MAPÚA INSTITUTE OF TECHNOLOGY Department of Mathematics
VISION Mapua shall be among the best universities in the world.
MISSION a) The Institute shall provide a learning environment in order for its students students to acquire the attributes that will make them globally competitive. b) The Institute shall engage in economically viable research, development, and innovation. c) The Institute shall provide state-of-the-art state-of-the-art solutions to problems problems of industries and and communities.
PROGRAM EDUCATIONAL OBJECTIVES (ELECTRICAL ENGINEERING, ELECTRONICS ENGINEERING AND COMPUTER ENGINEERING)
MISSION
a
b
c
Within the five years after graduation, the graduates of Electrical Engineering, Electronics Electronics Engineering and Computer Engineering programs shall have: 1. Undertaken, singly or in teams, projects that show ability to solve complex engineering problems. 2. Had substantial involvement in projects that take into consideration consideration safety, health, environmental environmental concerns and the public welfare, partly through adherence to required codes and laws. 3. Demonstrated professional success via promotions and/or positions of increasing responsibility. 4. Demonstrated life-long learning via progress toward completion of an advanced degree, professional development/continuing development/continuing education courses, or industrial training courses. 5. Exhibited professional behavior and attitude in engineering practice.
6. Initiated and implemented actions toward the improvement of engineering practice.
COURSE SYLLABUS 1.
Course Code
: MATH24-1
2.
Course Title
: DIFFERENTIAL EQUATIONS
3.
Pre-requisite
4.
Co-requisite
: MATH23-1 and MATH23-1X for ECE, EE : MATH23-1 for CpE : None
5.
Credit
: 3 units
6.
Course Description
: This course covers useful methods of solving first-order, first-degree differential equations and higher-order, first-degree linear differential equations that have relevant and important applications to the sciences and engineering. It also includes methods of solving higherorder differential equations - the method of undetermined coefficients and variation of parameters. Other topics include the construction of differential equations as mathematical models and introductory discussions on the Laplace Transforms.
Course Title:
Date Effective:
3rd Quarter DIFFERENTIAL EQUATIONS
SY 2014-2015
Date Revised:
January 2015
Prepared by: Cluster V Committee
Approved by:
LD SABINO Subject Chair
Page 1 of 8
7.
Student Outcomes and Relationship to Program Educational Objectives
Program Educational Objectives
Student Outcomes
(a)
8.
an ability to apply knowledge of mathematics, science, and engineering
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2
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3
(b)
an ability to design and conduct experiments, as well as to analyze and interpret from data
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(c)
an ability to design a system, component, or process to meet desired needs
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√
(d)
an ability to function on multidisciplinary teams
(e)
an ability to identify, formulate, and solve engineering problems
(f)
an understanding of professional and ethical responsibility
(g)
an ability to communicate effectively
(h)
the broad education necessary to understand the impact of engineering solutions in the global and societal context
(i)
a recognition of the need for, and an ability to engage in life-long learning
(j)
a knowledge of contemporary issues
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(k)
an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice
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(l)
knowledge and understanding of engineering and management principles as a member and leader in a team, to manage projects and in multidisciplinary environments
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Course Outcomes (COs) and Relationship to Student Outcomes: Course Outcomes
Student Outcomes*
The student should be able to:
a
1. Analyze and demonstrate algebraic quantitative manipulation of data graphically, numerically, analytically and descriptively in solving first order first degree differential equations. 2. Interpret scientific and engineering applications of first order first degree DE through critical thinking, problem solving skills, and integration of mathematical modeling to real life problem situations using appropriate algorithms and technology into mathematical processes. 3. Communicate quantitatively mathematical problems on higher order differential equations and determine which numerical technique to use to solve it logically.
