Kantorovich L. Mathematics for Natural Scientists: Fundamentals and Basics

Springer, 2016. — 526 p. — (Undergraduate Lecture Notes in Physics). — ISBN: 978-1-4939-2785-2, 978-1-4939-2784-5.This book covers a course of mathematics designed primarily for physics and engineering students. It includes all the essential material on mathematical methods, presented in a form accessible to physics students, avoiding precise mathematical jargon and proofs which are comprehensible only to mathematicians. Instead, all proofs are given in a form that is clear and convincing enough for a physicist. Examples, where appropriate, are given from physics contexts. Both solved and unsolved problems are provided in each section of the book.
Mathematics for Natural Scientists: Fundamentals and Basics is the first of two volumes. Advanced topics and their applications in physics are covered in the second volume.Basic Knowledge
Functions
Derivatives
Integral
Functions of Many Variables: Differentiation
Functions of Many Variables: Integration
Infinite Numerical and Functional Series
Ordinary Differential Equations