Department of Mathematics King Abdulaziz University
Math 205 Syllabus
2018\01 - Textbook: Calculus, 8th Edition Author: James Stewart
Chapter Title Section Title Theoretical (Definitions &
Theorem)
Examples HW
Chapter 11
Infinite Sequences and
Series
11.1
Sequences
- Definition of sequence - Definitions 1,9,10,11 - Limit Laws for
Sequences
- The Squeeze Theorem
1,2, 4,5,7,11,13 3,9,77
11.2
Series
-
Definitions 2,4-
Theorems 6,8-
Note 2-
Test of Divergence1-3,6,8-10 23,25,27,33
11.3
The Integral Test and Estimate of
Sums
- The integral Test 1-3 3 ,17
11.4
The Comparison Tests
- The Comparison Test - The Limit
Comparison Test
1-4 4,5,8,18
Chapter 11
Infinite Sequences and
Series
11.5
Alternating Series
- Alternating Series Test
1 4,5,9
11.6
Absolute Convergence and the Ratio and Root Tests.
- The Ratio Test
- The Root Test 1,4,6 2,3,20,21
11.7
Strategy for Testing Series
1,6 6,10,34,37,38
11.8
Power Series
- Definition of Power Series
- Theorem 3
4 5,6, 8,12,18
11.9
Representations of Functions as Power Series
- Equation 1
1,2 4,5
11.10
Taylor and Maclaurin Series
- Theorem 5
- Equations 6&7 1,4,5
11
Chapter 15
Multiple Integrals
15.2
Iterated Integrals
- Equations 1,2&3 - Fubini’s Theorem
- Equation5 1-5 2,3,5,10,13,15,16
15.3
Double Integrals over General Regions
- Equations 2,3,4&5 - Properties of Double
Integrals 1,2,6 1-5,7-10,14
Chapter 15
Multiple Integrals
15.4
Double Integrals in Polar Coordinates
- Equations 2&3 1,2,3,4 1-5,7,29,31
15.6
Surface Area - Equations 2&3 1,2 1,2,3,7,9,13,21
15.7
Triple Integrals
- Fubini’s Theorem for Triple Integrals
- Equation 6,7,8,10&11 1-3 1,3,5,8,11,19,28
15.8
Triple Integrals in Cylindrical Coordinates
- Equations 1,2&4 - Evaluating Triple
Integrals with Cylindrical Coordinates
1,3,4 1-6,9(a), 17,23,24,29
15.9
Triple Integrals in Spherical Coordinates
- Spherical Coordinates - Equations 1,2&3 - Evaluating Triple
Integrals with
Spherical Coordinates
1-4 1-6,9(a),11,21
16.1
Vector fileds
- Equations 1&2
- Gradient Fields 1,6 23
16.2
Line Integrals
- Equations 1,3,7&8 - Line Integrals in Space - Equation 9
- Definition 13
1,2,4,5,7,8 3,10,21
16.3
The Fundamental Theorem For Line Integrals
- Theorems 2,3,4,5&6 - Definition of
Independence of Path 2-5 5,7,12,15
16.4
Green’s Theorem
- Green’s Theorem
- Equation 5 1-4 7,8,9
16.5
Curl And Divergence
- Equations 1,2,9&10
- Theorems 3,4&11 1-4 1,4,13,15
16.7
Surface Integrals
- Parametric Surfaces - Equation 2
- Graphs - Equation 4
- Surface Integrals of Vector Fields - Definition 8
1,2,4 9,23
Instructions:
1. All the mentioned examples and exercises will be solved in the class by the instructor.
3. Marks Distribution: Exam.I (20 marks), Exam.II (20 marks), Exam.II (20 marks), and Final Exam. (40 marks).
Dr sadah alkhateeb
Faculty of Science, Office #409D.
