1 | Week | Date | Topic | |
---|---|---|---|---|
2 | ||||
3 | 1. PARAMETRIC EQUATIONS AND POLAR COORDINATES | |||
4 | ||||
5 | 1 | 5/9/16 - 9/9/16 | 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 | 12/9/16 - 18/9/16 | Special Leave (Raya Haji) | ||
17 | ||||
18 | ||||
19 | 2 | 19/9/16 - 23/9/16 | Polar Coordinates | |
20 | - Polar Coordinate Systems | |||
21 | - Relationship Between Polar and Rectangular Coordinates | |||
22 | - Graphs in Polar Coordinates (Lines, Circles and Cardioids) | |||
23 | ||||
24 | Polar Curves | |||
25 | ||||
26 | Tangent Lines and Arc Length for Polar Curves | |||
27 | ||||
28 | Tutorial/Lab | |||
29 | ||||
30 | ||||
31 | 3 | 26/9/16 - 30/9/16 | 2. THREE DIMENSIONAL SPACE; VECTORS | |
32 | ||||
33 | Rectangular Coordinates in Three-Space | |||
34 | - Rectangular Coordinate Systems | |||
35 | - Distance, Midpoint, and Spheres | |||
36 | ||||
37 | Vectors | |||
38 | - Vectors Viewed Geometrically | |||
39 | - Vectors in Coordinate Systems | |||
40 | - Arithmetic Operations on Vectors | |||
41 | - Vectors with Initial Point Not at the Origin | |||
42 | - Rules of Vector Arithmetic | |||
43 | - Norm of a Vector | |||
44 | - Unit Vectors | |||
45 | - Normalizing a Vector | |||
46 | - Vectors Determined by Length and Angle | |||
47 | - Vectors Determined by Length and a Vector | |||
48 | in the Same Direction | |||
49 | ||||
50 | Tutorial/Lab | |||
51 | ||||
52 | QUIZ 1 | |||
53 | ||||
54 | ||||
55 | 4 | 3/10/16 - 7/10/16 | Dot Products; Projections | |
56 | - Definition of the Dot Product | |||
57 | - Algebraic Properties of the Dot Product | |||
58 | - Angle Between Vectors | |||
59 | - Interpreting the Sign of the Dot Product | |||
60 | - Direction Angles | |||
61 | - Decomposing Vectors into Orthogonal Components | |||
62 | - Orthogonal Projections | |||
63 | ||||
64 | Cross Products | |||
65 | - Determinants | |||
66 | - Cross Product | |||
67 | - Algebraic Properties of the Cross Product | |||
68 | - Geometric Properties of the Cross Product | |||
69 | - Scalar Triple Products | |||
70 | - Algebraic Properties of Scalar Triple Product | |||
71 | ||||
72 | Tutorial/Lab | |||
73 | ||||
74 | 2/10/16 (Sun) | Maal Hijrah | ||
75 | ||||
76 | ||||
77 | 5 | 10/10/16 - 14/10/16 | Parametric Equations of Lines | |
78 | - Lines Determined by a Point and a Vector | |||
79 | - Line Segments | |||
80 | - Vector Equation of Lines | |||
81 | ||||
82 | Planes in Three-Space | |||
83 | - Planes Parallel to the Coordinate Planes | |||
84 | - Planes Determined by a Point and a Normal Vector | |||
85 | - Distance Problems Between Planes | |||
86 | ||||
87 | Tutorial/Lab | |||
88 | ||||
89 | ||||
90 | 6 | 17/10/16 - 21/10/16 | Cylindrical and Quadric Surfaces | |
91 | - Techniques for Graphing Plane, Quadric Surfaces | |||
92 | (Circular/Elliptic Cylinder, Parabolic Cylinder) | |||
93 | and Quadratic Surfaces (Sphere, Ellipsoid, Paraboloid | |||
94 | and Cone) | |||
95 | - Translation of Cylindrical and Quadric Surfaces | |||
96 | ||||
97 | Tutorial/Lab | |||
98 | ||||
99 | ||||
100 | 7 | 24/10/16 - 28/10/16 | 3. PARTIAL DERIVATIVES | |
101 | ||||
102 | Functions of Two or More Variables | |||
103 | - Notation and Terminology | |||
104 | - Graphs of Functions of Two Variables | |||
105 | ||||
106 | Limits and Continuity | |||
107 | - Limits along Curves | |||
108 | - General Limits of Functions of Two Variables | |||
109 | - Properties of Limits | |||
110 | - Relationship Between General Limits | |||
111 | and Limits Along Smooth Curves | |||
112 | ||||
113 | Tutorial/Lab | |||
114 | ||||
115 | TEST 1 | |||
116 | ||||
117 | ||||
118 | 8 | 31/10/16 - 4/11/16 | Limits and Continuity | |
119 | - Continuity | |||
120 | - Limits at Discontinuities | |||
121 | - Continuity on a Set | |||
122 | ||||
123 | Partial Derivatives | |||
124 | - Partial Derivatives of Functions of Two Variables | |||
125 | - Partial Derivatives Viewed as Rates of Change and Slopes | |||
