| | 初等數學 Elementary Mathematics (一)教材 老師講義 (二)課程介紹 銜接高中數學與大學數學，主要配合微積分。 (三)課程大綱 1. 邏輯概念
2. 集合論
3. 數字系統
4. 函數概念
5. 方程式概念及應用
6. 不等式概念及應用
7. 三角函數
8. 應用問題之探討 基礎數學 Basic Mathematics | (一)教材 高中數學, 老師講義 (二)參考書 無 (三)課程內容 以數學系專業的態度檢視高中數學的根本原理。配合電腦視覺化軟體，建立同學堅強的數學能力為以後的課程打好基礎。 (四)課程大綱 1. 探討四則運算的原理及應用
2. 深入了解集合的定義
3. 何謂函數
4. 方程式及參數式
5. 用電腦視覺化軟體模擬簡單的運動
6. 動畫與數學
7. 三角函數的運用
8. 了解指數、對數函數
9. 不等式的用處及解法 | | 工程數學 Engineering Mathematics | 預備知識: 微積分(一) (二) , 線性代數 (一)教材 Advanced Engineering Mathematics, Erwin Kreyszig, John Wiley & Sons, Inc. (二)參考書 Advanced Engineering Mathematics Michael D. Greenberg Prentice Hall Advanced Engineering Mathematics Peter V. O'eil PWS Publishing Company (三)課程大綱 1. Periodic Functions. Trigonometric Series. 2. Fourier Series. Euler Formulas 3. Functions Having Arbitrary Period 4. Even and Odd Functions 5. Half-Range Expansions 6. Determination of Fourier Coefficients without Integration. 7. Forced Oscillations. 8. Approximation by Trigonometric Polynomails. Square Error. 9. The Fourier Integral. |  | (四)課程內容 Periodic functions occur frequently in engineering problems. Their representation in terms of simple periodic functions, such as sine and cosine, is a matter of great practical importance, which leads to Fourier series. These series are a very powerful tool in connection with various problems involving ordinary and partial differential equations. In the present course we shall discuss basic concepts, facts and techniques in connection with Fourier series. Illustrative examples and some important engineering applications will be included. The theory of Fourier series is rather complicated, but the application of these series is simple. Fourier series are, in a certain sense, more universal than Taylor series, because many discontinuous periodic functions of practical interest can be developed in Fourier Series, but, of-course, do not have Taylor series representations. The last section of this course is devoted to Fourier integrals. Applications to partial differential equations will also be introduced. 流體力學(一) Fluid Mechanics (I) | (一)教材 流體力學(上) 杜鳳棋譯 (二)參考書 Fundamental of Fluid Mechanics, Fourth Edition by B. R. Munson, D. F. Young and T. H. Okiishi (三)課程大綱 1. Introduction 2. Fluid Statics 3. Elementary Fluid Dynamics - The Bernoulli Equation 4. Fluid Kinematics 5. Finite Control Volume Analysis |  | 流體力學(二) Fluid Mechanics (II) | (一)教材 流體力學(下) 杜鳳棋譯 (二)參考書 Fundamental of Fluid Mechanics, Fourth Edition by B. R. Munson, D. F. Young and T. H. Okiishi (三)課程大綱 1. Differential Analysis of Fluid Flow 2. Similitude, Dimensional Analysis, and Modeling 3. Viscous Flow in Pipes 4. Flow over Immersed Bodies 5. Open-Channel Flow | | 理論力學 Theoretical Mechanics | (一)教材 1. Mechanics of Materials, Gere & Timoshenko.
