1. Introduction -- 2. Power series -- 3. Spherial and cylindrical coordinates -- 4. The gradient -- 5. The divergence of a vector field -- 6. The curl of a vector field -- 7. The theorem of Gauss -- 8. The theorem of Stokes -- 9. The Laplacian -- 10. Conservation laws -- 11. Scale analysis -- 12. Linear algebra -- 13. The Dirac delta function -- 14. Fourier analysis -- 15. Analytic functions -- 16. Complex integration -- 17. Green's functions: principles -- 18. Green's functions: examples -- 19. Normal modes -- 20. Potential theory -- 21. Cartesian tensors -- 22. Perturbation theory -- 23. Epilogue, on power and knowledge

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