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 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 stor e of 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, ENVIRONMENTAL AND SANITARY ENGINEERING, INDUSTRIAL ENGINEERING, MECHANICAL ENGINEERING AND MANUFACTURING ENGINEERING)) 1. To enable our graduates to practice as successful engineers for the advancement of society. 2. To promote professionalism in the engineering practice.
a
MISSION b c
COURSE SYLLABUS 1.
Course Code:
MATH 22-1
2.
Course Title:
Calculus 2
3.
Pre-requisite: Pre-requisite:
MATH 21-1
4.
Co-requisite:
None
5.
Credit:
5 units
6.
Course Description: This course in Calculus starts with discussions on derivatives of trigonometric and hyperbolic functions, as well as their inverses, limits of indeterminate forms, the differentials and its application. It progresses to the discussion of the basic and advance integration of algebraic and transcendental functions. The definite integral is used extensively in solving application problems involving area of regions bounded by algebraic/polar curves, volume of solids of revolution and of solids with known cross-section, centroids of plane regions and of solid of revolution, length of curves, surface area of revolution, force due to liquid pressure and work. And lastly, this course also deals with the application of improper integrals.
Course Title: CALCULUS 2
Date Effective: 4th Quarter SY 2013 - 2014
Date Revised: July 2014
Prepared by:
Committee on Calculus 3
d
Approved by: LDSABINO Subject Chair
Page 1 of 8
7.
Student Outcomes and Relationship to Program
Educational Objective Program Educational Objectives 1 2
Student Outcomes (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l)
8.
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 an ability to design a system, component, or process to meet desired needs an ability to function on multidisciplinary 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 the 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 member and leader, to manage projects and in multidisciplinary environments.
√
√
√
√
√
√
√
√
√
√
√
√ √
√
√
√
√
√
√
√
√
√
√
Course Outcomes (COs) and Relationship to Student Outcomes Course Outcomes
Student Outcomes*
After completing the course, the student must be able to: 1. Solve problems involving the derivative of algebraic, exponential and logarithmic functions, as well as problems on different planar and space geometries by applying concepts and principles learned in the prerequisites. 2. Solve problems involving derivatives of the other transcendental functions, evaluate limits of indeterminate forms and solve problems concerning the differentials. 3. Solve definite and indefinite integrals using basic integration formulas. Use simple substitution to transform integrals to forms yielding any of the transcendental functions. 4. Solve definite and indefinite integrals using appropriate integration technique. Course Title: CALCULUS 2
Date Effective: 4th Quarter SY 2013 - 2014
Date Revised: July 2014
a
b c d
e
f
g
i
j
k
D
R
I
D D D
D D D D
I
D D D
D D D D
I
D
Prepared by:
Committee on Calculus 3
R
h
R
D D D D D D Approved by: LDSABINO Subject Chair
Page 2 of 8
D
l
5. Solve, by integration, application problems concerning length of an arc, area under the curve and between curves, volume of solids of revolution, centroid of the area and solid of revolution, surface area of revolution, force to liquid pressure, work . Use Pappus’ Theorem in solving problems of volume and surface area of revolution
* Level: I- Introduced, R- Reinforced, 9.
D
D D D D D D
D
D- Demonstrated
Course Coverage
Week
TOPICS
TLA
Mission and Vision of Mapua Institute of Technology Orientation and Introduction to the Course Discussion on COs, TLAs, and ATs of the course
1
Overview on student-centered learning and eclectic approaches to be used in the course Derivatives of and Inverse Functions
Peer discussion on Mission and Vision of Mapua Institute of Technology
Diagnostic
CO1
Trigonometric Trigonometric
Derivatives of Hyperbolic and Inverse of Hyperbolic Functions INDETERMINATE FORMS:
COURSE OUTCOMES
AT
- Visually guided Learning
L’Hopital’s Rule
0/0, / - , 0* 00, , 1 THE DIFFERENTIALS Differential of the Dependent Variable Derivatives of Parametric Equations Application - Approximate Formula (nth root, volume of shells and others)
2
3
Class through
Produced
CO2
Working
Examples
Differential of Length of an Arc Radius of Curvature
Course Title: CALCULUS 2
Date Effective: 4th Quarter SY 2013 - 2014
Date Revised: July 2014
Prepared by:
Committee on Calculus 3
Approved by: LDSABINO Subject Chair
Page 3 of 8
LONG QUIZ 1
ANTIDERIVATIVES
Indeterminate Integrals and Basic Integration Formula Generalized Power Formula Integration by Simple Substitution
Class
Produced
CO3
THE DEFINITE INTEGRALS
3
Properties of the Definite Integral Integrals of Odd and Even Functions Integration of Absolute Value Function Average Value of a Function Mean Value Theorems for Integrals Simple U-substitution
CO3
TRANSCENDENTAL FUNCTIONS Integrals Yielding the Natural Logarithmic Functions Integration of Exponential Function Integral Forms Leading to the Trigonometric / Inverse Trigonometric Functions Transformations of Trigonometric Function – Powers of Sine and Cosine – Product of Sine and Cosine -Walli’s Formula – Powers and Product of Tangent and Secant – Powers and Product of Cotangent and Cosecant Integrals Yielding Inverse Trigonometric Functions Integration of Hyperbolic Functions Integrals Yielding Inverse Hyperbolic Function
4
5
- Visually guided Learning -Working through
Class Produced Reviewer 2
examples
LONG QUIZ 2 TECHNIQUES OF INTEGRATION Integration by Parts Integration by Algebraic Substitution Course Title: CALCULUS 2
Date Effective: 4th Quarter SY 2013 - 2014
Date Revised: July 2014
-Visually guided Class Prepared by:
Committee on Calculus 3
Produced
Approved by: LDSABINO Subject Chair
Page 4 of 8
6
7
Integration by Trigonometric Substitution Half-Angle Substitution / Reciprocal Substitution Partial Fraction - Linear Factors - Repeated Linear Factors - Quadratic Factors - Repeated Quadratic Factors Integration of Rational Function by Partial Fraction - Linear Factors - Repeated Linear Factors - Quadratic Factors - Repeated Quadratic Factors Improper Integrals
learning
Reviewer 3
CO4
Class Produced Reviewer 3
CO4
-Working through examples
LONG QUIZ NO. 3 (70% written, 30% on-line) PLANE AREAS Differential of Area Fundamental Theorem of Integral Calculus Area Under the Curve Area Between Curves VOLUME OF REVOLUTION Disk Method Circular Ring or Washer Method Cylindrical Shell Method Solids with Known Cross-Section CENTROID Centroid of a Region Centroid of Volume of Revolution Length of Curves Surface Area of Revolution Pappus’s Theorem : Preposition 1 and 2 Force Due to Liquid Pressure Work
8
9
10
-Visually guided learning -Working through examples Class
Produced
CO5
-Visually guided learning -Working through Examples
Project
LONG QUIZ 4
SUMMATIVE ASSESSMENT FINAL EXAMINATION
11
10.
