Course code: 09236 Title: Mathematical ModelingCredit rating: 3.0Time: Semester TwoPrerequisites: Mathematics,Linear algebra,computer programme languageSchool responsible: College of Mathematics and Computational Science Assessment: 2 hours end of semester examination; Weighting within unit 80% Brief description:本課程主要介紹用數(shù)學(xué)知識(shí)解決實(shí)際問題的手段建立數(shù)學(xué)模型。通過教學(xué),使學(xué)生掌握數(shù)學(xué)模型的基本知識(shí)；培養(yǎng)學(xué)生認(rèn)識(shí)問題，用數(shù)學(xué)模型和計(jì)算機(jī)分析解決實(shí)際問題的初步能力；增強(qiáng)學(xué)生學(xué)習(xí)數(shù)學(xué)的興趣和自學(xué)的能力，了解數(shù)學(xué)的一些應(yīng)用分支的理論，會(huì)建立相應(yīng)的簡(jiǎn)單模型，并能對(duì)模型進(jìn)行分析。This course mainly introduces the methods of the mathematic knowledge to solve practical problems, by establishing mathematical model. Through teaching , let the students master the basic knowledge of the mathematical model,cultivate the students preliminary ability that how to confront with problem and use mathematical model and computer to analysis and solve practical problems. In addition,it will enhance students interest in learning mathematics and the ability of self-study. Whats more,it will intrigue students to learn some applications of the theory of branch, be able to set up a corresponding simple model, and have capacity to analyze the model.Syllabus1. 建立數(shù)學(xué)模型Build up the mathematical modeling數(shù)學(xué)建模的背景，基本方法和步驟，數(shù)學(xué)模型的特點(diǎn)和分類The background ,basic methods and steps of mathematical modeling,the characteristics and classification of the mathematical model.2. 初等模型Elementary model光盤的數(shù)據(jù)容量，雙層玻璃窗的功效，劃艇比賽的成績(jī)，污水均流池的設(shè)計(jì)，交通流與道路通行能力，核軍備競(jìng)賽，天氣預(yù)報(bào)的評(píng)價(jià)CD data capacity, the effect of double glazing, Rowing match results, the design of the sewage flow pool, traffic flow and road traffic capacity, nuclear arms race, the evaluation of weather forecast3. 簡(jiǎn)單的優(yōu)化模型Simple optimization model存貯模型，生豬的出售時(shí)機(jī)，消費(fèi)者的選擇，生產(chǎn)者的決策，血管分支Storage model, the selling time of live pigs, consumers choice, decision-making of producers, vascular branch.4. 數(shù)學(xué)規(guī)劃模型Mathematical programming model奶制品的生產(chǎn)與銷售，自來(lái)水輸送與貨機(jī)裝運(yùn)，汽車生產(chǎn)與原油采購(gòu)，飲料廠的生產(chǎn)與檢修，鋼管和易拉罐下料Production and sales of dairy products, water transport and cargo shipping, automobile production and crude oil procurement, beverage factory production and maintenance , distribution of steel pipe and cans.5. 微分方程模型Differential equation model傳染病模型，經(jīng)濟(jì)增長(zhǎng)模型，正規(guī)戰(zhàn)與游擊戰(zhàn)，藥物在體內(nèi)的分布與排除，人口的預(yù)測(cè)和控制Infectious disease model, economic growth model, regular war and guerrilla war, the distribution of drug in the body and ruled out, prediction and control of the population.6. 代數(shù)方程與差分方程模型Algebraic equation and difference equation model投入產(chǎn)出模型，原子彈爆炸的能量估計(jì)與量綱分析，市場(chǎng)經(jīng)濟(jì)中的蛛網(wǎng)模型，減肥計(jì)劃Input-output model, the atomic bomb explosion energy estimation and dimensional analysis, the cobweb model of market economy, a weight-loss program.7. 穩(wěn)定性模型Stability of the model軍備競(jìng)賽，差分形式的阻滯增長(zhǎng)模型，微分方程與差分方程穩(wěn)定性理論簡(jiǎn)介An arms race, the differential form of retarding growth model, differential equation and difference equation stability theory.8. 離散模型Discrete model 層次分析模型Hierarchical analysis model.9. 