126 | - Partial Derivative Notation | |||
127 | - Partial Derivatives of Functions with More than Two Variables | |||
128 | - Higher Order Partial Derivatives | |||
129 | - Equality of Mixed Partials | |||
130 | ||||
131 | Tutorial/Lab | |||
132 | ||||
133 | QUIZ 2 | |||
134 | ||||
135 | ||||
136 | 9 | 7/11/16-11/11/16 | Chain Rule | |
137 | - The Chain Rule for Derivatives | |||
138 | - Implicit Differentiation | |||
139 | - Related Rates Problems | |||
140 | - The Chain Rule for Partial Derivatives | |||
141 | ||||
142 | Tangent Plane; Total Differentials | |||
143 | - Tangent Plane | |||
144 | - Differentials | |||
145 | ||||
146 | Directional Derivatives | |||
147 | - Directional Derivatives | |||
148 | - The Gradient | |||
149 | - Properties of the Gradient | |||
150 | ||||
151 | Tutorial/Lab | |||
152 | ||||
153 | ||||
154 | 10 | 14/11/16 - 18/11/16 | Maxima and Minima of Functions of Two Variables | |
155 | - Extrema | |||
156 | - Finding Relative Extrema | |||
157 | - The Second Partial Test | |||
158 | ||||
159 | 4. MULTIPLE INTEGRALS | |||
160 | ||||
161 | Double Integrals in Rectangular Coordinates | |||
162 | - Definition of a Double Integral | |||
163 | - Properties of Double Integrals | |||
164 | - Evaluating Double Integrals | |||
165 | ||||
166 | Tutorial/Lab | |||
167 | ||||
168 | ||||
169 | 11 | 21/11/16 - 25/11/16 | Double Integral Over Nonrectangular Regions | |
170 | - Double Integral Over Nonrectangular Regions | |||
171 | - Setting up Limits of Integration for Evaluating Double Integrals | |||
172 | - Reversing the Order of Integration | |||
173 | - Area Calculated as a Double Integral | |||
174 | ||||
175 | Tutorial/Lab | |||
176 | ||||
177 | ||||
178 | 28/11/16 - 4/12/16 | Mid-Semester Break | ||
179 | ||||
180 | ||||
181 | 12 | 5/12/16 - 9/12/16 | Double Integrals in Polar Coordinates | |
182 | - Simple Polar Regions | |||
183 | - Double Integrals in Polar Coordinates | |||
184 | - Evaluating Polar Double Integrals | |||
185 | - Finding Areas Using polar Double Integrals | |||
186 | ||||
187 | Triple Integrals in Rectangular Coordinates | |||
188 | - Definition of a Triple Integral | |||
189 | - Evaluating Triple Integrals Over Rectangular Boxes | |||
190 | ||||
191 | Tutorial/Lab | |||
192 | ||||
193 | QUIZ 3 | |||
194 | ||||
195 | ||||
196 | 13 | 12/12/16 - 16/12/16 | Triple Integrals in Rectangular Coordinates | |
197 | - Evaluating Triple Integrals Over More General Regions | |||
198 | - Volume Calculated as a Triple Integral | |||
199 | - Integration in Other Orders | |||
200 | ||||
201 | Triple Integrals in Cylindrical and Spherical Coordinates | |||
202 | - Triple Integrals in Cylindrical Coordinates | |||
203 | - Converting Triple Integrals From Rectangular to | |||
204 | Cylindrical Coordinates and vice versa | |||
205 | ||||
206 | Tutorial/Lab | |||
207 | ||||
208 | 12/12/16 (Mon) | Maulidur Rasul | ||
209 | ||||
210 | ||||
211 | 14 | 19/12/16 - 23/12/16 | Triple Integrals in Cylindrical and Spherical Coordinates | |
212 | - Triple Integral in Spherical Coordinates | |||
213 | - Converting Triple Integrals From Rectangular to | |||
214 | Spherical Coordinates and vice versa | |||
215 | ||||
216 | Tutorial/Lab | |||
217 | ||||
218 | TEST 2 | |||
219 | ||||
220 | ||||
221 | 25/12/16 (Sun) | Christmas | ||
222 | ||||
223 | 26/12/16 - 28/12/16 | Revision Week | ||
224 | ||||
225 | ||||
226 | 29/12/16 - 21/1/17 | Final Examination | ||
227 | ||||
228 | ||||
229 | 22/1/17 - 5/3/17 | Semester Break | ||
230 | ||||
231 | ||||
232 | Assessment: | |||
233 | Final examination – One 3-hour paper | : 60% | ||
234 | Continuous assessment | : 40% | ||
235 | Test 1 (15%) | |||
236 | Test 2 (15%) | |||
237 | Quiz 1 (2%) | |||
238 | Quiz 2 (2%) | |||
239 | Quiz 3 (2%) | |||
240 | Lab Assignment 1 (2%) | |||
241 | Lab Assignment 2 (2%) | |||
242 | ||||
243 | Recommended Text: | |||
244 | James Stewart, Calculus, 7th Edition, Cengage Learning, 2012, ISBN: 9780538497817 |