1 | Week | Date | Topic | |
---|---|---|---|---|

2 | ||||

3 | 1 | 12/9/2017-15/9/2017 | 1. PARAMETRIC EQUATIONS AND POLAR COORDINATES | |

4 | ||||

5 | Parametric Equations | |||

6 | - Definition of Parametric Equations | |||

7 | - Orientation of a Parametric Curve | |||

8 | - Eliminating the Parameter | |||

9 | - Representing Graphs of Functions Parametrically | |||

10 | - Tangent Lines to Curves Defined Parametrically | |||

11 | - Arc Length of Curves Defined Parametrically | |||

12 | ||||

13 | Tutorial | |||

14 | ||||

15 | 16/9/2017 | Malaysia Day | ||

16 | ||||

17 | ||||

18 | 2 | 18/9/2017-22/9/2017 | Polar Coordinates | |

19 | - Polar Coordinate Systems | |||

20 | - Relationship Between Polar and Rectangular Coordinates | |||

21 | - Graphs in Polar Coordinates (Lines, Circles and Cardioids) | |||

22 | ||||

23 | Polar Curves | |||

24 | ||||

25 | Tangent Lines and Arc Length for Polar Curves | |||

26 | ||||

27 | Tutorial/Lab | |||

28 | ||||

29 | 22/9/2017 | Awal Muharram | ||

30 | ||||

31 | ||||

32 | 3 | 25/9/2017-29/9/2017 | 2. THREE DIMENSIONAL SPACE; VECTORS | |

33 | ||||

34 | Rectangular Coordinates in Three-Space | |||

35 | - Rectangular Coordinate Systems | |||

36 | - Distance, Midpoint, and Spheres | |||

37 | ||||

38 | Vectors | |||

39 | - Vectors Viewed Geometrically | |||

40 | - Vectors in Coordinate Systems | |||

41 | - Arithmetic Operations on Vectors | |||

42 | - Vectors with Initial Point Not at the Origin | |||

43 | - Rules of Vector Arithmetic | |||

44 | - Norm of a Vector | |||

45 | - Unit Vectors | |||

46 | - Normalizing a Vector | |||

47 | - Vectors Determined by Length and Angle | |||

48 | - Vectors Determined by Length and a Vector | |||

49 | in the Same Direction | |||

50 | ||||

51 | Tutorial/Lab | |||

52 | ||||

53 | QUIZ 1 | |||

54 | ||||

55 | ||||

56 | 4 | 2/10/2017-6/10/2017 | Dot Products; Projections | |

57 | - Definition of the Dot Product | |||

58 | - Algebraic Properties of the Dot Product | |||

59 | - Angle Between Vectors | |||

60 | - Interpreting the Sign of the Dot Product | |||

61 | - Direction Angles | |||

62 | - Decomposing Vectors into Orthogonal Components | |||

63 | - Orthogonal Projections | |||

64 | ||||

65 | Cross Products | |||

66 | - Determinants | |||

67 | - Cross Product | |||

68 | - Algebraic Properties of the Cross Product | |||

69 | - Geometric Properties of the Cross Product | |||

70 | - Scalar Triple Products | |||

71 | - Algebraic Properties of Scalar Triple Product | |||

72 | ||||

73 | Tutorial/Lab | |||

74 | ||||

75 | ||||

76 | 5 | 9/10/2017-13/10/2017 | Parametric Equations of Lines | |

77 | - Lines Determined by a Point and a Vector | |||

78 | - Line Segments | |||

79 | - Vector Equation of Lines | |||

80 | ||||

81 | Planes in Three-Space | |||

82 | - Planes Parallel to the Coordinate Planes | |||

83 | - Planes Determined by a Point and a Normal Vector | |||

84 | - Distance Problems Between Planes | |||

85 | ||||

86 | Tutorial/Lab | |||

87 | ||||

88 | ||||

89 | 16/10/2017-22/10/2017 | Mid-Sem Break | ||

90 | ||||

91 | 18/10/2017 | Deepavali | ||

92 | ||||

93 | ||||

94 | 6 | 23/10/2017-27/10/2017 | Cylindrical and Quadric Surfaces | |

95 | - Techniques for Graphing Plane, Quadric Surfaces | |||

96 | (Circular/Elliptic Cylinder, Parabolic Cylinder) | |||

97 | and Quadratic Surfaces (Sphere, Ellipsoid, Paraboloid | |||

98 | and Cone) | |||

99 | - Translation of Cylindrical and Quadric Surfaces | |||

100 | ||||

101 | Tutorial/Lab | |||

102 | ||||

103 | ||||

104 | 7 | 30/10/2017-3/11/2017 | 3. PARTIAL DERIVATIVES | |

105 | ||||

106 | Functions of Two or More Variables | |||

107 | - Notation and Terminology | |||

108 | - Graphs of Functions of Two Variables | |||

109 | ||||

110 | Limits and Continuity | |||

111 | - Limits along Curves | |||

112 | - General Limits of Functions of Two Variables | |||

113 | - Properties of Limits | |||

114 | - Relationship Between General Limits | |||

115 | and Limits Along Smooth Curves | |||

116 | ||||

117 | Tutorial/Lab | |||

118 | ||||

119 | TEST 1 | |||

120 | ||||

121 | ||||

122 | 8 | 6/11/2017-10/11/2017 | Limits and Continuity | |

