Boundary value problems for elliptic systems

Part I. A Spectral Theory of Matrix Polynormials: 1. Matrix polynomials 2. Spectral triples for matrix polynomials 3. Monic matrix polynomials 4. Further results Part II. Manifolds and Vector Bundles: 5. Manifolds and vector bundles 6. Differential forms Part III. Pseudo-Differential Operators and Elliptic Boundary Value Problems: 7. Pseudo-differential operators on Rn 8. Pseudo-differential operators on a compact manifold 9. Elliptic systems on bounded domains in Rn Part IV. Reduction Of A Boundary Value Problem To An Elliptic System On The Boundary: 10. Understanding the L-condition 11. Applications to the index 12. BVPs for ordinary differential operators and the connection with spectral triples 13. Behaviour of a pseudo-differential operator near a boundary 14. The Main Theorem revisited Part V. An Index Formula For Elliptic Boundary Problems In The Plane: 15. Further results on the Lopatinskii Condition 16. The index in the plane 17. Elliptic systems with 2 x 2 real coefficients.