UNIVERSITY OF THE PHILIPPINES MANILA
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT OF PHYSICAL SCIENCES AND MATHEMATICS
MATHEMATICAL AND COMPUTING SCIENCES UNIT
Course Code: Mathematics 74
Course Title: Fundamentals of Analysis II
Credit Units: 3
Lecture Unit(s): 2 units; 2 hrs/week
Laboratory Unit(s): 1 unit; 3hrs/week
Course Description: Derivatives and integrals of transcendental functions, techniques of integration, applications of integration to area of a plane region, volumes and solids of revolution,
arclength, area of surfaces of revolution, center of mass, and polar coordinates
Instructional Materials and References:
1. Leithold, L. The Calculus 7 Harper Collins College Publishers 1996
2. Anton, H. et al. Calculus Early Transcendentals Hoboken NJ: Wiley 2009 Ninth edition
Student Outcomes
1.
2.
3.
4.
Demonstrate application of knowledge of mathematics, science, and engineering in practical situations
Exhibit moral, ethical and social responsibilities as a professional and as a Filipino citizen
Can work both independently and with a group
Communicate effectively in oral and written form
Mapping of Course Outcomes vis-à-vis Program Outcomes
1.
2.
3.
4.
Understand the extension of the concepts of limits, derivatives, and integrals to transcendental functions
Handle and evaluate integrals using additional integration techniques
Apply the principle of integral evaluation in solving physical problems
Discuss a new kind of coordinate system and relate the rectangular coordinate system
COURSE OUTCOMES
Understand the extension
of the concepts of limits,
derivatives, and integrals
to transcendental
functions
TOPICS
Limits of Trigonometric Functions
Derivatives and Integrals of
Trigonometric Functions
Derivatives of Exponential and
Logarithmic Functions
Integrals Yielding Exponential and
TIME
FRAME
7.5 hrs
lecture
12 hrs
laboratory
INTENDED LEARNING OUTCOMES
TEACHING-LEARNING
ACTIVITIES
ASSESSMENT TASKS
Calculate the limit of a transcendental function
at a point numerically using appropriate
techniques and manipulation
Lecture/Class Discussion
Lecture Exam
Laboratory Exercises
Quiz
Understand how hyperbolic functions and
inverse hyperbolic functions are defined from
exponential and logarithmic functions,
respectively
Computer-aided graphing
and discussions
Laboratory Exam
Laboratory Exercises
Problem set discussion
Boardworks
2|P a g e F u n d a m e n t a l s o f A n a l y s i s
Logarithmic Functions
Obtain fundamental hyperbolic identities
Derivatives of Inverse
Trigonometric Functions
Find the derivatives of exponential and
logarithmic functions, trigonometric and
inverse trigonometric functions, and
hyperbolic and inverse hyperbolic functions in
implicit and/or explicit forms
Integrals Yielding Inverse
Trigonometric Functions
Derivatives and Integrals of
Hyperbolic Functions
Boardwork discussion by
the students
II OBE SYLLABUS
Problem Sets
Homework
Find the general antiderivatives of exponential
and logarithmic functions, trigonometric and
inverse trigonometric functions, and
hyperbolic and inverse hyperbolic functions
Derivatives and Integrals of Inverse
Hyperbolic Functions
Evaluate a definite integral with a
transcendental function as integrand using an
appropriate antiderivative
Integration by Parts
Integration of Powers of
Trigonometric Functions
Integration by Trigonometric
Substitution
5.5 hrs
lecture
9 hrs
laboratory
Find the general antiderivative of a product of
functions using a simple intergration by parts,
repeated integration by parts, or tabular
integration by parts
Recognize and implement appropriate
techniques to find the general antiderivative of
product of trigonometric functions
Lecture/Class Discussion
Lecture Exam
Laboratory Exercises
Quiz
Computer-aided graphing
and discussions
Laboratory Exam
Laboratory Exercises
Problem set discussion
Integration by Partial Fractions
Miscellaneous Techniques
Boardworks
Devise and apply a trigonometric substitution
in finding the general antiderivative of certain
forms of functions
Boardwork discussion by
the students
Problem Sets
Homework
Evaluate the integral of a rational function by
decomposing the rational integrand into
partial fractions
Apply other substitution techniques to
transform the integral into a form easier to
integrate
3|P a g e F u n d a m e n t a l s o f A n a l y s i s
Apply the principle of
integral evaluation in
solving physical problems
Area of a Plane Region
5 hrs
lecture
Interpret the area enclosed between curves as
a definite integral and compute its value
9 hrs
laboratory
Find the length of arc of a curve defined by the
graph of a function using a definite integral
Volumes of Solids of Revolution
Length of Arc
Surface Area of a Solid of
Revolution
Interpret the volume of a solid defined by the
graph of a function revolved about an axis as a
sum of volumes of disks, washers, or
cylindrical shells; convert such sum to a
definite integral, and compute its value
Center of Mass of a Plane Region
II OBE SYLLABUS
Lecture/Class Discussion
Lecture Exam
Laboratory Exercises
Quiz
Computer-aided graphing
and discussions
Laboratory Exam
Laboratory Exercises
Problem set discussion
Boardworks
Boardwork discussion by
the students
Express the surface area of a solid defined by
the graph of a function revolved about an axis
as a sum of areas of rings; convert such sum to
a definite integral, and compute its value
Problem Sets
Homework
Use definite integration to find the center of
mass of a thin rod of uniform and non-uniform
density
Apply definite integration to find the center of
mass of region of uniform area density and to
find the centroid of a plane region
Discuss a new kind of
coordinate system and
relate the rectangular
coordinate system
Polar Coordinate System
3 hrs
lecture
Equations and Graphs in Polar Form
Area in Polar Coordinates
4.5 hrs
laboratory
Relate the Polar and the Rectangular Cartesian
Coordinates, converting from one form to
another
Lecture/Class Discussion
Lecture Exam
Laboratory Exercises
Quiz
Identify and sketch the graphs of certain
equations in polar form
Computer-aided graphing
and discussions
Laboratory Exam
Apply definite integration in finding the area of
a plane region bounded by polar curves
Problem set discussion
Laboratory Exercises
Boardworks
Boardwork discussion by
the students
Problem Sets
Homework
4|P a g e F u n d a m e n t a l s o f A n a l y s i s
Grading System:
Final Lecture Grade = [2/3*(90% Average of 3 Lecture Exams)+ 10% (Homework & Quiz)] + [1/3* Final Exam]
Final Laboratory Grade = [(3/4) Average of 3 Laboratory Exams + 1/4 (Laboratory Exercises & Boardworks)]
FINAL GRADE = (50% Final Lecture Grade) + (50% Final Laboratory Grade)
GRADING SCALE
≥ 93
1.0
90–92
1.25
87–89
1.5
84–86
1.75
80–83
2.0
75–79
2.25
70–74
2.5
65–69
2.75
60–64
3.0
55–59
4.0
≤ 55
5.0
II OBE SYLLABUS