MAPÚA INSTITUTE OF TECHNOLOGY Department of Mathematics
VISION The Mapua Institute of Technology shall be a global center of excellence in education by providing instructions that are current in content and state-of-the-art in delivery; by engaging in cutting-edge, high-impact research; and by aggressively taking on present-day global concerns.
MISSION The Mapua Institute of Technology disseminates, generates, preserves and applies knowledge in various fields of study. The Institute, using the most effective and efficient means, provides its students with highly relevant professional and advanced education in preparation for and furtherance of global practice. The Institute engages in research with high socio-economic impact and reports on the results of such inquiries. The Institute brings to bear humanity’s vast store of knowledge on the problems of industry and community in order to make the Philippines and the world a better place.
PROGRAM EDUCATIONAL OBJECTIVES (ELECTRICAL ENGINEERING, ELECTRONICS ENGINEERING AND COMPUTER ENGINEERING ENGINEERING) 1. The graduates are able to apply the broad fundamental concepts in social and natural sciences, mathematics, and engineering, and the depth o f knowledge gained in engineering, as professionals in their chosen career s. 2. The graduates are practicing professionals who are qualified and proficient in the use and creation of appropriate and up-to-date research and design methodologies and tools required to successfully perform their tasks in accordance with ethical norms and standards. 3. The graduates demonstrate effective communication skills, the ability to work well either individually or as part of a team, who have embraced lifelong learning values for continuous self and professional or career development. 4. As professionals, the graduates utilize appropriate knowledge and technology in dealing with local and global, industrial, community, and environmental concerns for the advancement of society.
MISSION a
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COURSE SYLLABUS 1. Course Code
:
MATH15
2. Course Title
:
LINEAR ALGEBRA
3. Pre-requisite
:
MATH13, MATH14, 2 YEAR STANDING
4. Co-requisite
:
None
5. Credit
:
2 units
6. Course Description
:
This course deals with the study of matrices and determinants, and its applications in solving systems of equations. It also covers vectors in the plane, vector spaces and subspaces, linear transformations, orthogonality, eigenvalues and eigenvectors.
Course Title:
LINEAR ALGEBRA
Date Effective: st 1 Quarter SY 2013- 2014
nd
Date Revised: April 2013
Prepared by: Cluster V Committee
Approved by: LD SABINO Subject Chair
Page 1 of 6
7. Student Outcomes and Relationship to Program Educational Objectives
:
Program Educational Objectives 1 2 3 4
Student Outcomes (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l)
An ability to apply knowledge of mathematics, science, and engineering An ability to design and conduct experiments, as we ll as to analyze and interpret data An ability to design a system, component, or process to meet desired needs An ability to function on multi-disciplinary teams An ability to identify, formulate, and solve engineering problems An understanding of professional and ethical responsibility An ability to communicate effectively The broad education necessary to understand the impact of engineering solutions in a global and societal context. A recognition of the need for, and an ability to engage in life-long learning A knowledge of contemporary issues An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice. 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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8. Course Outcomes (COs) and Relationship to Student Outcomes :
Course Outcomes After completing the course, the student must be able to: 1. Articulate the properties of matrices and determinants in solving linear systems and apply the concepts effectively and coherently in a simple machine problem and determine if implications are accurate. 2. Comprehend through guided learning the properties of Real Vector Spaces, Subspaces and infer their meanings and applications as to whether the set Vectors: forms a spanning set, are Iinearly independent and forms a basis for the vector space. 3. Analyse, discuss, evaluate and communicate with other students the solution space spanned by the eigenvectors associated with each eigenvalue of matrix and to develop a broad understanding of concepts in linear transformation through narrative learning experience.
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* Level: I- Introduced, R- Reinforced, D- Demonstrated 9. Course Coverage: WEEK
TOPIC
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COURSE OUTCOMES
Orientation and Introduction to the Course 1
Mapúa’s Vision and Mission, Department’s Specific Objectives, Course Policies and Guidelines,
Course Title:
LINEAR ALGEBRA
Date Effective: st 1 Quarter SY 2013- 2014
Date Revised: April 2013
Prepared by: Cluster V Committee
Approved by: LD SABINO Subject Chair
Page 2 of 6
l
Nature and Scope of the course
LINEAR SYSTEMS Types of Linear Systems Methods of Finding a solution
MATRICES Classification of Matrices 1. Row and Column Matrix 2. Null Matrix 3. Square and Triangular Matrix 4. Diagonal and Scalar Matrix 5. Identity Matrix 6. Singular Matrix 7. Transpose of A Matrix 8. Symmetric Matrix
Matrix Operations and Properties Matrix Equality Matrix Addition and Subtraction Scalar and Matrix Multiplication
Reduced Row Echelon Form 2
The Row Echelon Form Row Equivalence Elementary Row Operation Reduction to Row Echelon Form
Working through examples Individual or Group Presentation Class Critique or One-on-one Critique of machine problem
