Methods of Mathematical Physics, Volume 1

Since the first volume of this work came out in Germany in 1924, this book, together with its second volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's second and final revision of 1953. I. THE ALGEBRA OF LINEAR TRANSFORMATIONS AND QUADRATIC FORMS 1

II. SERIES EXPANSION OF ARBITRARY FUNCTIONS 48

III. LINEAR INTEGRAL EQUATIONS 112

IV. THE CALCULUS OF VARIATIONS 164

V. VIBRATION AND EIGENVALUE PROBLEMS 275

VI. APPLICATION OF THE CALCULUS OF VARIATIONS TO EIGENVALUE PROBLEMS 397

VII. SPECIAL FUNCTIONS DEFINED BY EIGENVALUE PROBLEMS 466

Additional Bibliography 546

Index 551