TEP-001-18-136
POLYTECHNIC COLLEGE OF THE CITY OF MEYCAUAYAN
Pag-asa Street, Malhacan, City of Meycauayan, Bulacan, 3020
(044) 320-5653 / pccmbulacan@gmail.com
TEACHER EDUCATION PROGRAM
COURSE SYLLABUS
COURSE CODE:
DESCRIPTIVE TITLE:
PREREQUISITE(S):
CREDIT UNITS:
MATH 109
CALCULUS II (DIFFERENTIAL AND INTEGRAL CALCULUS)
MATH 105
4
COURSE DESCRIPTION: Calculus II is the continuation of Calculus I with Analytic Geometry - the second of a series of
three calculus courses. The course aims to further develop and strengthen the students’
understanding of differential and integral calculus. Topics include the applications of definite
integrals, techniques of integration, indeterminate forms, improper integrals of algebraic and
transcendental functions.
COURSE OUTCOMES:
After successful completion of the course, students should be able to:
1.
select and use appropriate models and techniques of integration for finding solutions to
integral-related problems with and without the use of technology.
COURSE COVERAGE
Week
Topic
No.
1
PCCM VISION,
MISSION, VALUES
COURSE OUTLINE
2-5
6-8
Integration concepts and
formulas
1. Review on Antidifferentiation
2. Review on
Indefinite integrals
3. Simple Power
formula
4. Simple
trigonometric
functions
5. Logarithmic
functions
6. Exponential
functions
7. Inverse
Trigonometric
functions
8. Hyperbolic
functions
9. General power
formula
Techniques of
Integration
1. Integration by
Course Learning
Outcomes
- Acquire understanding
of PCCM's vision,
mission, and values.
- Gain an overview and
understanding of the
translation and editing
course.
Instructional
Modality
Class Discussion
Assessment
At the end of the week,
the pre-service teacher
(PST) should be able to:
- integrate using power
formula;
- integrate using power
formula; and,
Integrate trigonometric
functions, logarithmic,
exponential, inverse
trigonometric and
hyperbolic functions.
Class Discussion
Quiz
Course Syllabus
Graded
Recitation/
Board work
Textbook
- perform integration
by parts;
- perform integration
Class Discussion
N.A
Resources
Student Handbook
Online /Electronic
Resources
Learning Guide
Quiz
Course Syllabus
Graded
Textbook
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TEP-001-18-136
Parts
2. Integration of
Powers of
Trigonometric
Functions
3. Integration by
Trigonometric
Substitution
4. Integration of
Rational
Functions by
Partial Fractions
5. Miscellaneous
Substitution
9
10-11
12-14
15
of powers of
trigonometric
functions;
- perform integration
by trigonometric
substitution;
- integrate rational
functions using partial
fractions; and,
Perform integration using
miscellaneous
substitution.
Definite Integrals
1. Summation
Notation&
Riemann Sum
2. Definition of
Definite Integrals
3. Properties of
Definite Integrals
4. The Mean Value
Theorem for
Integrals
5. The Fundamental
Theorem of
Calculus
-
-
Board work
MIDTERM EXAMINATION
write and compute
Class Discussion
long sums using sigma
notation;
define and evaluate
definite integrals;
identify and apply the
properties of definite
integrals;
discuss and
verify/prove the
Mean Value Theorem
for Integrals; and
Discuss and
verify/prove the
Fundamental
Theorem of Calculus
find the area of the
Class Discussion
region bounded by
curves using Riemann
sum and definite
integrals;
find the volume of a
solid of revolution
using different
methods; and,
Apply definite
integrals in solving
work problems and
finding the length of
arc of a plane curve.
-
Indeterminate
Forms
1. Definition
2. L’ Hospital’s Rule
- enumerate the
different
indeterminate forms;
and,
evaluate limits of
rational functions at a
point where the limit is
indeterminate.
Class Discussion
- evaluate improper
integrals with infinite
upper limit;
Class Discussion
-
-
Improper Integrals
1. Definition of
Improper Integrals
Online /Electronic
Resources
Learning Guide
Applications of the
Definite Integral
1. Area of a Region
in a Plane
2. Volume of a Solid
of Revolution
3. Work
4. Length of Arc of
a Plane Curve
5. Other
miscellaneous
application topic
(free topic)
-
16-17
-
Recitation
Quiz
Course Syllabus
Graded
Recitation
Textbook
Board work
Online /Electronic
Resources
Learning Guide
Quiz
Course Syllabus
Graded
Recitation
Textbook
Board work
Online /Electronic
Resources
Learning Guide
Quiz
Course Syllabus
Graded
Recitation
Textbook
Board work
Online /Electronic
Resources
Learning Guide
Quiz
Course Syllabus
Graded
Textbook
Page 2 of 3
TEP-001-18-136
2. Improper
Integrals:
a. with Infinite
Upper Limit
b. with Infinite
Lower Limit
c. with Both Upper
& Lower Limits
Infinite
3. Improper
Integrals with
Infinite
Discontinuities of
the Integrand
- evaluate improper
integrals with infinite
lower limit;
- evaluate improper
integrals with infinite
upper and lower
limits; and,
- evaluate improper
integrals with infinite
discontinuities of the
Integrand.
18
Recitation
Board work
Online /Electronic
Resources
Learning Guide
FINAL EXAMINATION
GRADING SYSTEM:
Quizzes: 20%
Recitation: 20%
Project / Other Requirements: 20%
Major Examinations (midterm and finals): 40%
Total: 100%
The final grade of the student is interpreted as shown on the table below:
AVERAGE
97–100
94–96
91–93
88–90
85–87
82–84
79–81
76–78
75
FINAL GRADE
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
74 and
below
5.00
Prepared by:
Endorsed by:
Noted by:
MARJORIE B. MALVEDA
Instructor
FREDERICK BERBOSO,MAEd
Program Head, TEP
RENELIZA C. STA. ANA, Ph.D
College Dean / OIC-PCCM
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