MODULE INFORMATION
OVERVIEW:
Module Name: Calculus II
Module Code: MATH 172
Synopsis:
This module is a standard second course in calculus. It is part of a three-semester sequence in calculus courses for mathematics, science, and engineering
students. Students who take this module will study: Applications of Integration, Transcendental Functions, Techniques of Integration, Sequence and Series,
Analytic Geometry in the Plane: Conic Sections, Parameterized Curves and Polar Coordinates.
The students will be exposed to the rigor of proofs and the focus will be on conceptual understanding of calculus from four points of view: geometric (graphs),
numeric (tables), symbolic (formulas), and verbal descriptions.
This module is delivered in a blended learning approach; a combination of online and face-to-face teaching and learning activities. Weekly topics are
introduced, and students are to explore the topics before attending class lectures. Discussion in the form of solving multiple examples are encouraged during
lectures, and students are given assigned homework to complete and then to discuss. With this, students are expected to develop their reading, writing and
questioning skills.
To ensure that students are meeting the standards set in the learning outcomes of this module, students are assessed via in-class discussions, quizzes, tests,
and assignments throughout the semester, as well as a final examination which is comprehensive at the end of the semester.
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Name(s) of academic staff teaching the module, module leader and staff email:
Staff teaching the module: Theresa Chiew Gim Ean, theresa.chiew@taylors.edu.my; Alvin Ng Eng Hui, enghui.ng@taylors.edu.my
Module leader: Theresa Chiew Gim Ean, theresa.chiew@taylors.edu.my
Year-level: 1
Semester Offered: January (Long), May (Short), August (Long)
Credit Value: 5
Pre-requisite: A minimum grade C in MATH 171 (Calculus I)
Co-requisite: Nil
Anti-requisite: Nil
School offering the module: School of Liberal Arts and Sciences
Module offered as: Major (core)
Programme Name: American Degree Transfer Program
Domain Name (for free electives only): N/A
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2. LEARNING OUTCOMES:
Upon completion of the module you should be able to:
Module
Learning
Outcome
Identify concepts in differential and integral calculus to
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calculate derivatives and integrals of a single real variable.
Apply appropriate methods to solve application problems in
2
science and engineering.
Communicate mathematical solutions effectively during class
3
discussions.
4
Manage self and time effectively in completing given tasks.
Programme
Learning
Outcomes
1
(TGC 1.1, 1.2)
2
(TGC 2.1, 2.3, 2.5)
3
(TGC 3.1)
CPA
5
(TGC 5.1)
MQF
Assessment/s
C1
1, 3e
C3
2, 3e
A2
3c
A4
4a
1
2, 4
3
3
Transferable Skills: Skills learned in this module of study which can be utilized in other settings. These transferable skills include numeracy, cognitive and
personal skills.
3
TEACHING, LEARNING AND ASSESSMENT
Description of assessment components:
Assessment Task
Assessment Task 1:
(average of 5 scaled to 30%)
Quiz 1
Quiz 2
Quiz 3
Quiz 4
Quiz 5
Weight
Module Learning
Outcomes Assessed
Programme Learning
Outcomes Assessed
Due Date
30%
1
1
Week 2
Week 4
Week 6
Week 12
Week 14
20%
2
2
Week 7
Week 13
Assessment Task 3:
Assignments (in-class (10%) & takehome (10%))
20%
3,4
3,5
Weekly
Assessment Task 4:
Final Examination
30%
2
2
Week 16
Assessment Task 2:
Test 1 (10%)
Test 2 (10%)
4
Teaching and learning approach:
MLO 1
Identify concepts in differential and integral
calculus to calculate derivatives and integrals
of a single real variable.
Assessment Task/Activities
Assessment Task 1: Quizzes
For these quizzes, students must show a clear understanding of concepts introduced in the topics; and to
utilize them to answer and evaluate using algebra, differentiation, or integration where it is appropriate.
Teaching and Learning Activities:
MLO1 is achieved after students are introduced to the general concepts and various calculation techniques involving differential and integral calculus.
