Chapter 1. Topology
Chapter 2. Hilbert Spaces
Chapter 3. Fourier Analysis
Chapter 4. Complex Analysis: Hands On
Chapter 5. Understanding Differential Equations
Chapter 6. Solving Differential Equations
Chapter 7. Differential Geometry and Tensors
Chapter 8. The Rotation Group, Lorentz Group and Lie Groups
Chapter 9. Probability and Random Variables
Chapter 10. Probability Distributions in Physics
Chapter 11. The Statistical Detection of Signals in Noisy Data

Modern mathematics has become an essential part of today’s physicist’s arsenal and this book covers several relevant such topics. The primary aim of this book is to present key mathematical concepts in an intuitive way with the help of geometrical and numerical methods - understanding is the key. Not all differential equations can be solved with standard techniques. Examples illustrate how geometrical insights and numerical methods are useful in understanding differential equations in general but are indispensable when extracting relevant information from equations that do not yield to standard methods. --- Summary provided by publisher