Are matrices and indices causing you fear and dread? Is integration in curved coordinates a book sealed with seven seals? And is the meaning of Stokes' theorem for electrodynamics also a mystery? Then this textbook is the perfect companion for you! The computational techniques you need in the first semesters of your physics studies are introduced here in an engaging way and demonstrated through numerous entertaining examples. The author also points out typical pitfalls and useful tricks, incorporating his own experiences as a student, tutor, and exercise leader. Important calculations are fully written out, and mathematical proofs are deliberately omitted. First, the most important mathematical foundations are presented: vectors, matrices, complex numbers, derivatives, integrals, differential equations, and vector analysis.