DEPARTMENT OF MATHEMATICS COURSE SYLLABUS
COURSE TITLE ENGLISH
CODE/NO
ARABIC CODE/NO.
CREDITS
Th. Pr. Tr. Total
Calculus II for Engineers Math 206 4 0 0 4
Prerequisites: Math 110 (Calculus I)
Course Role in Curriculum (Required/Elective): Required Course Catalogue Description:
This is the second course in a three-course sequence on differential and integral calculus. Topics include integrals of algebraic and transcendental functions of one variable, applications of definite integrals, techniques of integration, improper integrals, infinite series, conic sections, parametric equations, and polar coordinates. Upon completion, students should be able to use differentiation, integration, and approximation techniques to solve application problems.
Instructor Information
Name of the instructor: Dr. Amani Saloom Office location: 003-7
Office Hours: Monday, Wednesday: 12:30-2 pm, Tuesday 9-11 pm E-mail address:
[email protected]
Textbooks:
(Author, Title, Pub., year)
Stewart, James. Calculus, Early Transcendentals, Metric Version,8th ed, Cengage Learning 2015.
ISBN: 978-1-305-27237-8
Course Learning Outcomes:
Upon completion of this course, the students should be able to:
1. Differentiate the Hyperbolic functions.
2. Compute the limit of indeterminate form functions using L’Hospital rule.
3. Evaluate the indefinite integral of a variety of functions using a variety of integration techniques 4. Evaluate the definite integral of a variety of functions analytically and numerically
5. Evaluate improper integrals
6. Utilize the techniques of integration together with appropriate technology to solve practical engineering problems and to analyze and communicate results.
7. Convert functions among rectangular, polar, and parametric forms
8. Differentiate and integrate expressions in parametric and polar form
9. Write the equation, graph, state the properties of, and analyze parabolas, ellipses, and hyperbolas.
10. Determine whether a sequence or a series converges absolutely, converges conditionally, or diverges.
11. Identify a geometric series, a p-series, an alternating series, and determine whether or not it converges; and if it does, find or estimate its sum.
12. Identify a power series and determine its interval of convergence.
13. Determine a Taylor Polynomial, a Maclaurin Series, or a Taylor Series for selected functions.
14. Use Taylor’s Theorem to place a bound on the error for selected Taylor and Maclaurin Series.
Student Outcomes addressed by the course: (Put a sign)
1 An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics
2 An ability to apply the engineering design to produce solutions that meet specified needs with consideration of public
health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors 3 An ability to communicate effectively with a range of audiences
4 An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts
5 An ability to function effectively on a team whose members together provide leadership, creates a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives
6 An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions.
7 An ability to acquire and apply new knowledge as needed, using appropriate learning strategies Key Student Outcomes assessed in the course: 1
Remarks:
1. Any student who misses more than 25% of the total number of classes including tutorials (11 classes or more) will receive DN and consequently the student will be forbidden from taking the final exam.
2. We emphasize that each student should have her textbook in the classes. It will be the source of the required examples and homeworks.
3. Students should exercise all the compulsory problems in the HW column.
4. Mobile phones should be in silent mode.
5. If one of the students is absent from one of the periodic exams due to an official acceptable excuse by the Academic Affairs, the exam will be repeated at the same day of the final. If she missed both periodic exams, she will repeat one of them only and the other will be of zero grade.
6. No make up for the quizzes if missed.
7. The requirements to get an IC grade due to being absent from the final exam are: an attendance of at least 75% of the total lectures, attendance of the first and second exams and an acceptable excuse by the Educational Affairs.
Marks distribution and important dates:
First periodic Exam (90 Min; 25 Marks): Chapters 3,4,5 and 7. Wednesday 17/2/1441H from 12:30-2.
Second periodic Exam (90 Min; 25 Marks): Chapters 6, 8, and 10. Wednesday 23/3/1441H from 12:30-2.
Quizzes (30 min; 15 Marks): 1st quiz (Chapters 5,3 and 4), 2nd quiz (Chapter 7), 3rd quiz (Chapter 6 and 8), 4th quiz (Chapter 10) and 5th quiz (Chapter 11). The quiz will be taken a week after finishing the chapters included.
Final Exam (120 Min; 35 Marks)
Note that chapter 7 will be given before Chapter 6.
Section 7.6 is excluded from the exams.