Applications of Row Echelon Form
Class Produced Reviewer Simple Machine Problem Rubric for CPR Rubric for Individual Presentation
CO1
Gaussian Elimination Gauss Jordan Elimination Inverse of a Matrix Linear Systems and Inverses
3
Determinants Properties and Theorems
Higher Order Square Matrices Triangular Method Cofactor Expansion Method of Pivotal Element
Applications of Determinants 4
Cramer’s Rule Adjoint of a Matrix Matrix Inversion by Adjoint Method
LONG QUIZ 1 Vectors in R 5
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Vectors in a Plane Vectors in Space Real Vectors Spaces
Class Produced Reviewer Rubric for CPR
Subspace 6
Linear Combination Linear Spans
Working through examples
Spanning Set Linear Independence Basis and Dimension
Guided Learning
Vectors that form a basis Basis that includes the Given Vectors 7
Rubric for Individual Presentation
CO2
Group Dynamics Class Argumentation
Solution Spaces Homogeneous System Non Homogeneous Systems
Rank of a Matrix Singularity Course Title:
LINEAR ALGEBRA
Date Effective: st 1 Quarter SY 2013- 2014
Date Revised: April 2013
Prepared by: Cluster V Committee
Approved by: LD SABINO Subject Chair
Page 3 of 6
Nullity
LONG QUIZ 2 Eigenvalues and eigenvectors 8
Characteristic Polynomial Eigenvalues Eigenvectors
Working through examples Group Dynamics Class Argumentation
Diagonalization
Linear Transformation
9
Proving Linear Transformations
Class Produced Reviewer Rubric for CPR Rubric for Individual Presentation
CO3
Finding the Linear Transformation 10
LONG QUIZ 3 SUMMATIVE ASSESSMENT FINAL EXAMINATION
11
CO1, CO2, CO3
10. Opportunities to Develop Lifelong Learning Skill A student completing this course should at the minimum be able to : determine and apply the properties of matrices and determinants in solving linear systems, identify the properties of Real Vector Spaces, Subspaces and to determine whether the set Vectors: forms a spanning set, are linearly independent and forms a basis for the vector space, and form the solution space spanned by the eigenvectors associated with each eigenvalue of matrix and to understand linear transformation.
11. Contribution of Course to Meeting the Professional Component: General Education : Engineering Topics : Basic Sciences and Mathematics:
25% 25% 50%
12. Textbook: Linear Algebra, Ron Larson and David C. Falvo, Philippine Ed.
13. Course Evaluation: Student performance will be rated based on the following:
Assessment Tasks CO1
CO2 CO3
Weight (%)
Long Quiz 1
Minimum Average for Satisfactory Performance (%)
20
Course Works
Simple Machine Problem Class Produced Reviewer 1
Long Quiz 2 Course Work Long Quiz 3
Class Produced Reviewer 2
Course Work Class Produced Reviewer 3 Summative Assessment Final Examination TOTAL
10 3 18 3 18 3
23.1
25
17.5
100
70
14.7 14.7
The Final Grades will correspond to the weighted average scores shown below
GRADING SYSTEM Final Average 96 ≤ x < 100 93 ≤ x < 96 90 ≤ x < 93 86 ≤ x < 90 Course Title:
LINEAR ALGEBRA
Date Effective: st 1 Quarter SY 2013- 2014
Date Revised: April 2013
Final Grade 1.00 1.25 1.50 1.75 Prepared by: Cluster V Committee
Approved by: LD SABINO Subject Chair
Page 4 of 6
83 ≤ x < 86 80 ≤ x < 83 76 ≤ x < 80 73 ≤ x < 76 70 ≤ x < 73 Below 70
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. Students incurring more than 9 hours of unexcused absences automatically gets a failing grade regardless of class standing.
b. Submission of Assessment Tasks (Student Outputs) should be on time; late submittal of coursework’s will not be accepted. If you have an extenuating 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. Written Major Examination (Long Quiz 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. Course Portfolio will be collected at the end of the quarter. Lost documents will not be given due credit.
e. 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.
f.
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/simple machine problems 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.
g. 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: Course Title:
LINEAR ALGEBRA
Date Effective: st 1 Quarter SY 2013- 2014
Date Revised: April 2013
Prepared by: Cluster V Committee
Approved by: LD SABINO Subject Chair
Page 5 of 6
14.1 Books a. b. c. d. e. f. g. h.
rd
Schaum’s Outline Series of Linear Algebra, 3 ed., Seymour Lipschitz, 1998 th Elementary Linear Algebra, 9 ed., Howard Anton, 2007 Linear Algebra: From the Beginning, Eric Carlen and Maria Carvalho, 2006 Algebra and It’s Applications, D.V. Huynh, S.K. Jain and S.R. Lopez -Permouth, 2006 Linear Algebra: A Modern Introduction, David Pole, 2007 Advanced Linear Algebra, Steven Roman, 2006 Linear Algebra Demystified, David McMahon, 2005 Linear Algebra and Its Applications, Gilbert Strang, 2005
14.2 Websites a.
Elementary Linear Algebra (Lecture Notes by Keith Matthews, 1991) http://www.numbertheory.org/book/
b. MIT Open CourseWare - http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall2011/ c. A First Course in Linear Algebra - http://linear.ups.edu/
15. Course Materials Made Available: Course schedules for lectures and quizzes Sample of class produced reviewer/guided learning outputs/narrative outputs/ Simple machine problem Sample of written examination of students End-of-course self assessment
16. Committee Members: Course Cluster Chair: Dr. Dante L. Silva CQI Cluster Chair: Engr. Melvyn T. Alviso Members: Engr. Charity Hope A. Gayatin Engr. Marie Chela A. Cenia Engr. Ma. Christina A. Valerio
Course Title:
LINEAR ALGEBRA
Date Effective: st 1 Quarter SY 2013- 2014
Date Revised: April 2013
Prepared by: Cluster V Committee
Approved by: LD SABINO Subject Chair
Page 6 of 6