2. Mechanics of Materials, Ferdinand P. Beer, E. Russell Johnston, Jr. and John T. DeWolf, McGraw Hill. (二)課程大綱 1. Concepts of Stress
2. Stress and Strain─Axial Loading
3. Torsion
4. Pure Bending
5. Analysis and Design of Beams for Bending
6. Shearing Stresses in Beams and Thin-Walled Membrane | | 統計概論 需先修過之課程: 高中數學 (一)教材 老師所編之講義 (二)參考書 Introduction to the Practice of Statistics, 5th edition, 2005, by D.S. Moore and G. P. McCabe (三)課程目的 機率與統計概念的介紹 (四)課程大綱 1. Introduction 2. Looking at data: Distribution 3. Looking at data: Change and Growth 4. Looking at data: Relationships 5. Looking at data: Categorical data 6. Survey Sampling: Sampling techniques and Design of Experiments 7. Statistical decision theory 8. Index numbers |  | 初等統計(一) Introduction to Statistics (I) 需先修過之課程: 高中數學 作業, 考古題及 解答, fall 1996(一)教材 Statistics for Business and Economics: A Practical Approach, 2006, by D.R. Anderson, D.J. Sweeney, T.A. Williams and Chen, J.C. (二)課程介紹 使學生對商業統計有初步的了解 (三)課程目的 This course covers the basic concepts of Statistics and it introduces the students to the most commonly applied methods of statistical analysis. (四)課程大綱 1 Introduction 2 Variables and Data 3 Descriptive Statistics I-Tabular and graphical methods 4 Descriptive Statistics II-Numerical methods 5 Introduction to Probability 6 Random Variables and Probability Functions 7 Normal Distribution 8 Sampling and Sampling Distribution 9 Estimation of the population mean, proportion and variance 10 Hypothesis testing about the mean, proportion and variance The emphasis is on applications. Examples are drawn from a wide range of academic areas. |  | 初等統計(二) Introduction to Statistics (II) 需先修過之課程: 初等統計(一) 作業,winter 1999 考古題及 解答,winter 1997(一)教材 Statistics for Business and Economics: A Practical Approach, 2006, by D.R. Anderson, D.J. Sweeney, T.A. Williams and Chen, J.C. (二)課程介紹 使學生對商業統計有初步的了解 (三)課程大綱 1. Analysis of Variance (變異數分析) 2. Chi-square Tests (卡方檢定) 3. Simple linear regression and correlation analysis (簡單線性迴歸與相關分析) 4. Nonparametric statistics (無母數統計方法) 5. Elementary survey sampling (基本抽樣調查方法) | | 初等統計(三) Introduction to Statistics (III) 需先修過之課程: 初等統計(一)(二)(一)教材 Statistics for Business and Economics: A Practical Approach, 2006, by D.R. Anderson, D.J. Sweeney, T.A. Williams and Chen, J.C. (二)課程介紹 使學生對商業統計有初步的了解 (三)課程大綱 1. Time series and forecasting (時間數列與預測) 2. Statistical decision theory (統計決策理論) 3. Index numbers (指數) 4. Statistical quality control (統計品質管制) 5. Multiple regression (複廻歸) 6. Regression analysis: model building (廻歸分析:模式建立) | | 迴歸分析 Regression Analysis 需先修過之課程: 數理統計或初等統計(二)(一)教材 Introduction to Linear Regression Analysis (4th Edition), 2006, by D.C. Montgomery, E.A. Peck and G. G. Vining. (二)參考書 Applied Linear Regression (3rd Edition), 2005, by Sanford Weisberg. (三)課程介紹 介紹常用的線性及非線性迴歸模式及建立模式的方法，並注重在實際 問題的應用 (四)課程大綱 1. Simple linear regression and correlation (簡單線性迴歸與相關) 2. Least squares method and Gauss-Markov theorem (最小平方法與高斯馬可夫定理) 3. Multiple regression (複迴歸) 4. Polynomial regression (多次迴歸) 5. Stepwise regression (逐步迴歸) 6. Estimation and hypothesis testing of the regression coefficient (迴歸係數的估計與檢定) 7. Forecasting (預測) 8. Residual analysis (殘差分析) |  | 實驗設計 Experimental Design 需先修過之課程: 數理統計 (一)教材 Design and analysis of experiments (6th Edition), 2004, by D.C. Montgomery. (二)參考書 實驗設計與分析(第 六版),2006, 黎正中、陳源樹譯 Statistics for experimenters: Design, Innovation, and Discovery (2nd Edition), 2005, by G. E. P. Box, J. S. Hunter and W. G. Hunter. (三)課程大綱 1. One-way and two-way ANOVA (一因子與二因子變異數分析) 2. Multiple comparison (多重比較) 3. Fixed and random effects models (固定與隨機效果模型) 4. Complete randomized block design (完全隨機區集設計) 5. Latin square and Graeco-Latin square design (拉丁方格與希臘拉丁方格設計) 6. Balanced and Partially balanced incomplete block design (均衡與部分均衡不完全區集設計) 7. 2k and 3k factorial design (2k and 3k因子設計) 8. Fractional factorial design (部分因子設計) 9. Analysis of covariance (共變數分析) |  | 計算機視覺化 Computational Visualization (一)教材 課程講義、動畫展示 (二)參考書 課程講義、網路資源 (三)課程內容 新的課程，將要求學生運用3D軟體及撰寫程式將抽象數學理論表現出來，將融合其他相關課程。