CO2, CO3, CO4, CO5
Opportunities to Develop Lifelong Learning Skill The primary learning outcome for this course to develop lifelong learning skill is the student’s capability to exhibit
Course Title: CALCULUS 2
critical and logical reasoning in different areas of learning specifically with
Date Effective: 4th Quarter SY 2013 - 2014
Date Revised: July 2014
Prepared by:
Committee on Calculus 3
Approved by: LDSABINO Subject Chair
Page 5 of 8
the maximization of mathematical principles in Integral Calculus, and the value integration of course will equip the takers to respond to different societal challenges.
11.
this
Contribution of Course to Meeting the Professional Component Engineering Topics : General Education : Basic Sciences and Mathematics :
12.
Textbook:
13.
Course Evaluation
0% 0% 100%
Calculus Early Transcendental Functions by Ron Larson and Bruce H. Edwards. 5 th edition
Student performance will be evaluated based on the following:
Assessment Tasks CO1
CO2
Weight (%)
Diagnostic Examination Long Quiz 1 Classwork 1 Class Produced Reviewer 1 Long Quiz 2
CO3
Classwork 2 Class Produced Reviewer 2 Long Quiz 3 CO4 Classwork 3 Class Produced Reviewer 3 Long Quiz 4 Classwork 4 CO5 Class Produced Reviewer 4 Project Summative Assessment Final Examination TOTAL
Minimum Average for Satisfactory Performance (%)
10 10 3 2 10 3 2 10 3 2 10 3 2 5 25.00
7 7 2.1 1.4 7 2.1 1.4 7 2.1
17.50
100
70
1.4
7 2.1 1.4 3.5
The final grades will correspond to the weighted average scores shown below:
Final Average
Final Grade
96
1.00 1.25 1.50 1.75 2.00
93 90 86 83 Course Title: CALCULUS 2
Date Effective: 4th Quarter SY 2013 - 2014
X X X X X
< 100 < 96 < 93 < 90 < 86 Date Revised: July 2014
Prepared by:
Committee on Calculus 3
Approved by: LDSABINO Subject Chair
Page 6 of 8
80 X < 83 76 X < 80 73 X < 76 70 X < 73 Below 70
2.25 2.50 2.75 3.00 5.0
(Fail)
Other Course Policies
13.1
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 15 hrs for a five-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 will not be accepted. c.
Written Examination (Long Quiz and Final Examination) will be administered as scheduled. No special examination will be given unless valid reason is presented like medical certificate / other acceptable documents and will be subject to approval by the Chairman of the Mathematics Department.
d. Course Portfolio will be collected at the end of the term. 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 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’s web-page ( http://math.mapua.edu.ph ). It is recommended that the
student first set an appointment to confirm the instructor’s availability.
14.
Other References 14.1
Course Title: CALCULUS 2
Books Date Effective: 4th Quarter SY 2013 - 2014
Date Revised: July 2014
Prepared by:
Committee on Calculus 3
Approved by: LDSABINO Subject Chair
Page 7 of 8
a. Calculus, 6th ed., Edwards and Penney b. The Calculus, 7th ed., by Louis Leithold
c. Differential and Integral Calculus by Schaum’s Outline Series d. Differential and Integral Calculus by Love and Rainville
14.2.1
Websites www.sosmath.com www.hmc.com www.intmath.com www.hivepc.com
15. Course Materials Made Available a. Course schedules for lectures and quizzes b. Samples of assignment / Problem sets of students c. Samples of written examinations of students d. End-of-course self-assessment
16. Committee Members:
Course Cluster Chair: Juanito E. Bautista CQI Cluster Chair: Robert P, Domingo Members: Robert M. Dadigan Rosario S. Lazaro Francis Anthony G. Llacuna
Course Title: CALCULUS 2
Date Effective: 4th Quarter SY 2013 - 2014
Date Revised: July 2014
Prepared by:
Committee on Calculus 3
Approved by: LDSABINO Subject Chair
Page 8 of 8