b
c
d
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e
f
R
D
D
D
I
g
h
i
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D
D
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l
R
D
R
I
D
D
* Level: I- Introduced, R- Reinforced, D- Demonstrated : 9. Course Coverage WEEK
DAY
1
1
TOPICS
TLA
AT
COURSE OUTCOMES
Orientation
Course Title:
Date Effective:
3rd Quarter DIFFERENTIAL EQUATIONS
SY 2014-2015
Date Revised:
January 2015
Prepared by: Cluster V Committee
Approved by:
LD SABINO Subject Chair
Page 2 of 8
1.1 Some Basic Mathematical Models; Direction Fields 1.2 Solutions of Some Differential Equations 1.3 Classification of Differential Equations 2.1 Linear Equations; Method of Integrating Factors 2.2 Separable Equations 2.4 Differences Between Linear and NonLinear Equations 2.4 Bernoulli’s Equation 2.3 Modeling with First Order Equations 2.3 Modeling with First Order Equations 2.5 Autonomous Equations and Population Dynamics
2 3 4 2
5 6 7
3
4
8 9 10 11
2.6 Exact Equations and Integrating Factors 2.7 Numerical Approximation: Euler’s Method 2.8 The Existence and Uniqueness Theorems 3.1 Homogenous Equations with Constant Coefficients; Second Order 4.2 Homogenous Equations with Constant Coefficients; Higher Order 3.2 Solutions of Linear Homogenous Equations; The Wronskian 3.3 Complex Roots of the Characteristic Equation 3.4 Repeated Roots; Reduction of Order
13 14 15 16 6
17 18 19
7
20 21
26
3.5 Non-Homogenous Equations; Method of Undetermined Coefficients; Second Order 4.3 The Method of Undetermined Coefficients; Higher Order 3.6 Variation of Parameters; Second Order 4.4 The Method of Variation of Parameters; Higher Order 3.7 Mechanical and Electrical Vibrations
27
3.8 Forced Vibrations
23 24 25
9
28 10
11
Written Long Quiz (Q)
Rounds Individual Presentation
Class Produced Reviewer (A)
Class Critique
Class work (Exr)
Students producing mind maps (storyboards)
On-line Quiz (Ex)
CO 1
Rubric for CPR
Case Study Analysis Creative (Technical and Algorithmic) Writing
Written Long Quiz 2(Q2)
Group Discussion
Class Produced Reviewer 2 (A2)
Class Argumentation
CO 2
Project (Prj) Rubric for Group Work Classwork 2 (Exr 2) Rubric for Group Presentation
On-line Quiz 2 (Ex2)
LONG QUIZ 2
22 8
Buzz Group
LONG QUIZ 1
12
5
Working through examples
Guided Learning Group Dynamics Class Argumentation
Written Long Quiz 3(Q3) Class Produced Reviewer 3 (A3)
Rubric for CPR
CO 3
On-line Quiz 3 (Ex 3) Classwork 3 ( Exr 3)
LONG QUIZ 3
29 30
6.1 Definition of the Laplace Transform 6.2 Solution of Initial Value Problems CO 1 (8%) CO 2 (9%) CO 3 (8%)
SUMMATIVE ASSESSMENT FINAL EXAMINATION (WRITTEN, Departmental, 25%)
31
Class Produced Reviewer CPR 1 (4%) Course Title:
CLASS PRODUCED REVIEWERS Topics
Due Date
1.1 Some Basic Mathematical Models; Direction Fields 1.2 Solutions of Some Differential Equations
WEEK 4 OR AS SCHEDULED
Date Effective:
3rd Quarter DIFFERENTIAL EQUATIONS
SY 2014-2015
Date Revised:
January 2015
Prepared by: Cluster V Committee
Approved by:
LD SABINO Subject Chair
Page 3 of 8
1.3 Classification of Differential Equations 2.1 Linear Equations; Method of Integrating Factors 2.2 Separable Equations 2.4 Differences Between Linear and Non-Linear Equations 2.3 Modeling with First Order Equations 2.5 Autonomous Equations and Population Dynamics 2.6 Exact Equations and Integrating Factors 2.7 Numerical Approximation: Euler’s Method 2.8 The Existence and Uniqueness Theorems 3.1 Homogenous Equations with Constant Coefficients; Second Order 4.2 Homogenous Equations with Constant Coe fficients; Higher Order 3.2 Solutions of Linear Homogenous Equations; The Wronskian 3.3 Complex Roots of the Characteristic Equation 3.4 Repeated Roots; Reduction of Order 3.5 Non-Homogenous Equations; Method of Undetermined Coefficients; Second Order 4.3 The Method of Undetermined Coefficients; Higher Order 3.6 Variation of Parameters; Second Order 4.4 The Method of Variation of Parameters; Higher Order 3.7 Mechanical and Electrical Vibrations 3.8 Forced Vibrations
CPR 2 (4%)
CPR 3 (4%)
WEEK 7 OR AS SCHEDULED
WEEK 9 OR AS SCHEDULED
10. Opportunities to Develop Lifelong Learning Skill To develop lifelong learning skill, the primary learning outcome for this course is the Student’s Quantitative Reasoning, which is to understand and apply the mathematical principles in Differential Equations that will provide students with the needed working knowledge of advanced mathematical concepts and methods, and an awareness of their relationship to increasingly complex world.
