工程分析

臺北科技大學 114-2 學期課程，課號 359442。

課程大綱

變分法，積分方程式， Green函數 Calculus of Variations and Application, Integral Equations, Green Function,

課程進度

1 Overview of Engineering Analysis Chapter Learning Objectives 1.1 Introduction 1.2 Engineering Analysis and Engineering Practices 1.2.1 Creation 1.2.2 Problem Solving 1.2.3 Decision Making 1.3 “Toolbox” for Engineering Analysis 1.4 The Four Stages in Engineering Analysis 1.5 Examples of the Application of Engineering Analysisin Design 1.6 The “Safety Factor” in Engineering Analysis of Structures 2 Mathematical Modeling Chapter Learning Objectives 2.1 Introduction 2.2 Mathematical Modeling Terminology 2.2.1 The Numbers 2.2.1.1 Real Numbers 2.2.1.2 Imaginary Numbers 2.2.1.3 Absolute Values 2.2.1.4 Constants 2.2.1.5 Parameters 2.2.2 Variables 2.2.3 Functions 2.2.3.1 Form1. Functions with Discrete Values 2.2.3.2 Form2.Continuous Functions 2.2.3.3 Form3. Piecewise Continuous Functions 2.2.4 Curve Fitting Technique in Engineering Analysis 2.2.4.1 Curve Fitting Using Polynomial Functions 2.2.5 Derivative 2.2.5.1 The Physical Meaning of Derivatives 2.2.5.2 Mathematical Expression of Derivatives 2.2.5.3 Orders of Derivatives 2.2.5.4 Higher-order Derivatives in Engineering Analyses 2.2.5.5 The Partial Derivatives 2.2.6 Integration 2.2.6.1 The Concept of Integration 2.2.6.2 Mathematical Expression of Integrals 2.3 Applications of Integrals 2.3.1 Plane Area by Integration 2.3.1.1 Plane Area Bounded by Two Curves 2.3.2 Volumes of Solids of Revolution 2.3.3 Centroids of Plane Areas 2.3.3.1 Centroid of a Solid of Plane Geometry with Straight Edges 2.3.3.2 Centroid of a Solid with Plane Geometry Defined by Multiple Functions 2.3.4 Average Value of Continuous Functions 2.4 Special Functions for Mathematical Modeling 2.4.1 Special Functions in Solutions in Mathematical Modeling 2.4.1.1 The Error Function and Complementary Error Function 2.4.1.2 The Gama Function 2.4.1.3 Bessel Functions 2.4.2 Special Functions for Particular Physical Phenomena 2.4.2.1 Step Functions 2.4.2.2 Impulsive Functions 2.5 Differential Equations 2.5.1 The Laws of Physics for Derivation of Differential Equations 3 Vectors and Vector Calculus Chapter Learning Objectives 3.1 Vector and Scalar Quantities 3.2 Vectors in Rectangular and Cylindrical Coordinate Systems 3.2.1 Position Vectors 3.3 Vectors in 2D Planes and 3D Spaces 3.4 Vector Algebra 3.4.1 Addition of Vectors 3.4.2 Subtraction of Vectors 3.4.3 Addition and Subtraction of Vectors Using Unit Vectors in Rectangular Coordinate Systems 3.4.4 Multiplication of Vectors 3.4.4.1 Scalar Multiplier 3.4.4.2 Dot Product 3.4.4.3 Cross Product 3.4.4.4 Cross Product of Vectors for Plane Areas 3.4.4.5 Triple product 3.4.4.6 Additional Laws of Vector Algebra 3.4.4.7 Use of Triple Product of Vectors for Solid Volume 3.5 Vector Calculus 3.5.1 Vector Functions 3.5.2 Derivatives of VectorFunctions 3.5.3 Gradient, Divergence, and Curl 3.5.3.1 Gradient 3.5.3.2 Divergence 3.5.3.3 Curl 3.6 Applications of Vector Calculus in Engineering Analysis 3.6.1 In Heat Transfer 3.6.2 In Fluid Mechanics 3.6.3 In Electromagnetism with Maxwell’s Equations 3.7 Application of Vector Calculus in Rigid Body Dynamics 3.7.1 Rigid Body in Rectilinear Motion 3.7.2 Plane Curvilinear Motion in Rectangular Coordinates 3.7.3 Application of Vector Calculus in the Kinematics of Projectiles 3.7.4 Plane Curvilinear Motion in Cylindrical Coordinates 3.7.5 Plane Curvilinear Motion with Normal and Tangential Components Advance lecture calculus of variations and applications 1.1 maxima and minima 1.2 simplest case: examples 1.3 natural boundary conditions and transition conditions 1.4 the variational notation 1.5 constraint and Lagrange multipliers&l

評量方式

平時 30% 期中考 30% 期末考 40%

教材

【遵守智慧財產權觀念，請使用正版教科書，不得使用非法影印教科書】 使用外文原文書：是 1. Applied Engineering Analysis Tai-Ran Hsu, Wiley 2. Methods of Applied Mathematics Francis B Hildebrand