123,123

內(nèi)容簡(jiǎn)介

　　本書的目標(biāo)是發(fā)展一個(gè)關(guān)于振動(dòng)和波的統(tǒng)一的數(shù)學(xué)理論。例子來自離散機(jī)械系統(tǒng)的物理學(xué)，連續(xù)的氣體、流體和彈性固體，電子電路，電磁波，光學(xué)系統(tǒng)，最后是量子力學(xué)系統(tǒng)。假設(shè)本書的讀者對(duì)物理定律有基本的了解，比如他們可能是從標(biāo)準(zhǔn)的兩學(xué)期的介紹性大學(xué)水平的調(diào)查課程中獲得了相關(guān)知識(shí)。我們還假定讀者熟悉大學(xué)水平的數(shù)學(xué)知識(shí)，包括代數(shù)、三角學(xué)、線性代數(shù)、常微分方程和偏微分方程。本書的一個(gè)不同尋常的特征是對(duì)振動(dòng)和波的傳統(tǒng)復(fù)表示的介紹被推遲到了絕對(duì)必要時(shí)（在討論量子力學(xué)波時(shí)）。這樣安排的原因是，盡管振動(dòng)和波的復(fù)表示極大地方便了計(jì)算，但它（至少在最初）是發(fā)展對(duì)此類現(xiàn)象的物理理解的重大障礙。作者認(rèn)為，在嘗試使用更方便、更抽象、更復(fù)雜的表示之前，學(xué)生應(yīng)該先徹底地理解如何用正則三角函數(shù)來表示振動(dòng)和波。本書只討論控制微分方程是線性的那一類振動(dòng)和波。在大多數(shù)物理系統(tǒng)中，這意味著對(duì)相對(duì)低幅度現(xiàn)象的限制。作者抵制住了討論非線性振動(dòng)和波的誘惑，主要是因?yàn)檫@種現(xiàn)象需要用一種與描述線性振動(dòng)和波完全不同的數(shù)學(xué)分析來討論，而本書的重點(diǎn)是主題的數(shù)學(xué)統(tǒng)一性。

作者簡(jiǎn)介

暫缺《振動(dòng)與波：概論（第二版）》作者簡(jiǎn)介

圖書目錄

PrefaceCHAPTER 1 Simple Harmonic Oscillation1.1 Introduction1.2 Mass on Spring1.3 Simple Harmonic Oscillator Equation1.4 LC Circuit1.5 Simple Pendulum1.6 Compound PendulumExercisesCHAPTER 2 Damped and Driven Harmonic Oscillation2.1 Introduction2.2 Damped Harmonic Oscillation2.3 Quality Factor2.4 LCR Circuit2.5 Driven Damped Harmonic Oscillation2.6 Driven LCR Circuit2.7 Transient Oscillator ResponseExercisesCHAPTER 3 Coupled Oscillations3.1 Introduction3.2 Two Spring-Coupled Masses3.3 Two Coupled LC Circuits3.4 Three Spring-Coupled MassesExercisesCHAPTER 4 Transverse Standing Waves4.1 Introduction4.2 Normal Modes of Beaded String4.3 Normal Modes of Uniform String4.4 General Time Evolution of Uniform StringExercisesCHAPTER 5 Longitudinal Standing Waves5.1 Introduction5.2 Spring-Coupled Masses5.3 Longitudinal Waves on Thin Elastic Rod5.4 Sound Waves in Ideal Gas5.5 Fourier AnalysisExercisesCHAPTER6 Traveling Waves6.1 Introduction6.2 Standing Waves in Finite Continuous Medium6.3 Traveling Waves in Infinite Continuous Medium6.4 Wave Interference6.5 Energy Conservation6.6 Transmission Lines6.7 Normal Reflection and Transmission at Interfaces6.8 Electromagnetic Waves6.9 Doppler Effect6.10 Wave Propagation in Inhomogeneous MediaExercisesCHAPTER 7 Multi-Dimensional Waves7.1 Introduction7.2 Plane Waves7.3 Three-Dimensional Wave Equation7.4 Cylindrical Waves7.5 Spherical Waves7.6 Oscillation of an Elastic Sheet7.7 Polarization of Electromagnetic Waves7.8 Laws of Geometric Optics7.9 Fresnel Relations7.10 Total Internal Reflection7.11 Birefringence7.12 Sound Waves in FluidsExercisesCHAPTER 8 Wave Pulses8. l Introduction8.2 Fourier Transforms8.3 Dirac Delta Function8.4 General Solution of 1D Wave Equation8.5 Bandwidth8.6 Bandwidth TheoremExercisesCHAPTER 9 Dispersive Waves9.1 Introduction9.2 Pulse Propagation9.3 Electromagnetic Waves in Unmagnetized Plasmas9.4 Faraday Rotation95 Electromagnetic Waves in Magnetized Plasmas9.6 Low-Frequency EM Waves in Magnetized Plasmas9.7 Parallel EM Waves in Magnetized Plasmas9.8 Perpendicular EM Waves in Magnetized Plasmas9.9 Electromagnetic Waves in Conductors9.10 Waveguides9.11 Pulse Propagation in Two Dimensions9.12 Giavity Waves9.13 Wave Drag on Ships9.14 Ship Wakes9.15 Capillary WavesExercisesCHAPTER 10 Wave Optics10.1 Introduction10.2 Two-Slit Interference10.3 Coherence10.4 Multi-Slit Interference10.5 Thin-Film Interference10.6 One-Dimensional Fourier Optics10.7 Single-Slit Diffraction10.8 Multi-Slit Diffraction10.9 Two-Dimensional Fourier Optics10.10 Huygens-Fresnel Principle10.11 Babinet's Principle10.12 Diffraction from Rectangular Aperture10.13 Diffraction from Straight Edge10.14 Diffraction from Rectangular Slit10.15 Diffraction from Straight Wire10.16 Diffraction from Circular Aperture10.17 Diffraction from Circular DiskExercisesCHAPTER 11 Wave Mechanicsll.l Introduction11.2 Photoelectric Effect11.3 Electron Diffraction11.4 Representation of Waves via Complex Numbers11.5 Schrtidinger's Equation11.6 Probability Interpretation of Wavefunction11.7 Wave Packets11.8 Heisenberg's Uncertainty Principle11.9 Wavefunction Collapse11.10 Stationary States11.11 Particle in Finite Square Potential Well11.12 Square Potential Barrier11.13 WKB Approximation11.14 Cold Emission11.15 Alpha Decay11.16 Three-Dimensional Wave Mechanics11.17 Particle in Box11.18 Degenerate Electron Gas11.19 White-Dwarf StarExercisesBibliographyIndex編輯手記