11. Contribution of Course to Meeting the Professional Component: General Education: Engineering Topics: Basic Sciences and Mathematics:
25% 25% 50%
12. Textbook: Elementary Differential Equations and Boundary Value Problems, William E. Boyce, Richard C. DiPrima. John Wiley & Sons, Inc. 10 th ed.
Course Title:
Date Effective:
3rd Quarter DIFFERENTIAL EQUATIONS
SY 2014-2015
Date Revised:
January 2015
Prepared by: Cluster V Committee
Approved by:
LD SABINO Subject Chair
Page 4 of 8
13. Course Evaluation Student performance will be rated based on the following:
Assessment Tasks (All resources will be taken from wiley.plus) CO1
CO2
CO3
Weight (%)
Class Produced Reviewer 1 (A)
4
Class Work 1 (Exr)
2
On-Line Quiz 1 (Ex)
5
Written Long Quiz (Q)
12
Class Produced Reviewer 2 (A2)
4
Class Work 2 (Exr 2)
2
Design Project (Prj)
6
On-Line Quiz 2 (Ex 2)
5
Written Long Quiz 2 (Q2)
12
Class Produced Reviewer 3 (A3)
4
Class Work 3 (Exr 3)
2
On-Line Quiz 3 (Ex 2)
5
Written Long Quiz 3 (Q3)
12
Summative Assessment Final Examination (written)
Final Exam (FE)
8
Final Exam (FE2)
9
Final Exam (FE3)
8
TOTAL
100
Minimum Average for Satisfactory Performance (%)
16.1
20.3
16.1
17.5 70
The final grades will correspond to the we ighted average scores shown below Final Average 96 x < 100 93 x < 96 90 x < 93 86 x < 90 83 x < 86 80 x < 83 76 x < 80 73 x < 76 70 x < 73 Below 70
Final Grade 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 5.00 (Fail)
13.1 Other Course Policies a. Attendance According to CHED policy, total number of absences by the students should not be more than 20% of the total number of meetings or 9 hrs for a three-unit-course (6 meetings). Students incurring more than 9 hours of unexcused absences automatically gets a failing grade regardless of class standing. Course Title:
Date Effective:
3rd Quarter DIFFERENTIAL EQUATIONS
SY 2014-2015
Date Revised:
January 2015
Prepared by: Cluster V Committee
Approved by:
LD SABINO Subject Chair
Page 5 of 8
b. Submission of Assessment Tasks (Student Outputs) should be on time; late submittal of coursework’s will not be accepted. If you have a justifying circumstance, it must be discussed and a decision made before the due date or it is due when the assignment is due. Copied works/tasks or any required material to be submitted in the class are strictly prohibited and found guilty will be considered as cheating as well.
c. Major Examination (Long Quiz for both written and on-line and Final Exam) will be administered as scheduled. No special exam will be given unless with a valid reason subject for approval of the Chairman of the Mathematics Department. Furthermore, students of this course are required to participate actively in the events/activities organized for this course.
d. Guidelines for Taking On-Line Exams (in-campus) 1. Students are required to bring their own computer equipments, eg, Laptop,
2.
3.
4.
5.
6.
7.
8. 9.
10. 11.
12.
NetBook; and students must ensure that their gadgets are fully functioning and batteries are fully charged before the exam. Tablets, such as iPads and Android Tablets, are not recommended for use in online examinations. Students are required to submit written solutions of their answers in the online examination using BIG test booklet with lines. Students are highly recommended to bring their own source of internet connection, eg., Broadband Sticks, Portable/Pocket WiFi Connections, Mobile Hotspots. The use of the Mapua WiFi Service might cause the student delays connecting to the internet. During the period of exam, a student is only allowed to use a single browser, in its most recent updated version and as recommended by Wiley.PLUS. The student may opt to use Mozilla Firefox, Google Chrome, Safari, Rockmelt, Internet Explorer as his/her browser, or any internet-browsing software. Entering into private sessions/windows and/or having multiple active sessions/tabs is strictly prohibited. For Google Chrome users, if problems should arise, such as the failure of the loading of exam questions and/or digital images in the WileyPlus examination, the student may right-click-select the frame/pane of the exam question and choose the “reload frame” option. The use of softwares/applications other than the student's browser during the exam is prohibited. The use of softwares/applications not categorized as browsers, such as MS Excel, MATLab, Algebrator, Adobe Reader, PhotoViewer, and the like, is not allowed and will be considered cheating. Access to websites other than WileyPlus.com is not allowed. Access to online solvers such as WolframAlpha, search engines, and third-party websites will be considered cheating. The use of gadgets, other than the student's computer machine, such as cellphones, tablets, and the like, during the exam is not allowed. Talking during the exam is not allowed. Students are to f ocus solely on their monitor screens and solution papers. Clarifications should be addressed directly to the teacher in charge. Students are not allowed to print-screen or save the exam questions, or any portion/part of the exam. Strict checking of attendance will be done before and after the exam. Students who send another person (ringer) in lieu of their presence will be considered cheating. Thus, students should take the exam on his/her assigned classroom not anywhere else. Students are required to come on time in their respective classes for the exam will open exactly during their respective class periods and close automatically at the end of the class period. It is suggested to finish the exam at least 5 minutes earlier to
Course Title:
Date Effective:
3rd Quarter DIFFERENTIAL EQUATIONS
SY 2014-2015
Date Revised:
January 2015
Prepared by: Cluster V Committee
Approved by:
LD SABINO Subject Chair
Page 6 of 8
ensure that the exams will be sent to Wiley.PLUS administrators before the due time. 13. Lastly, the professor will not be held responsible if technical problems should arise, such as loss of internet connection, machine malfunction, loss of battery charge and others.
