视频选集 片头 数学概论 1-Introduction to Mathematics 小数字的加减法 2-Addition and Subtraction of Small Numbers 小数字的乘法和除法 3-Multiplication and Division of Small Numbers 理解分数、假分数和混合数 4-Understanding Fractions, Improper Fractions, and Mixed Numbers 大整数位值和估计 5-Large Whole Numbers Place Values and Estimating 小数符号和运算 6-Decimals Notation and Operations 使用百分比 7-Working With Percentages 分数、小数和百分比之间的转换 8-Converting Between Fractions, Decimals, and Percentages 大数的加减法9-Addition and Subtraction of Large Numbers 算术分配律 10-The Distributive Property for Arithmetic 大整数相乘 11-Multiplication of Large Numbers 大数除法长除法 12-Division of Large Numbers Long Division 负数 13-Negative Numbers 理解指数及其运算 14-Understanding Exponents and Their Operations 算术运算的顺序 15-Order of Arithmetic Operations PEMDAS 整除，质数和质因数分解 16-Divisibility, Prime Numbers, and Prime Factorization 最小公倍数(LCM) 17-Least Common Multiple (LCM) 最大公因子 18-Greatest Common Factor (GCF) 分数的加法和减法 19-Addition and Subtraction of Fractions 分数的乘法和除法 20-Multiplication and Division of Fractions 分析数据集范围，平均值，中位数，和众数 21-Analyzing Sets of Data Range, Mean, Median, and Mode 使用变量的代数导论 22-Introduction to Algebra Using Variables 代数的基本数性质 23-Basic Number Properties for Algebra 代数方程及其解 24-Algebraic Equations and Their Solutions 两边都有变量的代数方程 25-Algebraic Equations With Variables on Both Sides 代数文字题 26-Algebraic Word Problems 解决代数不等式 27-Solving Algebraic Inequalities 平方根，立方根，和其他的根 28-Square Roots, Cube Roots, and Other Roots 用根和指数简化表达式 29-Simplifying Expressions With Roots and Exponents 用根和指数解代数方程 30-Solving Algebraic Equations With Roots and Exponents 多项式介绍 31-Introduction to Polynomials 加减多项式 32-Adding and Subtracting Polynomials 用FOIL方法乘二项式 33-Multiplying Binomials by the FOIL Method 通过因式分解求解二次方程 34-Solving Quadratics by Factoring 通过平方完成来解二次方程 35-Solving Quadratics by Completing the Square 用二次公式解二次方程 36-Solving Quadratics by Using the Quadratic Formula 用综合除法和有理根求解高次多项式 37-Solving Higher-Degree Polynomials by Synthetic Division 操作有理表达式简化和操作 38-Manipulating Rational Expressions Simplification and Operations 在代数有序对和坐标平面中绘图 39-Graphing in Algebra Ordered Pairs and the Coordinate Plane 在代数中绘制线了解斜率和 Y 截距 40-Graphing Lines in Algebra Understanding Slopes 以斜率截距形式绘制线 (y = mx + b) 41-Graphing Lines in Slope-Intercept Form (y = mx + b) 标准形式的绘图线 (ax + by = c) 42-Graphing Lines in Standard Form (ax + by = c) 绘制平行线和垂直线 43-Graphing Parallel and Perpendicular Lines 求解两个方程和两个未知数 44-Solving Systems of Two Equations and Two Unknowns Graphing 绝对值定义、计算和绘图 45-Absolute Values Defining, Calculating, and Graphing 实数与虚数、有理数与无理数的数字类型是什么 46-What are the Types of Numbers Real vs. 