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 1II. SERIES EXPANSION OF ARBITRARY FUNCTIONS 48III. LINEAR INTEGRAL EQUATIONS 112IV. THE CALCULUS OF VARIATIONS 164V. VIBRATION AND EIGENVALUE PROBLEMS 275VI. APPLICATION OF THE CALCULUS OF VARIATIONS TO EIGENVALUE PROBLEMS 397VII. SPECIAL FUNCTIONS DEFINED BY EIGENVALUE PROBLEMS 466Additional Bibliography 546Index 551