123 | - Continuity | |||

124 | - Limits at Discontinuities | |||

125 | - Continuity on a Set | |||

126 | ||||

127 | Partial Derivatives | |||

128 | - Partial Derivatives of Functions of Two Variables | |||

129 | - Partial Derivatives Viewed as Rates of Change and Slopes | |||

130 | - Partial Derivative Notation | |||

131 | - Partial Derivatives of Functions with More than Two Variables | |||

132 | - Higher Order Partial Derivatives | |||

133 | - Equality of Mixed Partials | |||

134 | ||||

135 | Tutorial/Lab | |||

136 | ||||

137 | QUIZ 2 | |||

138 | ||||

139 | ||||

140 | 9 | 13/11/2017-17/11/2017 | Chain Rule | |

141 | - The Chain Rule for Derivatives | |||

142 | - Implicit Differentiation | |||

143 | - Related Rates Problems | |||

144 | - The Chain Rule for Partial Derivatives | |||

145 | ||||

146 | Tangent Plane; Total Differentials | |||

147 | - Tangent Plane | |||

148 | - Differentials | |||

149 | ||||

150 | Directional Derivatives | |||

151 | - Directional Derivatives | |||

152 | - The Gradient | |||

153 | - Properties of the Gradient | |||

154 | ||||

155 | Tutorial/Lab | |||

156 | ||||

157 | ||||

158 | 10 | 20/11/2017-24/11/2017 | Maxima and Minima of Functions of Two Variables | |

159 | - Extrema | |||

160 | - Finding Relative Extrema | |||

161 | - The Second Partial Test | |||

162 | ||||

163 | 4. MULTIPLE INTEGRALS | |||

164 | ||||

165 | Double Integrals in Rectangular Coordinates | |||

166 | - Definition of a Double Integral | |||

167 | - Properties of Double Integrals | |||

168 | - Evaluating Double Integrals | |||

169 | ||||

170 | Tutorial/Lab | |||

171 | ||||

172 | ||||

173 | 11 | 27/11/2017-1/12/2017 | Double Integral Over Nonrectangular Regions | |

174 | - Double Integral Over Nonrectangular Regions | |||

175 | - Setting up Limits of Integration for Evaluating Double Integrals | |||

176 | - Reversing the Order of Integration | |||

177 | - Area Calculated as a Double Integral | |||

178 | ||||

179 | Tutorial/Lab | |||

180 | ||||

181 | ||||

182 | 12 | 4/12/2017-8/12/2017 | Double Integrals in Polar Coordinates | |

183 | - Simple Polar Regions | |||

184 | - Double Integrals in Polar Coordinates | |||

185 | - Evaluating Polar Double Integrals | |||

186 | - Finding Areas Using polar Double Integrals | |||

187 | ||||

188 | Triple Integrals in Rectangular Coordinates | |||

189 | - Definition of a Triple Integral | |||

190 | - Evaluating Triple Integrals Over Rectangular Boxes | |||

191 | ||||

192 | Tutorial/Lab | |||

193 | ||||

194 | QUIZ 3 | |||

195 | ||||

196 | ||||

197 | 13 | 11/12/2017-15/12/2017 | Triple Integrals in Rectangular Coordinates | |

198 | - Evaluating Triple Integrals Over More General Regions | |||

199 | - Volume Calculated as a Triple Integral | |||

200 | - Integration in Other Orders | |||

201 | ||||

202 | Triple Integrals in Cylindrical and Spherical Coordinates | |||

203 | - Triple Integrals in Cylindrical Coordinates | |||

204 | - Converting Triple Integrals From Rectangular to | |||

205 | Cylindrical Coordinates and vice versa | |||

206 | ||||

207 | Tutorial/Lab | |||

208 | ||||

209 | ||||

210 | 14 | 18/12/2017-22/12/2017 | Triple Integrals in Cylindrical and Spherical Coordinates | |

211 | - Triple Integral in Spherical Coordinates | |||

212 | - Converting Triple Integrals From Rectangular to | |||

213 | Spherical Coordinates and vice versa | |||

214 | ||||

215 | Tutorial/Lab | |||

216 | ||||

217 | TEST 2 | |||

218 | ||||

219 | ||||

220 | 25/12/2017-1/1/2018 | Revision Week | ||

221 | ||||

222 | 25/12/2017 | Christmas | ||

223 | ||||

224 | 2/1/2018-25/1/2018 | Final Examination | ||

225 | ||||

226 | 26/1/2018-4/3/2018 | Semester Break | ||

227 | ||||

228 | ||||

229 | Assessment: | |||

230 | Final examination – One 3-hour paper | : 60% | ||

231 | Continuous assessment | : 40% | ||

232 | Test 1 (15%) | |||

233 | Test 2 (15%) | |||

234 | Quiz 1 (2%) | |||

235 | Quiz 2 (2%) | |||

236 | Quiz 3 (2%) | |||

237 | Lab Assignment 1 (2%) | |||

238 | Lab Assignment 2 (2%) | |||

239 | ||||

240 | Recommended Text: | |||

241 | James Stewart, Calculus, 7th Edition, Cengage Learning, 2012, ISBN: 9780538497817 |