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以下是這整個學期將會提及的主題：
A. 波動的物理來源例證
- 緊繃的弦
- 彈性桿件
- 動脈中的血流
- 導管中的聲音
- 彈性基礎上的樑
- 高速公路的車流
- 線性化條件下的淺水長波
- 參觀非破壞性檢測實驗室
B. 一維傳遞
- 通解，動脈裡的分支，阻抗
- 無限場域裡的波、D'Alembert's德藍伯特理論
- 特徵函數
- 半無限場域及反射
- 一無限場域裡的強制波動
- 彈性環境下的弦，頻散
- 群波速及能量傳輸
- 暫態頻散、定常相位法
- 定常相位法
- 諧波的散射及輻射，弱散射
- 長水波由水深不連續引致之強散射
- 輻射條件，Green格林函數
- 一般等式，Green格林定理
- 緩變介質中的反射，WKB近似值法
C. 二維傳遞
- 平面波於介面中的反射與透射
- 複雜波的入射角及反射係數
- 固態平面彈性波，統御方程式
- 無限域中的自由波，平面彈性波
- 平面邊界中的彈性波反射
- P波和SV波
- SH波
- SH波的散射
- 散射中的光學原理
- SH波於圓孔穴的散射
- 線裂痕下的SH波繞射─拋物線近似
- 半平面下的雷利波表面波
- 地表面上移動的線負載所造成的彈性波：超音速、穿音速、次音速
D. 海洋中的波浪
- 線性化方程式
- 定水深之海洋前進波；頻散及流場；水粒子軌跡及能量傳輸
- 二維障礙物下的波阻
- 窄譜下的頻散波；由Schrodinger方程看包絡波。
- 由自由液面的振動線壓力源所強制引發的輻射表面波
- Kelvin船波
- 成層流體的內波；頻散關係
- 非侷限流的內波，St. Andrew's Cross
E. 隨機介質中的頻散波
依據同學興趣及時間，我們可能探討
F. 波通過夾層介質
或
G. 非線性波
- 交通量波動、綠燈及紅燈
- 震波及交通擁塞
- 湧浪及水躍
- 潰壩下的湧浪
The following topics will be covered throughout the semester:
A. Sample Physical Origins of Wave Motion
- Taut String
- Elastic Rod
- Blood Flow in Arteries
- Sound in a Pipe
- Beam on an elastic foundation
- Traffic Flow on a Freeway
- Long Waves in Shallow Seas, Linearization
- Visit to the Nondestructive Evaluation Laboratory
B. One dimensional propagation
- General Solution, Branching of Arteries, Impedance
- Waves in an Infinite Domain, D'Alembert's Theory
- Characteristics
- Semi-infinite Domain and Reflection
- Forced Waves in an Infinite Domain
- String in an Elastic Surrounding, Dispersion
- Group Velocity and Energy Transport
- Transient Dispersion, Method of Stationary Phase
- Method of Stationary Phase
- Scattering and Radiation of Harmonic Waves, Weak Scattering
- Strong Scattering of Long Water Waves by Depth Discontinuity
- Radiation Condition, Green's Function
- General Identities, Green Theorem
- Reflection in a Slowly Varying Medium, WKB Approximation
C. Two dimensional propagation
- Reflection and Transmission of Plane Waves at an Interface
- Angle of Incidence, Reflection coefficient in the Complex Wave
- Elastic Wave in Solid, Governing Equations
- Free Waves in Infinite Space, Plane Elastic Waves
- Reflection of Elastic Waves from a plane boundary
- P and SV waves
- SH Waves
- Scattering of SH waves
- The Optical Theorem on Scattering
- Scattering of SH Waves by a Circular Cavity
- Diffraction of SH Waves by a line crack - Parabolic Approximation
- Rayleigh Surface Waves in a Half Space
- Elastics Waves due to a line load traveling on a the Ground Surface. Supersonic, Transonic, and Subsonic
D. Waves in the sea
- Linearized Equations
- Progressive Waves in Sea of Constant Depth. Dispersion and Flow Field. Particle Orbit and Energy Transport
- Wave Resistance of a Two Dimensional Obstacle
- Narrow banded dispersive waves. The Schrodinger equation for the Wave Envelope.
- Radiation of Surface Waves Forced by an Oscillating Line Pressure on the Surface.
- Kelvin Ship Waves
- Internal Waves in a Stratified Fluid. Dispersion Relation.
- Internal Waves in an Unbounded Fluid, St. Andrew's Cross
E. Dispersive Waves in Random Media
Depending on class interest and time we may discuss
F. Waves through laminated media
- Effective Equation for Thin Laminates
- Effective Equation for Thick Laminates
or
G. Nonlinear waves
- Traffic Waves. Green and Red Lights.
- Shocks and Traffic Jam
- Bores and Hydraulic Jumps
- Bore from the Breaking of a Dam
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