几何学概论古希腊和毕达哥拉斯学派 47-Introduction to Geometry Ancient Greece 基本欧几里得几何点、线和平面 48-Basic Euclidean Geometry Points, Lines, and Planes 角度类型和角度关系 49-Types of Angles and Angle Relationships 欧几里得几何中的三角形类型 50-Types of Triangles in Euclidean Geometry 证明三角形的同余和相似性 51-Proving Triangle Congruence and Similarity 三角形平分线、中线和高度中的特殊线52-Special Lines in Triangles Bisectors, Medians, and Altitudes 三角形中段定理 53-The Triangle Midsegment Theorem 勾股定理 54-The Pythagorean Theorem 四边形和其他多边形的类型 55-Types of Quadrilaterals and Other Polygons 计算多边形的周长 56-Calculating the Perimeter of Polygons 圆半径、直径、弦、周长和扇形 57-Circles Radius, Diameter, Chords, Circumference, and Sectors 计算形状的面积 58-Calculating the Area of Shapes 证明勾股定理 59-Proving the Pythagorean Theorem 三维形状第 1 部分：计算表面积计60-Three-Dimensional Shapes Part 1 Types 三维形状第 2 部分：计算体积 61-Three-Dimensional Shapes Part 2 Calculating Volume 什么是函数 62-Back to Algebra What are Functions 以代数方式操作函数和评估复合函数 63-Manipulating Functions Algebraically and Evaluating 绘制代数函数域和范围、最大值和最小值 64-Graphing Algebraic Functions Domain and Range 变换代数函数移位、拉伸和反射 65-Transforming Algebraic Functions Shifting, Stretching 连续、不连续和分段函数 66-Continuous, Discontinuous, and Piecewise Functions 反函数 67-Inverse Functions 求两点之间距离的距离公式 68-The Distance Formula Finding the Distance Between Two Points 绘制圆锥曲线第 1 部分: 圆 69-Graphing Conic Sections Part 1 Circles 绘制圆锥截面第 2 部分: 椭圆 70-Graphing Conic Sections Part 2 Ellipses 以标准形式绘制圆锥截面第 3 部分: 抛物线 71-Graphing Conic Sections Part 3 Parabolas 绘制圆锥曲线第 4 部分: 双曲线 72-Graphing Conic Sections Part 4 Hyperbolas 绘制高次多项式 73-Graphing Higher-Degree Polynomials The Leading Coefficient Test 绘制有理函数及其渐近线 74-Graphing Rational Functions and Their Asymptotes 求解和绘制多项式和有理不等式 75-Solving and Graphing Polynomial and Rational Inequalities 绘制指数函数 76-Evaluating and Graphing Exponential Functions 对数函数绘图77-Logarithms Part 1 Evaluation of Logs and Graphing Logarithmic Functions 10 为底的对数、自然对数和基数变化特性 78-Logarithms Part 2 Base Ten Logs, Natural Logs 对数的属性，扩展对数表达式 79-Logarithms Part 3 Properties of Logs, Expanding Logarithmic 求解指数和对数方程 80-Solving Exponential and Logarithmic Equations 复数运算、复共轭和线性分解 -Complex Numbers Operations, Complex Conjugates 并集和交集的类型 82-Set Theory Types of Sets, Unions and Intersections 序列、阶乘和求和符号 83-Sequences, Factorials, and Summation Notation 理论概率、排列和组合 84-Theoretical Probability, Permutations and Combinations 三角学角度和弧度简介 85-Introduction to Trigonometry Angles and Radians 三角函数 正弦、余弦、正切、余割、正割和余切 86-Trigonometric Functions Sine, Cosine 记住三角单位圆的最简单方法 87-The Easiest Way to Memorize the Trigonometric Unit Circle 基本三角恒等式毕达哥拉斯恒等式和函数恒等式 88-Basic Trigonometric Identities Pythagorean Identitie 绘制三角函数 89-Graphing Trigonometric Functions 反三角函数 90-Inverse Trigonometric Functions 验证三角恒等式 91-Verifying Trigonometric Identities 三角函数和差分公式 92-Formulas for Trigonometric Functions SumDifference 求解三角方程 93-Solving Trigonometric Equations 正弦定律 94-The Law of Sines 余弦定律 95-The Law of Cosines 极坐标和绘制极坐标方程 96-Polar Coordinates and Graphing Polar Equations 参数方程 97-Parametric Equations 微积分导论 希腊人、牛顿和莱布尼茨 98-Introduction to Calculus The Greeks, Newton, and Leibniz 理解微分第 1 部分 : 切线的斜率 99-Understanding Differentiation Part 1 The Slope 了解微分第 2 部分：变化率 100-Understanding Differentiation Part 2 Rates of Change 微积分中的极限和极限定律 101-Limits and Limit Laws in Calculus 什么是推导幂律的导数 102-What is a Derivative Deriving the Power Rule 多项式函数的导数幂律、乘积律和商 R 103-Derivatives of Polynomial Functions Power Rule 三角函数的导数 104-Derivatives of Trigonometric Functions 复合函数的导数链式法则 105-Derivatives of Composite