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DEPARTMENT OF PHYSICAL SCIENCES AND MATHEMATICS
COLLEGE OF ARTS AND SCIENCES
UNIVERSITY OF THE PHILIPPINES MANILA
Course Code: Mathematics 75
Course Title: Fundamentals of Analysis III
Credit: 3 units (2 units lecture / 1 unit laboratory)
Hours / week: 2 hrs. lecture / 3 hrs. laboratory
Course Description: Vectors and applications, cylinders and quadrics, sequences and series, tests for convergence or
divergence, functions of two or more variables, partial differentiation, multiple integration.
Learning Outcomes:
On the completion of the course, the student should be able to:
Learning Outcomes
LO1 understand the geometry of lines, planes, and other basic
surfaces in three dimensions and apply operations on three
dimensional vectors
LO2 determine the convergence of infinite sequences and series, and
use infinite series to approximate values of transcendental
functions
LO3
understand the extension of the concepts of limits, derivatives,
and integrals to functions of several variables
Learning Plan:
Week
Topic
Program/Student Outcomes
PO1 (Apply the knowledge of mathematics,
science, and engineering)
PO1 (Apply the knowledge of mathematics,
science, and engineering)
PO5 (Communicate effectively in oral and
written form)
PO1 (Apply the knowledge of mathematics,
science, and engineering)
Learning
Outcome
LO1
Teaching-Learning Activities
Lecture, Laboratory Exercises, Problem Sets
1
Three-Dimensional Coordinate System Lines
and Planes
2
Quadric Surfaces
LO1
Lecture, Laboratory Exercises, Problem Sets
3
Operations and Properties of Vectors in R3,
Cross Product of Two Vectors
LO1
Laboratory Exercises, Problem Sets
4
Calculus of Vector Valued Functions
 Domain
 Limits
 Derivatives
 Operations
LO1
Laboratory Exercises, Problem Sets
5
First Lecture Exam
First Laboratory Exam
6
Spheres and Cylinders
Cylindrical Coordinate System
LO2
Laboratory Exercises, Problem Sets
7
Functions of Several Variables
Limits and Continuity
LO2
Laboratory Exercises, Problem Sets
DEPARTMENT OF PHYSICAL SCIENCES AND MATHEMATICS
COLLEGE OF ARTS AND SCIENCES
UNIVERSITY OF THE PHILIPPINES MANILA
8
Spherical Coordinates
Double and Triple Integrals
LO2
Laboratory Exercises, Problem Sets
9
Second Lecture Exam
Second Laboratory Exam
10
L’hopitals rule
LO3
Laboratory Exercises, Problem Sets
11
Improper Integrals
Sequences of Constant Terms
LO3
Laboratory Exercises, Problem Sets
12
Series of Constant Terms
Tests for Convergence
LO3
Laboratory Exercises, Problem Sets
13
Power Series
Differentiation and Integration of Power Series
LO3
Laboratory Exercises, Problem Sets
14
Taylor Series
LO3
Laboratory Exercises, Problem Sets
15
Third Lecture Exam
Third Laboratory Exam
16
Final Exam
References:
The Calculus 7 by Louis Leithold
Calculus, Early Transcendentals 9th edition by Anton et.al.
Course Requirements:
Lecture Component
3 Departmental Exams, 1 Final Exam
Non-Departmental Items (Quizzes, Homeworks, Seatworks)
Laboratory Component
3 Departmental Exams
Laboratory Exercises
Grading System:
Computation of Grade
DEPARTMENT OF PHYSICAL SCIENCES AND MATHEMATICS
COLLEGE OF ARTS AND SCIENCES
UNIVERSITY OF THE PHILIPPINES MANILA
Laboratory Grade = (Average of 3 Laboratory Exams) + (Laboratory Exercises)
Lecture Grade =
Final Grade =
Grading Scale
1.0
1.25
93 - 100
90 - 92
1.5
1.75
2.0
2.25
2.5
2.75
3.0
4.0
5.0
87-89
84 -86
80 – 83
75 – 79
70 – 74
65 – 69
60 – 64
55 – 59
0 – 54
Rules of Conduct / Classroom Policy
1) Attendance is required. A student who is absent for more than 6 times and fails to officially drop the course will
automatically be given a grade of 5.0.
2) Cheating is punishable at least with a grade of 5.0.
3) A student is allowed to make up for only one missed exam, provided that the reason is valid. If another exam is missed, the
student will get a grade of zero in that exam. The special exam is usually scheduled after the final exam and covers all topics
of the entire course.
4) Those who need to take an early or advance exam, provided that the reason is valid, must inform me at least a week before
the scheduled exam.
5) No special projects are to be given to compensate for either low or failing grades.
6) Complaints regarding the exam results will only be entertained within a week after the results are released.
7) A student may officially drop the course on or before the deadline for dropping. Only after a dropping slip is accomplished
and the instructor’s copy is submitted can a student be considered to have officially dropped the subject.