Mathematics for Natural Scientists II : Advanced Methods This book covers the advanced mathematical techniques useful for physics and engineering students presented in a form accessible to physics students avoiding precise mathematical jargon and laborious proofs. Instead all proofs are given in a simplified form that is clear and convincing for a physicist. Examples where appropriate are given from physics contexts. Both solved and unsolved problems are provided in each chapter. Mathematics for Natural Scientists II: Advanced Methods is the second of two volumes. It follows the first volume on Fundamentals and Basics. 1. Elements of linear algebra 2. Complex numbers and functions 3. Fourier series 4. Special Functions 5. Fourier Transform 6. Laplace Transform 7. Curvilinear coordinates 8. Partial differential equations of mathematical physics 9. Calculus of variations.