Chapter Title Section
Title Examples HW Hours
Chapter 3 Differentiation
Rules
3.11
Hyperbolic Functions 1,2,5
Compulsory:
9,10,17,31,35,37,43,44
Optional: 1-45 2
Chapter 4 Application of Differentiation
4.4 Indeterminant forms and L’Hospital’s rule
1-10 Compulsory:
13,21,27,35,52,55,59,63
Optional: 1-68 2
Chapter 5 Integrals
5.1
Areas and Distances 1,2,3 Compulsory: 21,22,23,24,25
Optional: 3,4,5 2
5.2
The Definite Integral 1,4,6,7,8
Compulsory:
18,29,31,32,47,48,49 Optional: 17-20,41-50
2
5.3
The Fundamental Theorem of Calculus 2,4-9
Compulsory:
7,9,11,13,29,32,35,37,57 Optional: 7-44
2
5.4
Indefinite Integrals and the Net Change
Theorem 1-6
Compulsory:
11,13,15,18,25,27,33,35,37 Optional: 1-46
2
5.5
The Substitution Rule 1-11
Compulsory:
3,8,13,21,23,25,28,35,37,41,45 Optional: 1-73
2
Chapter 6 Applications of
Integration
6.1
Areas Between Curves 1,2,6,7
Compulsory:
1,5,9,11,12,14,22,26 Optional: 1-28
1
6.2
Volumes 2- 6
Compulsory:
1,3,8,11,12,15,16,18,47
Optional: 1-18 3
6.3
Volumes by Cylindrical Shells 1-4
Compulsory: 3-7,9,15
Optional: 3-20,37-43 2
Chapter Title Section
Title Examples HW Hour
s
Chapter 7 Techniques of
Integration
7.1
Integration by Parts 1-5
Compulsory:
3,5,6,9,10,15,18,19,25,37,38
Optional: 1-42 2
7.2
Trigonometric Integrals 1-9
Compulsory:
1,3,7,11,17,21,23,27,41,42,43
Optional: 1-49 2.5
7.3
Trigonometric Substitution 1,3-7
Compulsory:
1,4,5,9,13,17,19,22,31 Optional: 1-30
2
7.4
Integration of Rational function by Partial
Fractions 1-5,7-9
Compulsory:
1,3,5,7,9,11,19,21,23,26,31 Optional: 1-38
3
7.5
Strategy for Integration - Optional:1-82 -
7.6
Integration Using Tables and Computer Algebra System
. - Optional: 1-32 -
7.8
Improper Integrals 1-8
Compulsory:
7,11,13,14,15,21,29,31
Optional: 1-40 2
Chapter Title Section
Title Examples Exercises Hours
8.1
Arc Length 1-4
Compulsory:
7,8,9,11,12,14,15,17,19
Optional: 1-22 1
8.2
Area of a Surface of Revolution 1-3
Compulsory: 1,3,5,7,9,13,15,17
Optional: 1-18 2
8.3
Applications to Physics and Engineering 3-6
Compulsory: 23,24,25,26,27,28,33
Optional: 21-33 2
10.1
Curves Defined by Parametric Equations 1-5 Compulsory: 5,6,7,9,11,13,15,17
Optional: 1-18 2
Chapter 10
10.2
Calculus with Parametric Curves 1- 6
Compulsory:
3,4,5,11,13,15,31,41,43,58
Optional: 1-20, 37-44 2
10.3
Polar Coordinates 1-8,9(a)
Compulsory:
1,3,5,15,17,22,25,55,57
Optional: 1-60 2
Parametric
10.4
Areas and Arc Length in Polar
Coordinates 1,2,4
Compulsory:
1,3,9,12,17,19,23,45,47 Optional: 1-34
2
Equations and Polar Coordinates
10.5
Conic Sections 1-7 Compulsory: 1,3,13,19,20,31,37,43
Optional: 1-48 2
10.6 Conic section in polar
coordinates 1-4
Compulsory: 1,2,3,4,5,913,15
Optional: 1-16 2
Chapter Title Section
Title Examples Exercises Hours
Chapter 11 Infinite Sequences and
Series
11.1
Sequences 1,2, 4-13 Compulsory:
3,5,7,13,17,19,21,23,35,43,45,49 Optional: 1-54,72-78
2
11.2
Series
1-4,6-11 Compulsory:
9,11,15,23,24,26,27,28,37,42
Optional: 1-48 2
11.3
The Integral Test and Estimate of Sums 1-4 Compulsory:
3,5,7,11,13,17,21,22,27,31
Optional: 3-32 2
11.4
The Comparison Tests 1-4 Compulsory:
4,5,7,16,17,18,24,28,31
Optional: 3-32 2
11.5
Alternating Series 1-3 Compulsory: 3,4,7,8,10,11,17,19
Optional: 2-20 2
11.6
Absolute Convergence and the Ratio and Root Tests.
1-6 Compulsory:
3,7,8,13,15,20,22,32,35
Optional: 2-38 3
11.7
Strategy for Testing Series - Optional:1-28 -
11.8
Power Series 1,2,4,5 Compulsory: 3,5,7,8,915,18,19,23
Optional: 3-26 3
11.9
Representations of Functions as Power Series
1-3,5-8(a) Compulsory: 3,4,5,8,9,13,15,18
Optional: 3-20 2
11.10
Taylor and Maclaurin Series 1,3-6 Compulsory: 5,6,7,9,11,13,21,25
Optional: 1-26, 31-34 1
