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UNIVERSITY OF THE PHILIPPINES MANILA
COLLEGE OF ARTS AND SCIENCES
DEPARTMENT OF PHYSICAL SCIENCES AND MATHEMATICS
MATHEMATICAL AND COMPUTING SCIENCES UNIT
Course Code: Math 73
Course Title: Fundamentals of Analysis 1
Credit Units: 3
Lecture Unit(s): 2 units; 2 hrs/week
Laboratory Unit(s): 1 unit; 3hrs/week
Course Description: Lines and conics, functions and their graphs, limits and continuity, derivatives, application to simple differential equations, related rates problem, maxima
and minima problems, curve sketching, antidifferentiation and the definite integral.
Instructional Materials and References:
1. Leithold, L. The Calculus 7
2. Purcell, E. Calculus with Analytic Geometry
3. Anton, H., et al. Calculus: Early Transcendentals, 10th 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
Course Outcomes:
At the end of the course, students shall be able to:
1. Understand the concept of limits (from informal, intuitive notion to precise mathematical definitions) and its applications; calculate and evaluate limits
2. Know the concept of the derivative of a function – its definition and applications, and the precise mathematical methods in differentiation
3. Discern the concept of antidifferentiation and integration, and understand the fundamental theorems of Calculus
COURSE OUTCOMES
Understand the concept of limits
from informal, intuitive notion to
precise mathematical definitions;
calculate and evaluate limits
TOPICS
1. Review of Functions
a. Definition of a Function
b. Domain and Range
c. Type of Functions
TIME
FRAME
1.5 hours
INTENDED LEARNING
OUTCOMES
TEACHING-LEARNING
ACTIVITIES
Explain class policies and university rules,
course topics and requirements and the
grading system
Syllabi Discussion
Discuss the main objective/s of the course,
its importance as a prerequisite to higher
Math subjects and its relevance to the
Computer Science Education
Exemplification in the Laboratory
ASSESSMENT TASKS
1. Give supplementary problems as
exercises and assignment
Recall lecture on functions
2. Short quiz at the start of next
meeting regarding Chapter 1
3. Boardwork and oral recitation in
the laboratory
Recall the notion of a function, domain and
range, the different types of functions and
their graphs
2. Lines and Circles
1 hour
a. Slope of a line
b. Forms of equations of a line
c. Parallel and perpendicular lines
d. Forms of equations of a circle
Determine the important points and solve
all relevant quantities of a line/circle given
its equation in any form
Lecture/Class Discussion
1. Give supplementary problems as
exercises and assignment
Exemplification in the Laboratory
2. Short quiz at the start of next
meeting regarding Chapter 2
Determine the equation of a line and a circle
given sufficient information and sketch its
graph
3. Written exercises and oral
recitation in the laboratory
Determine if two lines are parallel or
perpendicular
3. Conics
2 hours
a. Parabola
b. Ellipse
c. Hyperbola
4. Limit of Functions
a. Intuitive Notion
b. Formal Definition (ɛ-δ)
c. Limit Theorems
d. One-sided limits
e. Infinite limits, Limits at infinity
and Infinite Limits at Infinity
f. Asymptotes
g. Curve Tracing
Determine the important points and solve all
relevant quantities of a conic given its
equation in any form
Lecture/Class Discussion
Exemplification in the Laboratory
2. Boardwork and written exercises
in the laboratory
Determine the equation of a conic given
sufficient information and sketch its graph.
3 hours
Define the limit of a function
Lecture/Class Discussion
Evaluate limits using limit theorems
Exemplification in the Laboratory
Interpret limits geometrically
Prove limits using the Formal Definition
Determine the asymptotes of a function
analytically
1. Give supplementary problems as
exercises and assignment
1. Give supplementary problems as
exercises and assignment
2. Short quiz at the start of next
meeting regarding Chapter 4
3. Boardwork and written exercises
in the laboratory
Sketch the graph of a function using limits
5. Continuity
2 hours
a. Definitions
b. Types of Discontinuities
c. Theorems on continuity
Define the continuity of a function at a point,
on an interval and on its domain
Lecture/Class Discussion
1. Give supplementary problems as
exercises and assignment
Exemplification in the Laboratory
Discuss the continuity of a given function,
i.e., the intervals for which it is continuous
and its points of discontinuity.