Students will understand and learn through lecture and online learning. Students will benefit from doing assigned homework.
MLO 2
Apply appropriate methods to solve
application problems in science and
engineering.
Assessment Task/Activities
Assessment Task 2: Tests
For these tests, students must show their ability to use appropriate methods and techniques in solving
application problems in the context of science and engineering.
Assessment Task 4: Final Examination
For this comprehensive final examination, students must show their effectiveness in responding to specific
questions under time-constrained conditions.
Teaching and Learning Activities:
MLO2 is achieved after students are taught how to recognise the problems at hand and to use methods and techniques that are appropriate to solve and
evaluate an answer or solution. Students will learn through lecture and assigned homework. Students will benefit from appropriate independent learning.
MLO 3
Communicate mathematical solutions
effectively during class discussions.
Assessment Task/Activities
Assessment Task 3: Assignments (in-class)
For this in-class assignments, students must communicate their ideas and solutions to mathematical
problems during class discussions. Students must also display active listening and interaction during class
lectures.
Teaching and Learning Activities:
MLO 3 is achieved after students can communicate an analysis of problems during class discussions in which they need to propose a solution using concepts
introduced during lectures. Students will be involved in regular discussions during lecture and gain confidence in communicating their ideas.
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MLO 4
Manage self and time effectively in
completing given tasks.
Assessment Task/Activities
Assessment Task 3: Assignments (take-home)
Students’ computational skills will be developed through homework assignments. Students are expected to
complete the given tasks meticulously and in a timely manner.
Teaching and Learning Activities:
MLO 4 is achieved when students can complete homework and assignments on time, able to work in groups, and show responsibility in producing accurate,
well-ordered, neat, and original work.
Details of each assessment task:
Assessment Task 1: Quizzes
Quizzes are continuous individual assessments. They are typically ‘open book’ and done after every unit. Students are allowed to refer to any form of
books/notes made available to them. The quizzes are conducted either online (done at home) or in a classroom setting with a prescribed time limit.
Assessment Task 2: Tests
Two mid-semester written tests are conducted as individual assessments. They are non-comprehensive (done after 2 or 3 units) closed book paper
examinations. They consist of structured questions to be answered within a prescribed time frame.
Assessment Task 3: Assignments
- in-class assignments are for students to show their ability to communicate their facts and solutions confidently as well as to articulate their problems during
class discussions.
- take-home assignments are for students to perform self-directed learning or learn in groups to solve problems in the form of practice exercises at the end
of each unit. Students will complete the tasks at hand and be responsible to ensure that the work is done by themselves and submitted on or before the
scheduled date and time.
Assessment Task 4: Final Examination
Final examination is a comprehensive closed-book examination and is an individual assessment which is conducted at the end of the semester. It seeks to
assess students’ understanding of the module as a whole. It is also to determine students’ individual effectiveness in responding to specific questions under
time-constrained invigilated conditions. The duration for this exam is 2 hours.
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Rubrics for Each Assessment Task:
Assessment Task 1: Quizzes (30%) - average scaled to 30%
5 quizzes to be assessed at the end of every unit.
Rubrics will be guided by marking schemes.
Assessment Task 2: Tests (20%) – 10% for each test.
2 tests – non-comprehensive at the end of 2 or 3 units.
Rubrics will be guided by marking schemes.
Assessment Task 3: Assignments (20%)
In-class and take-home.
Criteria
In-class:
Demonstrate ability to
communicate mathematical
solutions effectively and the
ability to display active
listening and interaction.
Take-home:
Demonstrate ability to
manage self and time
effectively in completing
given tasks in a responsible
manner (in terms of effort,
accuracy, neatness, and
timeliness).
Weightage
10
Average
calculated
based on
14 weeks
Outstanding (9-10)
Display consistent ability
to interact positively,
actively participate and
cooperate in group
settings and in the
classroom.
Mastering (7-8)
Display frequent ability to
interact positively, actively
participate and cooperate
in group settings and in the
classroom.
Developing (5-6)
Display ability to
interact positively,
actively participate and
cooperate in group
settings and in the
classroom.
