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振動與波:概論:an introduction:英文 版權信息
- ISBN:9787576709438
- 條形碼:9787576709438 ; 978-7-5767-0943-8
- 裝幀:一般膠版紙
- 冊數:暫無
- 重量:暫無
- 所屬分類:>
振動與波:概論:an introduction:英文 內容簡介
本書的目標是發展一個關于振動和波的統一的數學理論。例子來自離散機械系統的物理學,連續的氣體、流體和彈性固體,電子電路,電磁波,光學系統,*后是量子力學系統。 假設本書的讀者對物理定律有基本的了解,比如他們可能是從標準的兩學期的介紹性大學水平的調查課程中獲得了相關知識。我們還假定讀者熟悉大學水平的數學知識,包括代數、三角學、線性代數、常微分方程和偏微分方程。 本書的一個不同尋常的特征是對振動和波的傳統復表示的介紹被推遲到了絕對必要時(在討論量子力學波時)。這樣安排的原因是,盡管振動和波的復表示極大地方便了計算,但它(至少在*初)是發展對此類現象的物理理解的重大障礙。作者認為,在嘗試使用更方便、更抽象、更復雜的表示之前,學生應該先徹底地理解如何用正則三角函數來表示振動和波。 本書只討論控制微分方程是線性的那一類振動和波。在大多數物理系統中,這意味著對相對低幅度現象的限制。作者抵制住了討論非線性振動和波的誘惑,主要是因為這種現象需要用一種與描述線性振動和波完全不同的數學分析來討論,而本書的重點是主題的數學統一性。
振動與波:概論:an introduction:英文 目錄
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
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