統(tǒng)計(jì)回歸模型The statistical regression model牙膏的銷售量，酶促反應(yīng)，教學(xué)評(píng)估Sales of toothpaste, enzymatic reaction, the teaching evaluationRecommended Textbooks Jiang QI-yuan, Xie Jing-xing,Ye Jun,Mathematical Modelling, Higher Education Press, 2011Course code: 09327 Title: Electromagnetic Field and Electromagnetic waveCredit rating: 3.0Time: Semester ThreeSchool responsible: College of Physics Science and Technological Science Assessment: 2 hours end of semester examination; Weighting within unit 80% Brief description: 本課程使學(xué)生掌握電磁場(chǎng)的有關(guān)定理、定律、麥克斯韋方程等的物理意義及數(shù)學(xué)表達(dá)式。其包括電磁場(chǎng)與電磁波兩部分。電磁場(chǎng)部分是在電磁學(xué)課程的基礎(chǔ)上，運(yùn)用矢量分析的方法，描述靜電場(chǎng)和恒定磁場(chǎng)的基本物理概念，在總結(jié)基本實(shí)驗(yàn)定律的基礎(chǔ)上給出電磁場(chǎng)的基本規(guī)律，研究靜態(tài)場(chǎng)解題方法。電磁波部分主要是介紹有關(guān)電磁波在各種介質(zhì)中的傳播規(guī)律及天線的基本理論。This course makes students master the theorem and the physical meaning of the Maxwell equations and mathematical expressions. It includes the electromagnetic field and electromagnetic wave.Part one is the electromagnetic field .It makes students to learn using the method of vector analysis on the basis of electromagnetism course to describe the essential physical concept of electrostatic field and constant magnetic field, and giving the basic law of electromagnetic field based on summarizing the basic law of experiment, and studying the method to solve problems in the static field. Electromagnetic wave part mainly introduces about the propagation rules of electromagnetic waves in a variety of media and the basic theory of antenna.Syllabus1. 矢量分析Vector analysis矢量代數(shù)，三種常用的正交坐標(biāo)系，標(biāo)量場(chǎng)的梯度，矢量場(chǎng)的通量與散度，矢量場(chǎng)的環(huán)流與旋度，無(wú)旋場(chǎng)與無(wú)散場(chǎng)，拉普拉斯運(yùn)算與格林定理Vector algebra, three kinds of commonly used orthogonal coordinate system, the gradient of a scalar field, vector field flux and the divergence of the vector field of circulation and curl, irrotational field and solenoidal field, Laplace operation with greens theorem.2. 電磁場(chǎng)的基本規(guī)律The basic rule of electromagnetic field電荷守恒定律，真空中靜電場(chǎng)的基本規(guī)律，真空中恒定磁場(chǎng)的基本規(guī)律，媒質(zhì)的電磁特性，電磁感應(yīng)定律和位移電流，麥克斯韋方程組，電磁場(chǎng)的邊界條件Charge conservation law, the basic rule of electrostatic field in vacuum, the basic law of constant magnetic field in vacuum, electromagnetic properties of medium, the law of electromagnetic induction and the displacement current, Maxwells equations, boundary conditions of electromagnetic field.3. 靜態(tài)電磁場(chǎng)及其邊值問題的解 Static electromagnetic field and its solution of boundary value problems靜電場(chǎng)分析，導(dǎo)電媒質(zhì)中的恒定電場(chǎng)分析，恒定磁場(chǎng)分析，靜態(tài)場(chǎng)的邊值問題及解的唯一性定理，鏡像法，分離變量法，有限差分法Electrostatic field analysis, a conductive medium constant electric field analysis, constant magnetic field analysis, the boundary value problem of a static field and uniqueness theorem of solution, image method, separation variable method, finite difference method.4. 時(shí)變電磁場(chǎng)Time-varying electromagnetic field波動(dòng)方程，電磁場(chǎng)的位函數(shù)，電磁能量守恒定律，唯一性定理，時(shí)諧電磁場(chǎng).Wave equation, the electromagnetic field of a function, the law of conservation of electromagnetic energy, the uniqueness theorem ,time-harmonic electromagnetic field5. 均勻平面波在無(wú)界空間中的傳播 Uniform plane wave propagation in unbounded space理想介質(zhì)中的均勻平面波，電磁波的極化，均勻平面波在導(dǎo)電媒質(zhì)中的傳播，均勻平面波在各向異性媒質(zhì)中的傳播Ideal medium uniform plane wave, polarization of electromagnetic wave, Uniform plane wave propagation in conductive medium, Uniform plane wave propagation in anisotropic medium6. 均勻平面波的反射與透射Uniform plane wave reflection and transmission均勻平面波對(duì)分界平面的垂直入射，均勻平面波對(duì)多層介質(zhì)分界平面的垂直入射，均勻平面波對(duì)理想介質(zhì)分界平面的斜入射，均勻平面波對(duì)理想導(dǎo)體平面的斜入射The uniform