learning remotely.

Prof. Dr. Klaus Weltner (1927-2020) studied physics at the Technical University Hannover (Germany) and the University of Bristol (England). He graduated in plasma physics and was professor of physics and didactic of physics at the universities Osnabrück, Berlin, Frankfurt and visiting professor of physics at the Federal University of Bahia (Brazil).Prof. Dr. Jean Grosjean was Head of Applied Mechanics at the School of Engineering at the University of Bath (England).Wolfgang J. Weber studied mathematics at the Universities of Frankfurt (Germany), Oxford (England) and Michigan State (USA). He is currently responsible for the training of computer specialists at the computing center at the University of Frankfurt.Dr.-Ing. Peter Schuster was lecturer at the School of Engineering at the University of Bath (England). Different appointments in the chemical industry.Dr. S. T. John completed a Ph.D. in Physics at the University of Cambridge (England) and has been working in probabilistic machine learning research both in industry and academia.