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  • ISBN:9787576709438
  • 装帧:一般胶版纸
  • 册数:暂无
  • 重量:暂无
  • 开本:25cm
  • 页数:307页
  • 出版时间:2024-01-01
  • 条形码:9787576709438 ; 978-7-5767-0943-8

内容简介

本书的目标是发展一个关于振动和波的统一的数学理论。例子来自离散机械系统的物理学,连续的气体、流体和弹性固体,电子电路,电磁波,光学系统,*后是量子力学系统。 假设本书的读者对物理定律有基本的了解,比如他们可能是从标准的两学期的介绍性大学水平的调查课程中获得了相关知识。我们还假定读者熟悉大学水平的数学知识,包括代数、三角学、线性代数、常微分方程和偏微分方程。 本书的一个不同寻常的特征是对振动和波的传统复表示的介绍被推迟到了绝对必要时(在讨论量子力学波时)。这样安排的原因是,尽管振动和波的复表示极大地方便了计算,但它(至少在*初)是发展对此类现象的物理理解的重大障碍。作者认为,在尝试使用更方便、更抽象、更复杂的表示之前,学生应该先彻底地理解如何用正则三角函数来表示振动和波。 本书只讨论控制微分方程是线性的那一类振动和波。在大多数物理系统中,这意味着对相对低幅度现象的限制。作者抵制住了讨论非线性振动和波的诱惑,主要是因为这种现象需要用一种与描述线性振动和波完全不同的数学分析来讨论,而本书的重点是主题的数学统一性。

目录

Preface CHAPTER 1 Simple Harmonic Oscillation 1.1 Introduction 1.2 Mass on Spring 1.3 Simple Harmonic Oscillator Equation 1.4 LC Circuit 1.5 Simple Pendulum 1.6 Compound Pendulum Exercises CHAPTER 2 Damped and Driven Harmonic Oscillation 2.1 Introduction 2.2 Damped Harmonic Oscillation 2.3 Quality Factor 2.4 LCR Circuit 2.5 Driven Damped Harmonic Oscillation 2.6 Driven LCR Circuit 2.7 Transient Oscillator Response Exercises CHAPTER 3 Coupled Oscillations 3.1 Introduction 3.2 Two Spring-Coupled Masses 3.3 Two Coupled LC Circuits 3.4 Three Spring-Coupled Masses Exercises CHAPTER 4 Transverse Standing Waves 4.1 Introduction 4.2 Normal Modes of Beaded String 4.3 Normal Modes of Uniform String 4.4 General Time Evolution of Uniform String Exercises CHAPTER 5 Longitudinal Standing Waves 5.1 Introduction 5.2 Spring-Coupled Masses 5.3 Longitudinal Waves on Thin Elastic Rod 5.4 Sound Waves in Ideal Gas 5.5 Fourier Analysis Exercises CHAPTER6 Traveling Waves 6.1 Introduction 6.2 Standing Waves in Finite Continuous Medium 6.3 Traveling Waves in Infinite Continuous Medium 6.4 Wave Interference 6.5 Energy Conservation 6.6 Transmission Lines 6.7 Normal Reflection and Transmission at Interfaces 6.8 Electromagnetic Waves 6.9 Doppler Effect 6.10 Wave Propagation in Inhomogeneous Media Exercises CHAPTER 7 Multi-Dimensional Waves 7.1 Introduction 7.2 Plane Waves 7.3 Three-Dimensional Wave Equation 7.4 Cylindrical Waves 7.5 Spherical Waves 7.6 Oscillation of an Elastic Sheet 7.7 Polarization of Electromagnetic Waves 7.8 Laws of Geometric Optics 7.9 Fresnel Relations 7.10 Total Internal Reflection 7.11 Birefringence 7.12 Sound Waves in Fluids Exercises CHAPTER 8 Wave Pulses 8. l Introduction 8.2 Fourier Transforms 8.3 Dirac Delta Function 8.4 General Solution of 1D Wave Equation 8.5 Bandwidth 8.6 Bandwidth Theorem Exercises CHAPTER 9 Dispersive Waves 9.1 Introduction 9.2 Pulse Propagation 9.3 Electromagnetic Waves in Unmagnetized Plasmas 9.4 Faraday Rotation 95 Electromagnetic Waves in Magnetized Plasmas 9.6 Low-Frequency EM Waves in Magnetized Plasmas 9.7 Parallel EM Waves in Magnetized Plasmas 9.8 Perpendicular EM Waves in Magnetized Plasmas 9.9 Electromagnetic Waves in Conductors 9.10 Waveguides 9.11 Pulse Propagation in Two Dimensions 9.12 Giavity Waves 9.13 Wave Drag on Ships 9.14 Ship Wakes 9.15 Capillary Waves Exercises CHAPTER 10 Wave Optics 10.1 Introduction 10.2 Two-Slit Interference 10.3 Coherence 10.4 Multi-Slit Interference 10.5 Thin-Film Interference 10.6 One-Dimensional Fourier Optics 10.7 Single-Slit Diffraction 10.8 Multi-Slit Diffraction 10.9 Two-Dimensional Fourier Optics 10.10 Huygens-Fresnel Principle 10.11 Babinet's Principle 10.12 Diffraction from Rectangular Aperture 10.13 Diffraction from Straight Edge 10.14 Diffraction from Rectangular Slit 10.15 Diffraction from Straight Wire 10.16 Diffraction from Circular Aperture 10.17 Diffraction from Circular Disk Exercises CHAPTER 11 Wave Mechanics ll.l Introduction 11.2 Photoelectric Effect 11.3 Electron Diffraction 11.4 Representation of Waves via Complex Numbers 11.5 Schrtidinger's Equation 11.6 Probability Interpretation of Wavefunction 11.7 Wave Packets 11.8 Heisenberg's Uncertainty Principle 11.9 Wavefunction Collapse 11.10 Stationary States 11.11 Particle in Finite Square Potential Well 11.12 Square Potential Barrier 11.13 WKB Approximation 11.14 Cold Emission 11.15 Alpha Decay 11.16 Three-Dimensional Wave Mechanics 11.17 Particle in Box 11.18 Degenerate Electron Gas 11.19 White-Dwarf Star Exercises Bibliography Index 编辑手记
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