eCalculus@CSU

CHAPTER 1  LIMITS OF FUNCTIONS

Section 1-1     Limits

Section 1-2     One-Sided Limit

Section 1-3     Continuity

Section 1-4     A Limit at Infinity and Infinite Limit

CHAPTER 2  DERIVATIVE

Section 2-1    Definition of Derivative

Section 2-2    The Rule of Differentiation

Section 2-3    Chain Rule and Implicit Differentiation

Section 2-4    Derivatives of Exponential and Logarithmic F

Section 2-5    Numerical Approximate –Differentials

Section 2-6    Derivatives of Trigonometric Functions

Section 2-7    Derivatives of Inverse Trigonometric F

CHAPTER 3  APPLICATIONS OF DERIVATIVES

Section 3-1    The Mean Value Theorem and its Applications

Section 3-2    Increasing and Decreasing Functions

Section 3-3    Maximum and Minimum Values

Section 3-4    The Max -Min Problems

Section 3-5    Concavity and Points of Inflection

Section 3-6    Asymptotes

Section 3-7    Sketching curve

Section 3-8    L' Hopital's Rule

Section 3-9    Taylor Series

Section 3-10  Applications In Marginal Analysis

Section 3-11  Elasticity

CHAPTER 4    THE INDEFINITE INTEGRALS

Section 4-1     Antiderivative and The Indefinite Integrals

Section 4-2     Integration by Changing Variables

Section 4-3     Integration by Parts

Section 4-4     The Trigonometric Integrals

Section 4-5     The Integration by Partial Fractions

Section 4-6     Trigonometric and Half-Angle Substitution

CHAPTER 5    THE DEFINITE INTEGRALS

Section 5-1    Areas and the Definition of Definite Integral

Section 5-2    The Fundamental Theorem of Calculus

Section 5-3    The Approximate Integration

Section 5-4    The Improper Integrals

CHAPTER 6    APPLICATIONS OF INTEGRATION

Section 6-1    Areas between Curves

Section 6-2    Areas in Polar Coordinates

Section 6-3    Arc Length

Section 6-4    Volumes and The Volumes of Revolution

Section 6-5    Area of a Surface of Revolution

Section 6-6    Centroid of A Plane Region

Section 6-7    Work and The Problems of The Engineering

CHAPTER 7     PARTIAL DERIVATIVES

Section 7-1     Limits and Continuity

Section 7-2     Partial Derivatives

Section 7-3     The Differentials and Chain Rules

Section 7-4     Extrema of Functions of Two Variables

Section 7-5     Directional Derivatives, Gradient and Tangent Plane

CHAPTER 8      MULTIPLE INTEGRALS

Section 8-1     Integrals over a Rectangle

Section 8-2     Integrals over a Region

Section 8-3     Three-Dimensional Iterated Integrals

Section 8-4     Multiple Integration in Polar, Cylindrical and  Spherical Coordinates

Section 8-5     Applications of Multiple Integrals

微積分

1. 丁雲龍老師的課程 

2. 林永祥老師的課程

高中職數學(一)

一）數

二）二次函數與一元二次不等式

三）直線方程式與線性規劃

四）指數與對數

五）敘述統計

高中職數學(二)

一)   集合與函數

二)   多項式、分式與無理式

三） 分式與無理式

四）函數與反函數

五）三角函數

六） 三角形的性質與解法

七）反三角函數、三角方程式

八）複數

九）方程式

高中職數學(三)

第一章   圓與直線

第二章   圓錐曲線

第三章   參數方法

第四章   不等式
第五章   向　量

第六章   矩陣與行列式

第七章   數學歸納法
第八章   排列與組合

國高中數學銜接教材

一、乘法公式與多項式

二、因式分解

三、平方根與立方根

四、一元二次方程式

五、線型函數與二次函數

六、不等式

七、數列與級數

正修數學科

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