Calculus and Linear Algebra in Recipes (PDF)

Have you ever cooked a 3-course meal from a recipe? That generally works out pretty well, even if you're not much of a cook. What does this have to do with mathematics? Well, you can solve a lot of math problems recipe-wise, too: Need to solve a Riccati's differential equation or the singular value decomposition of a matrix? Look it up in this book, you'll find a recipe for it here. Recipes are available for problems in the following topics:

We have tried to summarize these recipes as good and also as understandable as possible in this book.

It is often said that one must understand higher mathematics in order to be able to apply it. We show in this book that understanding also comes naturally by doing: no one learns the grammar of a language from cover to cover if he wants to learn a language. You learn a language by reading up a bit on the grammar and then getting going; you have to speak, make mistakes, have mistakes pointed out to you, know example sentences and recipes, work out topics in tidbits, then it works. In higher mathematics it is no different.

Other features of this book include:

• The division of calculus and linear algebra into approximately 100 chapters of roughly equal length. Each chapter covers approximately the material of a 90-minute lecture.
• Numerous examples.
• Many tasks, the solutions to which can be found in the accompanying workbook.
• Many problems in calculus and linear algebra can be solved with computers. We always indicate how it works with MATLAB®.
• Due to the clear presentation, the book can also be used as an annotated collection of formulas with numerous examples.

Prof. Dr. Christian Karpfinger teaches at the Technical University of Munich; in 2004 he received the State Teaching Award of the Free State of Bavaria.

This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com).