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.
a. b. c. d.
MISSION The Mapua Institute Institute of Technology Technology disseminates, disseminates, generates, generates, preserves and applies knowledge in in various fields of of study. study. The Institute, Institute, using using the most effective effective and efficient efficient means, means, provides provides its students students with with highly relevant relevant professional professional and advanced education in preparation for and furtherance of global practice. The Institute Institute engages engages in research with high high socio-economic socio-economic impact impact and reports reports on on the results results of of such inquiries. The Institute brings to bear humanity’s vast store of knowledge knowledge on the problems of industry and community in order to make the Philippines and the world a better place.
PROGRAM EDUCATIONAL OBJECTIVES (BIOLOGICAL ENGINEERING, CHEMICAL ENGINEERING, CIVIL ENGINEERING, ENIRONMENTAL AND SANITARY ENGINEERING, INDUSTRIAL ENGINEERING, MECHANICAL ENGINEERING AND MANUFACTURING ENGINEERING) 1. To enable our graduates graduates to to practice practice as successful successful engineers engineers for the advancement advancement of society. 2. To promot promotee professi professional onalism ism in in the engine engineerin eringg practic practice. e.
MISSION b c
a
d
COURSE SYLLABUS 1.
Course Code:
MATH 21 - 1
2.
Course Title:
CALCULUS 1
3.
Pre-requisite: Pre-requisit e:
MATH 10 – 4, MATH 13 – 1 MATH 10 – 4, MATH 12 – 1 for CS
4.
Co-requisite: Co-requisit e:
none
5.
Credit:
5 units
6.
Course Description :
This course in Calculus covers discussion on functions, limits and continuity of functions, basic rules on differentiation of algebraic and transcendental functions, higher order and implicit differentiation, applications of the derivatives which include curve tracing, equations of tangent and normal lines, applied maxima/minima and rate of change problems. This course also covers topics in Analytic Geometry that are essential in the study of Calculus. The use of the Rectangular and Polar coordinate systems facilitate the thorough discussion of the fundamental concepts and theorems of Analytic Geometry and the properties and graphs of the different algebraic and polar functions.
7.
Student Outcomes and Relationship Relationshi p to Program Educational Objectives Program Educational Objectives 1 2
Student Outcomes (a) (b)
an ability to apply knowledge of mathematics, science, and engineering an ability to design and conduct experiments, as well as to analyze and interpret from data
Course Title:
CALCULUS I
Date Effective:
Date Revised:
Prepared by
April 2014
Cluster II Committee
th
4 Term SY2013-2014
√
Approved by: LD SABINO Subject Chair
Page 1 of 6
(c) (d) (e) (f) (g)
an ability to design a system, component, or process to meet desired needs an ability to function on multidisciplinary multidisci plinary teams an ability to identify, formulate, and solve engineering problems an understanding of professional and ethical responsibility responsibilit y an ability to communicate effectively the broad education necessary to understand the impact of engineering solutions in the global and societal context a recognition recognitio n of the need for, and an ability to engage in life-long 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
(h) (i) (j) (k) (l)
√ √ √ √ √ √ √
√
8. Course Outcomes (COs) and Relationship to Student Outcomes Course Outcomes After completing completing the course, the the student student must be able to: 1. Apply principles gained from the prerequisite courses 2. Discuss comprehensively the fundamental concepts in Analytic Geometry Geometry and and use them them to solve application application problems and problems involving lines. 3. Distinguish Distinguis h equations representing the circles and the conics; use the properties of a particular geometry to sketch the graph in using the rectangular or the polar coordinate system. Furthermore, to be able to write the equation and to solve application problems involving a particular geometry. 4. Discuss and apply comprehensively the concepts, properties and theorems of functions, limits, continuity and the derivatives in determining the derivatives of algebraic functions. 5. Analyze correctly correctl y and solve properly application problems concerning the derivatives to include writing equation of tangent/normal line, curve tracing ( including all types of algebraic curves and cusps), optimization problems, rate of change and related-rates problems (time-rate problems). * Level: I- Introduced, R- Reinforced, D- Demonstrated
a
b
c
Student Outcomes* d e f g h i
j
D
D
D
R
R
D
D
D
R
R
D
D
D
R
R
D
D
D
R
R
D
D
D
R
R
k
9. Course Coverage WEEK
TOPIC
TLA
Mission and Vision of Mapua M apua Institute of Technology
Peer discussion on Mission and Vision of Mapua Institute of Technology
Orientation and Introduction to the
Course
Discussion
on COs, TLAs, and ATs of the course Overvie w on
1
CALCULUS I
CO
student-centered learning and eclectic approaches to be used in the course. Fundamental Concept of Analytic Geometry: Rectangular Coordinate System, Directed Distance, Distance Formula Division of Line Segment Slope
Course Title:
AT
Date Effective:
Date Revised:
Prepared by
April 2014
Cluster II Committee
th
4 Term SY2013-2014
- Working through examples
- Class Produced Reviewer I
Approved by: LD SABINO Subject Chair
Page 2 of 6
l
and Inclination of a Line Angle Between Lines Area of a Triangle/Polygon
- Visually Guided Learning
- Classwork 1 CO2
Locus of a Moving Point Normal Form of Equation of Line Distance of Point from Line Distance between Parallel Lines 2 Long quiz 1
CO2 -Working through examples
CIRCLES and the CONICS:
3
