教學時程

微積分及應用

因舊版課程無指定課堂作業與考試，因此統整所有作業、講義、考試內容合併列出。

本課程被設計為自學微積分。內容被劃分為以下的“章節”。

章節	課程單元
	前言Preface
0	電子資料表The Spreadsheet
1	哲學，數字和函數 Philosophy, Numbers and Functions
2	指數函數與三角函數 The Exponential Function and Trigonometric Functions
3	向量，內積，矩陣乘法和距離 Vectors, Dot Products, Matrix Multiplication and Distance
4	平行四邊形的面積，行列式，體積，超體積以及向量積 Area of a Parallelogram, Determinants, Volume and Hypervolume, the Vector Product
5	二維和三維中的向量與幾何 Vectors and Geometry in Two and Three Dimensions
6	微分函數，積分和微分 Differentiable Functions, the Derivative and Differentials
7	根據定義的積分計算 Computation of Derivatives from their Definition
8	根據法則的積分演算 Calculation of Derivatives by Rule
9	向量場的積分和極座標系中的梯度 Derivatives of Vector Fields and the Gradient in Polar Coordinates
10	高等積分，泰勒級數，二次逼近和逼近精確度 Higher Derivatives, Taylor Series, Quadratic Approximations and Accuracy of Approximations
11	多維空間中的二次逼近 Quadratic Approximations in Several Dimensions
12	微分的應用：直接用於線性逼近 Applications of Differentiation: Direct Use of Linear Approximation
13	解方程Solving Equations
14	極值Extrema
15	曲線Curves
16	幾個重要的例子和一個物理學中的表述 Some Important Examples and a Formulation in Physics
17	積的規則和向量的微分 The Product Rule and Differentiating Vectors
18	複數和複數方程 Complex Numbers and Functions of Them
19	反導數或不定積分 The Anti-derivative or Indefinite Integral
20	曲線下方的面積及其多種推廣 The Area under a Curve and its Many Generalizations
21	微積分在一維中的基本定理 The Fundamental Theorem of Calculus in One Dimension
22	微積分在多維中的基本定理：加性測度，斯托克斯定理以及散度定理 The Fundamental Theorem of Calculus in Higher Dimensions; Additive Measures, Stokes Theorem and the Divergence Theorem
23	線積分化簡為通常積分和相對簡化形式 Reducing a Line Integral to an Ordinary Integral and Related Reductions
24	面積分化簡為多重積分和雅可比矩陣 Reducing a Surface Integral to a Multiple Integral and the Jacobian
25	數值積分法Numerical Integration
26	微分方程的數值解 Numerical Solution of Differential Equations
27	積分練習Doing Integrals
28	介紹電場和磁場 Introduction to Electric and Magnetic Fields
29	磁場，電磁感應和電動力學 Magnetic Fields, Magnetic Induction and Electrodynamics
30	級數Series
31	平面，曲面，體積的積分練習 Doing Area, Surface and Volume Integrals
32	一些線性代數Some Linear Algebra
33	二階微分方程Second Order Differential Equations