Beginning (0-4)
Display little to no
ability to interact
positively, actively
participate and
cooperate in group
settings and in the
classroom.
10
Calculated
based on
14 weeks
Full completion of tasks
with excellent effort, few
errors and related work is
neat and well organized.
Frequent completion of
tasks with good effort,
some errors and related
work is neat and well
organized.
Some late completion
of tasks with little
effort, many errors and
related work is not neat
nor well organized.
Little to no completion
of tasks in terms of
effort, accuracy, and
neatness.
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Assessment Task 4: Final Examination (30%)
Comprehensive final examination at the end of the semester.
Rubrics will be guided by marking schemes.
Hurdle assessment guideline for the module:
A student must achieve at least a grade C (70%) for the module to be able to transfer the module successfully to US universities.
A student who obtains below grade C will have to repeat the module.
Students are allowed to take the module for a maximum of 3 times over the duration of their study.
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4. STUDENT LEARNING TIME
Student Learning Time (SLT) per topic/week of the content outline
SLT mapping against a) MLO, b) Teaching & Learning Activities [Physical Face-to-Face (L,T,P,O), Online Synchronous Face-to-Face (L,T,P,O), Non Face-toFace Independent Learning (Asynchronous)] and c) Assessment Tasks
MLO
Date/Week
Physical F2F
Interactive Lecture,
Tutorial
Practical, Other
Online
Synchronous F2F
Interactive Lecture,
Tutorial
Practical, Other
Hours
Hours
Hours
3
2
5
NF2F
Independent
Learning
(Asynchronous)
Assessment
Tasks
(Physical F2F)
Assessment
Tasks
(Online
synchronous
F2F)
Hours
Hours
Assessment
Tasks
NF2F
Independent
Learning for
Assessment
( Asynchronous)
Hours
Student
Learning
Time (SLT)
1
11
As ynchr on
Week 1
Week 2
2,3
2,3,4
Unit 1:
Applications of Integrals
• General Review of
relevant topics in
Calculus I
• Volume of Solids of
Revolution: Disk and
Washer Method
Unit 1:
Applications of
Integrals
Independent
learning
(Reading &
exercises from
notes/textbook)
Unit 1
3
• Volume of Solids of
Revolution: Shell
Method
2
Unit 1:
Applications of
Integrals
5
Independent
learning
(Reading &
exercises from
notes/textbook)
Unit 1
Hours
Preparation for
assignment
1
Quiz
2
Homework
Assignment Unit 1
13
9
Week 3
1,3
Week 4
1,3,4
3
Unit 2: Transcendental
Functions
• Exponential and
Logarithmic Functions:
Properties, Derivatives
and Integrals
• Inverse Trigonometric
Functions
2
Unit 2:
Transcendental
Functions
5
Independent
learning
(Reading &
exercises from
notes/textbook)
Unit 2
3
• Derivatives and Integrals
of Inverse Trigonometric
Functions
• Hyperbolic Functions:
Definitions and
Identities, Derivatives
and Integrals, Inverse
Hyperbolic Functions
2
Unit 2:
Transcendental
Functions
5
Independent
learning
(Reading &
exercises from
notes/textbook)
Unit 2
Week 5
1,3
3
Unit 3: Techniques of
Integration
• Basic Integration
Formulas
• Integration by Parts
2
Unit 3: Techniques
of Integration
5
Independent
learning
(Reading &
exercises from
notes/textbook)
Unit 3
Week 6
1,3
3
• Partial Fractions and
Rational Functions
• Trigonometric
Substitutions
2
Unit 3: Techniques
of Integration
7
Independent
learning
(Reading &
exercises from
1
Discussion on
Quiz
1
Preparation for
assignment
12
2
Homework
Assignment Unit 2
13
1
Discussion on
Quiz
2
Preparation for
assignment &