Properties and Application Involving the Circles, Parabola, Ellipse and Hyperbola with Vertex/ Center at any point with Horizontal/Vertical/ Oblique Axis -
Visually Guided Learning
Classwork 2
- Class Produced Reviewer 2
CO3 4 Polar Curves and Parametric Curves; Sketching and Transformation to Rectangular forms of equations
LONG QUIZ 2
CO3
5 Limits: Definition and Concepts Theorems One-Sided Limits Limits of Functions Infinite Limits and Limits at Infinity: Evaluation And Interpretation Squeeze Theorem: Limits of Expression Involving Transcendental Functions
- Working through examples - Visually Guided Learning
Continuity : Definition and Theorem T ypes of Discontinuity; Relationship between limits and Discontinuity
6
The Derivative and Differentiability of a Function: Definition and concept Evaluation of the Derivative of a Function based on Definition (Increment Method or Four-Step Rule Method) Derivatives of Algebraic Functions Using the Basic Theorems of Differentiation and the Chain Rule Higher Order and Implicit Differentiation
- Class Produced Reviewer 3
- Classwork 3
- Group Dynamics
- Technology Guided Learning CO4
7 Derivatives of the Exponential and Logarithmic Functions with Applications
LONG QUIZ 3
Course Title:
CALCULUS I
Date Effective:
Date Revised:
Prepared by
April 2014
Cluster II Committee
th
4 Term SY2013-2014
CO4
Approved by: LD SABINO Subject Chair
Page 3 of 6
Applications : Equations of Tangent and Normal Lines 8
- Working through example Application of the Concepts of the Derivati ve and Continuity on Curve Tracing ( Include all t ypes of the Algebraic curves, cusps)
Class Produced Reviewer 4 Classwork 4
- Visually Guided learning Project
9
Optimization Problems: Applied Maxima/Minima Problems
CO5
Rate of Change Problems; Related-Rate Problems (Time-Rate Problems) 10
LONG QUIZ 4
CO5
Summative Assessment Final Examination
11
CO2, CO3, CO4. CO5
10. Opportunities to Develop Lifelong Learning Skill To help students understand and apply the mathematical principles of Calculus and Analytic Geometry and provide them with the needed working knowledge of the different mathematical concepts and methods for them to fully understand the relationship of Calculus with the increasingly complex world. 11. Contribution of Course to Meeting the Professional Component Engineering Topics General Education Basic Sciences and Mathematics
: : :
0% 0% 100%
12. Textbook: College Algebra and Trigonometry by Aufmann, et.al. Calculus Early Transcendental Functions 5 th ed. By Ron Larson and Bruce Edwards
13. Course Evaluation Student performance will be rated based on the following: Assessment Tasks
CO 1 CO 2
Course Title:
CALCULUS I
Weight (%)
Minimum Average for Satisfactory Performance (%)
10.0
7.0
CPR 1
2.0
1.4
Classwork 1
2.0
1.4
Diagnostic Examination
Date Effective:
Date Revised:
Prepared by
April 2014
Cluster II Committee
th
4 Term SY2013-2014
Approved by: LD SABINO Subject Chair
Page 4 of 6
CO 3
CO 4
Quiz 1
11.0
7.7
CPR 2
2.0
1.4
Classwork 2
2.0
1.4
Quiz 2
11.0
7.7
CPR 3
2.0
1.4
Classwork 3
2.0
1.4
Quiz 3
11.0
7.7
CPR 4
2.0
1.4
Classwork 4
2.0
1.4
Quiz 4
11.0
7.70
Project
5.0
3.50
25.0
17.5
CO 5
Summative Assessment: Final Examination TOTAL
70
The final grades will correspond to the weighted 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
13.1.
Final Grade 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 5.00 (Fail)
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 output should be submitted on time. Late submission of course works will not be accepted. c. Written Examination Long quizzes and final examination will be administered per schedule. No special exam will be given unless with a valid reason subject to approval of the Department Chairman. d. Course Portfolio Course portfolio will be collected at the end of the quarter. e. Language of Instruction Lectures, discussion, and documentation will be in English. Written Writt en and spoken work may receive a lower mark if it is, in the opinion of the instructor, deficient in English.
Course Title:
CALCULUS I
Date Effective:
Date Revised:
Prepared by
April 2014
Cluster II Committee
th
4 Term SY2013-2014
Approved by: LD SABINO Subject Chair
Page 5 of 6
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 and learning in this course. If a student is caught cheating on an exam, he or she will be given zero mark for the exam. If a student is caught cheating twice, the student will be referred to the Prefect of Student Affairs and be given a failing grade.
g. Consultation Schedule Consultation schedules with the Professor are posted outside the faculty room and in the Department’ Department ’s web-page ( http://math.mapua.edu.ph ). It is recommended that the student first set an appointment to confir m confir m the instructor’s availability.
14. Other References 14.1.
Books a. TCWAG by Louis Leithold, International Edition 2001. b. Schaumm’s Outline Series, Differential and Integral. c. Differential and Integral Calculus by Love and Rainville d. Calculus 6e by Edwards and Penny e. CALCULUS (One and Several variables) 10 th Ed by Salas, Hille and Etgen f. University Calculus by Hass, et al g. Analytic Geometry by Fuller and Tarwater h. Analytic Geometry by Riddle i. Analytic Geometry by Marquez, et al
14.2
Websites Enhanced Web Assign
15.Course 15. Course Materials Made Available Course schedules for lectures and quizzes Samples of assignment/Problem sets of students Samples of written examinations of students End-of-course self-assessment
16.Committee 16. Committee Members: Course Cluster Chair CQI Cluster Chair Members
Course Title:
CALCULUS I
Date Effective:
: Maria Rosario C. Exconde : Reynaldo Lanuza : Morris Martin Jaballas Marlon B. Quendangan Gerardo G. Usita Alberto C. Villaluz
Date Revised:
Prepared by
April 2014
Cluster II Committee
th
4 Term SY2013-2014
Approved by: LD SABINO Subject Chair
Page 6 of 6