e. Course Portfolio will be collected at the end of the quarter. Lost documents will not be given due credit.
f.
Language of Instruction Lectures, discussion, and documentation will be in English. Written and spoken work may receive a lower mark if it is, in the opinion of the instructor, deficient in English.
g. Honor, Dress and Grooming Codes All of us have been instructed on the Dress and Grooming Codes of the Institute. We have all committed to obey and sustain these codes. It will be expected in this class that each of us will honor the commitments that we have made. For this course the Honor Code is that there will be no plagiarizing on written work and no cheating on exams. Proper citation must be given to authors whose works were used in the process of developing instructional materials/class produced reviewers/design projects/video clips and learning in this course. If a student is caught cheating on an exam by his instructor or substitute teacher, he or she will be given zero mark for the exam. If a student is caught cheating twice on the same course, the student will be referred to the Prefect of Student Affairs and be given a failing grade. Grave misconduct other than cheating will likewise be given a failing grade. Disrespect to your teacher or to others in the classroom will not be tolerated in the least. Argument is great but bullying, fighting, mocking, and demeaning the teacher or other students will not be allowed. Come to class on time, there can be mitigating circumstances from time to time but if it becomes a chronic behavior you may lose points or credit for the class.
h. Consultation Schedule Consultation schedules with the Professor are posted outside the Math Faculty room and in the School’s web-page (http://che-chm.mapua.edu.ph). It is recommended that the student first set an appointment to confirm the instructor’s availability.
14. Other References 14.1 Books a) b) c) d)
A First Course in Differential Equations with Modern Applications by Dennis Zill, 7 th ed., 2000 Differential Equations Computing and Modeling by Edwards and Penny, 1996 Elementary Differential Equations by Boyce and Richard C. Diprima, 1997 Elementary Differential Equations by William Derrich and Stanley Grossman, 1997
14.2 Websites a) S.O.S Differential Equations http://www.sosmath.com/diffeq/diffeq.html b) Paul’s Online Math Notes http://tutorial.math.lamar.edu/Classes/DE/DE.aspx c) MIT Open Courseware http://ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall2011/ d) Differential Equations Interactive Mathematics http://www.intmath.com/differential-equations/desintro.php e) http://demonstrations.wolfram.com/topic.html?topic=Differential+Equations Course Title:
Date Effective:
3rd Quarter DIFFERENTIAL EQUATIONS
SY 2014-2015
Date Revised:
January 2015
Prepared by: Cluster V Committee
Approved by:
LD SABINO Subject Chair
Page 7 of 8
f)
These are interactive explorations of differential equations topics that can run in a free player. Boyce 10e WileyPLUS course includes some which are specifically associated with the textbook. http://odetoolkit.hmc.edu/ A Java program that helps users calculate, visualize, and explore solutions to differential equations, by the creators of the ODE Toolkit software.
15. Course Materials Made Available: Course Calendar Samples of Coursework’s /Design Projects/Video Presentations/Class Produced Reviewers Samples of written examinations of students End-of-course self-assessment
16. Committee Members (Cluster V): Course Cluster Chair: Dr. Dante L. Silva CQI Cluster Chair: Engr. Melvyn T. Alviso Members: Engr. Charity Hope A. Gayatin Engr. Ma. Christina A. Valerio
Course Title:
Date Effective:
3rd Quarter DIFFERENTIAL EQUATIONS
SY 2014-2015
Date Revised:
January 2015
Prepared by: Cluster V Committee
Approved by:
LD SABINO Subject Chair
Page 8 of 8
