Mathematics for Natural Scientists : Fundamentals and Basics I. Fundamentals Basic Knowledge Functions II. Basics Derivatives Integral Functions of Many Variables: Differentiation Functions of Many Variables: Integration Infinite Numerical and Functional Series Ordinary Differential Equations. This book the first in a two part series covers a course of mathematics tailored specifically for physics engineering and chemistry students at the undergraduate level. It is unique in that it begins with logical concepts of mathematics first encountered at A level and covers them in thorough detail filling in the gaps in students knowledge and reasoning. Then the book aids the leap between A level and university level mathematics with complete proofs provided throughout and all complex mathematical concepts and techniques presented in a clear and transparent manner. Numerous examples and problems (with answers) are given for each section and where appropriate mathematical concepts are illustrated in a physics context. This text gives an invaluable foundation to students and a comprehensive aid to lecturers. 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.