Softcover ISBN:  9780821842324 
Product Code:  CLN/13 
List Price:  $34.00 
MAA Member Price:  $30.60 
AMS Member Price:  $27.20 
Electronic ISBN:  9781470431136 
Product Code:  CLN/13.E 
List Price:  $32.00 
MAA Member Price:  $28.80 
AMS Member Price:  $25.60 

Book DetailsCourant Lecture NotesVolume: 13; 2006; 153 ppMSC: Primary 70; 74; 81; 82;
This book provides a rapid overview of the basic methods and concepts in mechanics for beginning Ph.D. students and advanced undergraduates in applied mathematics or related fields. It is based on a graduate course given in 2006–07 at the Courant Institute of Mathematical Sciences. Among other topics, the book introduces Newton's law, action principles, HamiltonJacobi theory, geometric wave theory, analytical and numerical statistical mechanics, discrete and continuous quantum mechanics, and quantum pathintegral methods.
The focus is on fundamental mathematical methods that provide connections between seemingly unrelated subjects. An example is HamiltonJacobi theory, which appears in the calculus of variations, in Fermat's principle of classical mechanics, and in the geometric theory of dispersive wavetrains. The material is developed in a sequence of simple examples and the book can be used in a onesemester class on classical, statistical, and quantum mechanics. Some familiarity with differential equations is required but otherwise the book is selfcontained. In particular, no previous knowledge of physics is assumed.ReadershipAdvanced undergraduates, graduate students and research mathematicians interested in mechanics, mathematical physics, and applied probability.

Table of Contents

Chapters

Chapter 1. Classical mechanics of discrete systems

Chapter 2. Wave mechanics

Chapter 3. Statistical mechanics

Chapter 4. Quantum mechanics


Additional Material

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This book provides a rapid overview of the basic methods and concepts in mechanics for beginning Ph.D. students and advanced undergraduates in applied mathematics or related fields. It is based on a graduate course given in 2006–07 at the Courant Institute of Mathematical Sciences. Among other topics, the book introduces Newton's law, action principles, HamiltonJacobi theory, geometric wave theory, analytical and numerical statistical mechanics, discrete and continuous quantum mechanics, and quantum pathintegral methods.
The focus is on fundamental mathematical methods that provide connections between seemingly unrelated subjects. An example is HamiltonJacobi theory, which appears in the calculus of variations, in Fermat's principle of classical mechanics, and in the geometric theory of dispersive wavetrains. The material is developed in a sequence of simple examples and the book can be used in a onesemester class on classical, statistical, and quantum mechanics. Some familiarity with differential equations is required but otherwise the book is selfcontained. In particular, no previous knowledge of physics is assumed.
Advanced undergraduates, graduate students and research mathematicians interested in mechanics, mathematical physics, and applied probability.

Chapters

Chapter 1. Classical mechanics of discrete systems

Chapter 2. Wave mechanics

Chapter 3. Statistical mechanics

Chapter 4. Quantum mechanics