"Applied Mathematics: Body and Soul" is a comprehensive textbook developed as part of an educational reform project at Chalmers University of Technology. It offers an innovative approach to mathematics inspired by the capabilities of computer technology. The book combines mathematical analysis, numerical calculations, and their applications, targeting students in engineering and natural sciences. The first three volumes present a modern version of analysis and linear algebra, supplemented by constructive and numerical techniques. Subsequent volumes cover advanced topics such as dynamic systems, fluid dynamics, solid mechanics, and electromagnetism, suitable for undergraduate and graduate students. The authors are leading researchers in the field of Computational Mathematics and have published numerous successful works.