FOREWORD ...................................................... vii
INTRODUCTION .................................................... 1
CHAPTER I. HOMOLOGICAL ALGEBRA ............................... 49
CHAPTER II. JET THEORY ........................................ 61
A. Fibered Operations .......................................... 61
B. Jet Bundles ................................................. 70
CHAPTER III. NONLINEAR SYSTEMS ................................. 81
A. Prolongations ............................................... 81
B. Spencer Cohomology .......................................... 86
C. Formal Integrability ........................................ 94
D. Examples ................................................... 102
CHAPTER IV. LINEAR SYSTEMS ................................... 139
A. Linear Sequences ........................................... 139
B. Algebraic Properties ....................................... 155
C. Examples ................................................... 160
CHAPTER V. GROUP THEORY ..................................... 177
A. Groups and Algebras ........................................ 177
B. Groupoids and Algebroids ................................... 191
C. Differential Invariants .................................... 202
D. Nonlinear Sequences ........................................ 207
E. Examples ................................................... 225
CHAPTER VI. DIFFERENTIAL GALOIS THEORY ....................... 259
A. Pure Algebra ............................................... 259
B. Differential Algebra ....................................... 272
С Automorphic Systems ......................................... 281
D. Cascade Integration ........................................ 289
E. Examples ................................................... 300
CHAPTER VII. CONTROL THEORY ................................... 319
A. Ordinary Differential Control Theory ....................... 319
B. Partial Differential Control Theory ........................ 336
С. Examples ................................................... 347
CHAPTER VIII CONTINUUM PHYSICS ................................ 391
A. Variational Calculus ....................................... 401
B. Elasticity ................................................. 418
C. Heat ....................................................... 428
D. Electromagnetism ........................................... 433
E. Gravitation ................................................ 444
BIBLIOGRAPHY .................................................. 457
INDEX ......................................................... 469
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