饒瑞彬老師-理工微積分
167 videos • 9,241 views • by NCUx Media
1
10-1-1 Introduction
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2
10-1-2 Example 1
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3
10-1-3 Parametric Curves
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4
10-1-4 Example 2、3
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5
10-1-5 Example 4
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6
10-1-6 Example 7 Cycloid
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7
10-1-7 Cycloids
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8
10-2-1 Tangents
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9
10-2-2 Example 1
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10
10-2-3 Example 2
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11
10-2-4 Areas
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12
10-2-5 Example 3
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13
10-2-6 Arc Length
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14
10-2-7 Theorem 5
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15
10-2-8 Example 4
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16
10-2-9 Example 5
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17
10-2-10 Surface Area
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18
10-2-11 Example 6
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19
10-3-1 Polar Coordinates
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20
10-3-2 Example 1
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21
10-3-3 Cartesian and Polar Coordinates
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22
10-3-4 Example 2、3
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23
10-3-5 Polar Curves
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24
10-3-6 Example 4、5
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25
10-3-7 Example 6
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26
10-3-8 Example 7
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27
10-3-9 Example 8
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28
10-3-10 Symmetric Rules
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29
10-3-11 Tangents to Polar Curves
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30
10-3-12 Example 9
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31
10-4-1 Areas in Polar Coordinates
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32
10-4-2 Example 1
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33
10-4-3 Example 2
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34
10-4-4 Area of Bounded Region by Curves and Caution
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35
10-4-5 Example 3
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36
10-4-6 Arc Length
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37
10-4-7 Example 4
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38
11-1-1 Sequences and Example 1、2、3c
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39
11-1-2 Graph and Limit of a Sequence and Theorem 3
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40
11-1-3 Divergent Sequence, Limit Laws, Squeeze Theorem and Theorem 6
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41
11-1-4 Example 4、6、7、8
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42
11-1-5 Theorem 7 and Example 9、10、11
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43
11-1-6 Monotonic Sequences and Example 12、13
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44
11-1-7 Bounded Sequences
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45
11-1-8 Monotonic Sequences Theorem 12
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46
11-2-1 Series
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47
11-2-2 Sum of Series v.s. Improper Integrals
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48
11-2-3 Example 2 Geometric Series
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49
11-2-4 Example 3、4、5
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50
11-2-5 Example 7
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51
11-2-6 Example 8 Harmonic Series
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52
11-2-7 Theorem 6、Test for Divergence、Example 9 and Note 3
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53
11-2-8 Theorem 8 and Example 10
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54
11-2-9 Note 4
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55
11-3-1 Foreword of Integral Test Example i
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56
11-3-2 Foreword of Integral Test Example ii
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57
11-3-3 Integral Test
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58
11-3-4 Example 1
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59
11-3-5 Example 2 p-series、Example 3a、3b and Note
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60
11-3-6 Example 4
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61
11-3-7 Estimating the Sum of a Series
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62
11-3-8 Example 5
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63
11-3-9 Estimate 3
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64
11-3-10 Example 6 and Compare Example 5 with Example 6
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65
11-4-1 Foreword of Comparison Tests
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66
11-4-2 Comparison Test
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67
11-4-3 Sequence vs Series、Known Series and Example 1
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68
11-4-4 Note 1 and Example 2
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69
11-4-5 Note 2 and Limit Comparison Test
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70
11-4-6 Example 3、4
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71
11-5-1 Alternating Series Test
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72
11-5-2 Proof of Alternating Series Test
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73
11-5-3 Example 1、2、 3
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74
11-5-4 Alternating Series Estimation Theorem
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75
11-5-5 Example 4
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76
11-6-1 Absolute Convergence, Example 1、2 and Conditional Convergence
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77
11-6-2 Theorem 3
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78
11-6-3 Example 3
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79
11-6-4 Ratio Test
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80
11-6-5 Proof of Case i
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81
11-6-6 Proof of Case ii
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82
11-6-7 Proof of Case iii
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83
11-6-8 Example 4、5
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84
11-6-9 Root Test and Example 6
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85
11-6-10 Rearrangements
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86
11-7-1 Strategy for Testing Series