目的是訓練學生將抽象理論運用計算機來視覺化。尤其加強數學系學生寫程式之能力，應該對其將來就業或進入計算機相關研究所深造都有明顯幫助。 內容包含： 1. 基礎數學性質的視覺化與3D動畫表現 2. 微積分觀念的視覺化與3D動畫表現 3. 線性代數基本性質的視覺化與3D動畫表現 4. 基礎物理性質的視覺化與3D動畫表現 (四)課程大綱： 1. 如何撰寫Vpython程式來製作互動式動畫 2. 如何撰寫flash程式來製作數學圖形及互動式動畫 3. 如何表現基礎數學及平面幾何性質 4. 如何表現3維幾何 5. 透視幾何(Projective Geometry) 6. 矩陣運用 7. 動畫及電腦遊戲中如何表現物理定律 8. 實作 計算幾何學 Computational Geometry | (一)教材 老師上課講義 (二)參考書 Computational Geometry in C 2nd edition by J. O'Rourke (三)課程內容 3D電腦動畫的製作牽涉到很多計算幾何學與傳統幾何學的精彩理論。本課程將探討如何運用幾何學結合電腦來模擬3D世界。 (四)課程大綱 1. Voronoi Diagrams and Applications 2. Delaunay Triangulations with Algorithms
3. Divide and Conquer with Fortune Algorithm
4. Minimum Spanning Tree and Kruskal algorithm
5. Connection between Voronoi Diagrams and Convex Hulls
6. Implementation of Delaunay triangulation
7. Incremental Algorithm in Three and Higher Dimensions
8. Duality
9. Higher-Order Voronoi Diagrams
10. Higher-Order Voronoi Diagrams in Higher Dimensions
11. Applications
|  | 資料結構 Data Structures | (一)教材 資料結構-使用C++, Horowitz, Sahni and Mehta 原著 (二)課程大綱 1. C++ Language
2. Performance Analysis And Measurement
3. Arrays
4. Stacks and Queues
5. Link Lists
6 Trees | | 物件導向程式語言 Object-Oriented Programming Language | (一)教材 新Java2, 550 個應用技巧大全集, By Takahashi, Igawa, Sato, Ueyama, Project A著, 博碩文化 (二)課程大綱 1. Introduction
2. java basics
3. Objects and Classes
4. ADT
5. Template
6. Inheritance
7. Graphics
8. Graphical Interface Components | | 拓樸學 Topology (一)參考書 Topology by Monkres.
Topology by Davis. (二)課程介紹 This Course aims at giving the elementary introduction to point set topology. No preliminary is required. (三)課程大綱 1 Metric spaces:
Open balls and open sets. Limit points. Closure and closed set. Convergence.
Density. Cantor Intersection Theorem and Baire Catgory Theorem.
2 Continuity:
Continuity and uniform continuity. Fixed points and contractions. Banach fixed-point theorem.
3 Topological spaces:
Examples of topologies. Properties of topology. Bases and local bases. Separability. 動力學 Dynamics | (一)教材 1. Vector Mechanics for Engineers, Dynamics, 7th Edition, Beer and Johnson
2. Mechanics of Materials, 6/E, Russell C. Hibbeler (二)參考書 1. Engineering Mechanics, Dynamics, 2/E, William Riley
2. Mechanics of Materials, 5/E, R. C. Hibbeler (三)課程大綱 1. Kinematics of Rigid Bodies
2. Plane Motion of Rigid Bodies: Force and Accelleration
3. Energy and Momentum Method
4. Stress and Strain
5. Mechanical Properties of Materials
6. Axial Load
7. Torsion
8. Bending and Shear
9. Combined Loading
10. Stress Transformation
11. Deflections of Beams
12. Energy Methods |  | (四)課程內容 The purpose of this course is to teach students the basic principles underlying the dynamics of rigid bodies in planar and 3D motion and to train students to identify, formulate and solve engineering problems in rigid body dynamics. The concepts of mechanics and mechanical behavior of materials will also be covered. 統計品質管制 Statistical quality control | (一)教材 品質管理, 傅和彥和黃士滔 (二)參考書 品質管理, 徐世輝 (三)課程內容 1.使學生瞭解品質管理的基礎理論與實務技術。 2.使學生熟悉品質管理的方法和應用。 3.培養學生建立品質的觀念和理念。 4.使學生實習品質管理的操作實務。 (四)課程大綱 1. 品質之意義與演變 2. 品質成本 3. PDCA循環 4. QC七大手法 5. 統計製程管制與管制圖 6. 相關分析 7. 抽樣方法與檢驗 8. 全面品質管理與品管圈 9. 品質活動 10. 可靠度 11. ISO制度 12. 田口式品管
|  | 離散數學 Discrete Mathematics | (一)教材 Elements of Discrete Mathematics 2nd edition, by C. L. Liu (二)課程內容 引導學生利用邏輯思考及數學來解決問題 。並進一步了解離散數學在計算機科學， 幾何， 商業等各方面之應用。 (三)課程大綱 1. Sets
2.Permutations and Combinations
3.Relations and Functions
4.Graphs
5.Trees
6.Generating Functions
7.Recurrence Relations |  | 線性規劃 Linear Programming | (一)教材 Introduction to Operations Research Seventh Edition by Hillier/Lieberman (二)課程大綱 1. Introduction
2. Overview of the Operations Research Modeling Approach
3. Introduction to Linear Programming
4. Solving Linear Programming Problems: The Simplex Method
5. The Theory of the Simplex Method
6. Duality Theory and Sensitivity Analysis
7. Other Algorithms for Linear Programming
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