2. Short quiz at the start of next
meeting regarding Chapter 5
3. Boardwork and reporting in the
laboratory
4. Comprehensive Exam
Know the concept of the derivative
of a function – its definition and
applications, and the precise
mathematical methods in
differentiation
6. Derivatives
4 hours
a. Slope of a Tangent Line
b. Definition of Derivative
c. Differentiability of a Function
d. Differentiability and Continuity
e. Rules on Differentiation
f. The Chain Rule
g. Implicit Differentiation
h. Higher Order Derivatives
Define the derivative of a function and the
derivative of a function at a point
Lecture/Class Discussion
1. Give supplementary problems as
exercises and assignment
Exemplification in the Laboratory
Find the derivative of a given algebraic
function using the rules on differentiation
and the chain rule
2. Short quiz at the start of next
meeting regarding Chapter 6
3. Boardwork and oral recitation in
the laboratory
Discuss the differentiablity of a given
function, i.e., the intervals for which it is
differentiable and the points where the
derivative DNE
Interpret derivatives geometrically
Contrast differentiability from continuity
Extend the idea differentiation to curves
which are not functions through implicit
differentiation
Calculate higher order derivatives
7. Applications of Derivatives
a. Tangent and Normal Lines
b. Rectilinear Motion
b. Related rates
d. Relative Extrema of a Function
e. Absolute Extrema of a function
f. Extreme Value Theorem
g. Rolle’s and Mean Value Theorem
h. Optimization Problems
i. Curve Tracing
5 hours
Determine the equations of tangent and
normal lines to a curve using derivative
Lecture/Class Discussion
1. Give supplementary problems as
exercises and assignment
Exemplification in the Laboratory
Analyze a particle moving in a rectilinear
motion
2. Short quiz at the start of next
meeting regarding Chapter 7
Determine the relative and absolute extrema
of a function on a given interval
3. Boardwork and reporting in the
laboratory
Solve related rates and optimization
problems using derivatives
4. Comprehensive Exam
Employ the idea of derivatives to sketch the
graph of a function
Discern the concept of
antidifferentiation and integration,
and understand the fundamental
theorems of Calculus
8. Antidifferentiation
2 hours
a. Antidifferentiation Formulas
b. Integration by substitution
c. Simple Differential Equations
9. The Definite Integral
Determine the anti-derivative of a given
function
Lecture/Class Discussion
Exemplification in the Laboratory
3 hours
a. Summation Notation and Riemann
Sum
b. Area under a Curve
c. Definition of the Definite Integral
d. Properties of the Definite Integral
e. The Mean Value Theorem for
Integrals
f. The Fundamental Theorems of
Calculus
g. Applications of the Definite
Integral
Evaluate antiderivatives using Integration by
Substitution
2. Short quiz at the start of next
meeting regarding Chapter 8
Solve simple differential equations using
antidifferentiation
3. Boardwork and oral recitation in
the laboratory
Define the Definite Integral
Lecture/Class Discussion
Apply the properties of the Definite Integral,
Mean Value Theorem and the Fundamental
Theorems of Calculus to solve problems
involving Definite Integrals
Exemplification in the Laboratory
Laboratory Grade = ¾ ( Average of 3 Laboratory Exams ) + ¼ ( Laboratory Exercises )
Lecture Grade = 2/3 [( 9/10 Average of 3 Lecture Exams ) + 1/10 (Non departmental items)] +1/3 (Final Exam)
Final Grade = ½ ( Lecture Grade ) + ½ ( Laboratory Grade )
Grading Scale
87–89
1.5
84–86
1.75
80–83
2.0
2. Short quiz at the start of next
meeting regarding Chapter 9
4. Comprehensive Exam
Computation of Grade
90–92
1.25
1. Give supplementary problems as
exercises and assignment
3. Boardwork and reporting in the
laboratory
Calculate the area of a plane region
Grading System:
≥ 93
1.0
1. Give supplementary problems as
exercises and assignment
75–79
2.25
70–74
2.5
65–69
2.75
60–64
3.0
55–59
4.0
≤ 55
5.0