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87
11-7-2 Example 1、2、3、4、5、6
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88
11-8-1 Power Series
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89
11-8-2 Example 1
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90
11-8-3 Example 2
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91
11-8-4 Example 3 Bessel Function
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92
11-8-5 Theorem 3, Radius of Convergence and Interval of Convergence
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93
11-8-6 Example 4
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94
11-8-7 Example 5
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95
12-1-1 3-D Coordinate Systems
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96
12-1-2 Example 1, Note and Example 3
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97
12-1-3 Distance Formula
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98
12-1-4 Example 4、5、6、7
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99
12-2-1 Vector
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100
12-2-2 Vector Addition and Example 1
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101
12-2-3 Multiplying Vectors and Subtracting Vectors
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102
12-2-4 Example 2
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103
12-2-5 Components and Position Vector
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104
12-2-6 Example 1、3
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105
12-2-7 Length of Vector
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106
12-2-8 Algebraic Vectors
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107
12-2-9 Example 4
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108
12-2-10 Components, Properties of Vectors, Standard Basis Vectors and Example 5
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109
12-2-11 Unit Vectors and Example 6
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110
12-2-12 Force, Example 7
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111
12-3-1 The Dot Product and Example 1
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112
12-3-2 Theorem 2 Properties of Dot Product
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113
12-3-3 Proof of Theorem 2
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114
12-3-4 Theorem 3 and Example 2
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115
12-3-5 Corollary 6 and Example 3
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116
12-3-6 Orthogonal Vectors, Theorem 7 and Example 4
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117
12-3-7 Dot Product a‧b
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118
12-3-8 Direction Angles and Cosines and Example 5
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119
12-3-9 Projection
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120
12-3-10 Example 6
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121
12-3-11 Applications of Peojections Work
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122
12-3-12 Example 7、8
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123
13-1-1 Vector Functions and Example 1
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124
13-1-2 Limit of a Vector and Example 2
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125
13-1-3 Continuous Vector Function, Space Curve
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126
13-1-4 Example 3
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127
13-1-5 Plane Curves, Example 4, Example 5 and Example 6
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128
13-2-1 Definition of Derivative, Unit Tangent Vector
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129
13-2-2 Theorem 2
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130
13-2-3 Example 1
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131
13-2-4 Example 2
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132
13-2-5 Example 3
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133
13-2-6 Second Derivative
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134
13-2-7 Theorem 3 Differentiation Rules
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135
13-2-8 Example 4
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136
13-3-1 Plane Space Curve Length, Arc Length
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137
13-3-2 Example 1
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138
13-3-3 Remark of Arc Length
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139
13-3-4 Arc Length Function
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140
13-3-5 Parametrization
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141
13-3-6 Example 2
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142
13-3-7 Smooth Parametrization and Smooth Curve
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143
13-3-8 Curvature
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144
13-3-9 Example 3 and Curvature of a Straight Line
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145
13-3-10 Theorem 10 and Example 4
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146
13-3-11 Curvature of a Plane Curve and Example 5
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147
13-3-12 Normal Vectors and Binormal Vectors
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148
13-3-13 Example 6
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149
13-3-14 TNB Frame, Normal Plane, Osculating Plane and Osculating Circle
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150
13-3-15 Example 7
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151
13-3-16 Example 8
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152
13-3-17 Summary
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153
13-4-1 Velocity and Acceleration
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154
13-4-2 Example 1 and Example 2
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155
13-4-3 Example 3
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156
13-4-4 Summary
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157
14-1-1 Functions of Two Variables and Example 1
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158
14-1-2 Example 2
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159
14-1-3 Example 4
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160
14-1-4 Graph and Example 5
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161
14-1-5 Example 6 and Example 8
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162
14-1-6 Graphs by Computers
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163
14-1-7 Level Curves
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164
14-1-8 Example 9 and Example 10
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165
14-1-9 Example 11 and Computer Generated Level Curves
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166
14-1-10 Function of Three Variables, Example 14 and Example 15
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167
14-1-11 Multiple Variable Functions
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