Test
13
1
2
Preparation for
assignment &
Test
15
1
Quiz
Quiz
10
notes/textbook)
Unit 3
Week 7
1,3,4
3
• Improper Integrals
2
Unit 3: Techniques
of Integration
7
Independent
learning
(Reading &
exercises from
notes/textbook)
Unit 1 – 3
Review
2
Test
Week 8
2,3
3
Unit 4: Further
Applications of Integrals
• Lengths of Plane Curves
• Moments and Centers
of Mass
2
Unit 4: Further
Applications of
Integrals
5
Independent
learning
(Reading &
exercises from
notes/textbook)
Unit 4
1
Discussion on
Quiz
Week 9
2,3
3
Unit 5: Sequences and
Series
• Sequences: Definition,
Notation, Finding
terms and Formula for
a Sequence,
Convergence and
Divergence
• Infinite Series:
Definition, Notation,
nth Test for Divergence
• Integral Test for Series
2
Unit 5: Sequences
and Series
7
Independent
learning
(Reading &
exercises from
notes/textbook)
Unit 5
1
Discussion on
Test
3
Homework
Assignment Unit 3
17
11
1
Preparation for
Assignment
14
11
Week 10
2,3
3
• Comparison Tests for
Series
• Ratio and Root Tests
for Series
• Alternating Series,
Absolute and
Conditional
Convergence
2
Unit 5: Sequences
and Series
7
Independent
learning
(Reading &
exercises from
notes/textbook)
Unit 5
1
Discussion /
Participation
1
Preparation for
assignment
14
Week 11
2,3,4
3
• Power Series
• Taylor and Maclaurin
Series
2
Unit 5: Sequences
and Series
7
Independent
learning
(Reading &
exercises from
notes/textbook)
Unit 5
5
Independent
learning
(Reading &
exercises from
notes/textbook)
Unit 6
1
Discussion /
Participation
1
Homework
Assignment Unit 3
14
1
2
Preparation for
assignment &
Test
13
2
3
Review Test &
Preparation for
Assignment
15
Review
Week 12
Week 13
2,3
2,3
3
Unit 6: Analytic Geometry
in the Plane
• Introduction to Conic
Sections: Circles,
Parabolas, Ellipses and
Hyperbolas
• Translation and
Rotation of Axes
[Optional]
3
Unit 7: Parametrized
Curves and Polar
Coordinates
• Parametric Equations
2
Unit 6: Analytic
Geometry in the
Plane
2
Unit 7:
Parametrized
5
Independent
learning
(Reading &
exercises from
Quiz
Test
12
• Calculus with
Parametrized Curves:
Slopes, Higher-order
Derivatives, Length of
Curve
Week 14
2,3,4
•
•
•
•
Week 15
-
Week 16
-
TOTAL
3
Polar Coordinate
System
Graphing in Polar
Coordinates
Polar Equations for
Conic Sections
[Optional]
Calculus of Polar
Curves: Area and
Length
Curves and Polar
Coordinates
2
Unit 7:
Parametrized
Curves and Polar
Coordinates
notes/textbook)
Unit 7
5
Independent
learning
(Reading &
exercises from
notes/textbook)
Unit 7
1
Quiz
2
Homework
Assignment Unit 7
13
10
Preparation for
final exam
10
2
Final Exam
42
28
80
17
2
33
200
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REFERENCES:
Main References supporting the module:
1. Thomas, G. B., Heil, C., Weir, M. D., Zuleta, E., José, L. & Hass, J. (2020). Thomas' Calculus (14th ed.). Harlow, England: Pearson Education Limited.
Other additional information:
1. Stewart, J., Clegg, D. K. & Watson, S. H. (2020). Calculus (9th ed.). Boston: Cengage.
2. Briggs, W., Cochran, L., Gillett, B. & Schulz, E. P. (2019). Calculus (3rd ed.). New York, NY: Pearson.
3. Larson, R., & Edwards, B. H. (2018). Calculus: with CalcChat & CalcView (11th ed.). Boston, MA: Cengage Learning.
4. Adams, R. A. & Essex, C. (2018). Calculus: A Complete Course (9th ed.). Don Mills, Ontario: Pearson Canada Inc.
Special requirements to deliver the module: NIL
Doc. Ref: THE-ACA-FORM-MI (Rev.5.0, Effective Date: 1 January 2022)
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