Functions The Chain Rule 对数和指数函数的导数 106-Derivatives of Logarithmic and Exponential Functions 隐微分 107-Implicit Differentiation 高阶导数及其应用 108-Higher Derivatives and Their Applications 微积分相关比率 109-Related Rates in Calculus 通过微分求局部最大值和最小值 110-Finding Local Maxima and Minima by Differentiation 绘图函数及其导数 111-Graphing Functions and Their Derivatives 微积分中的最优化问题 112-Optimization Problems in Calculus 理解极限和洛必达法则 113-Understanding Limits and L'Hospital's Rule 曲线下面积的积分 114-What is Integration Finding the Area Under a Curve 积分基本定理:重新定义积分 115-The Fundamental Theorem of Calculus Redefining Integration 积分的性质和定积分的计算 116-Properties of Integrals and Evaluating Definite Integrals 计算不定积分 117-Evaluating Indefinite Integrals 用三角函数计算积分 118-Evaluating Integrals With Trigonometric Functions 用代换法则积分 119-Integration Using The Substitution Rule 分步积分法 120-Integration By Parts 三角替换积分法 121-Integration By Trigonometric Substitution 微积分整合的高级策略 122-Advanced Strategy for Integration in Calculus 计算反常积分 123-Evaluating Improper Integrals 用积分法求两条曲线之间的面积 124-Finding the Area Between Two Curves by Integration 用积分法计算旋转固体的体积 125-Calculating the Volume of a Solid of Revolution by Integration 通过圆柱壳计算体积 126-Calculating Volume by Cylindrical Shells 积分的中值定理函数的平均127-The Mean Value Theorem For Integrals Average Value of a Function 数列和级数 128-Convergence and Divergence The Return of Sequences and Series 使用积分检验和比较检验计算总和129-Estimating Sums Using the Integral Test and Comparison Test 交替级数、收敛类型和比率检验 130-Alternating Series, Types of Convergence, and the Ratio Test 幂级数 131-Power Series 泰勒和麦克劳林级数 132-Taylor and Maclaurin Series 双曲函数定义、恒等式、导数和反函数 133-Hyperbolic Functions Definitions, Identities, Derivatives 三维坐标和右手定则 134-Three-Dimensional Coordinates and the Right-Hand Rule 介绍向量及其操作 135-Introduction to Vectors and Their Operations 向量点积 136-The Vector Dot Product 线性代数系统线性方程导论 137-Introduction to Linear Algebra Systems of Linear Equations 理解矩阵和矩阵符号 138-Understanding Matrices and Matrix Notation 矩阵的操作基本行运算 139-Manipulating Matrices Elementary Row Operations 矩阵类型与矩阵加法 140-Types of Matrices and Matrix Addition 矩阵乘法及其相关性质 141-Matrix Multiplication and Associated Properties 求矩阵行列式的值 142-Evaluating the Determinant of a Matrix 向量叉乘 143-The Vector Cross Product 逆矩阵及其性质 144-Inverse Matrices and Their Properties 利用克拉默法则求解方程组 145-Solving Systems Using Cramer's Rule 了解空间向量 146-Understanding Vector Spaces 子空间和跨度 147-Subspaces and Span 线性无关 148-Linear Independence 维数和基底 149-Basis and Dimension 基底的变化 150-Change of Basis 图像和内核 152-Image and Kernel 正交 153-Orthogonality and Orthonormality 正交化过程 154-The Gram-Schmidt Process 寻找特征值和特征向量 155-Finding Eigenvalues and Eigenvectors 对角化 156-Diagonalization 复矩阵、厄米矩阵和酉矩阵 157-Complex, Hermitian, and Unitary Matrices 二重和三重积分 158-Double and Triple Integrals 函数的偏导数和梯度 159-Partial Derivatives and the Gradient of a Function 向量场、散度和卷曲 160-Vector Fields, Divergence, and Curl 计算线积分 161-Evaluating Line Integrals 格林公式 162-Green's Theorem 计算曲面积分 163-Evaluating Surface Integrals 斯图姆定理 164-Stokes's Theorem 散度定理 165-The Divergence Theorem
