Polytechnic University of the Philippines Bansud Campus Poblacion, Bansud Oriental Mindoro
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Course Title: Course Code:
DIFFERENTIAL CALCULUS MATH 2073
Course Credit:
3 units
Course Description:
This course provides both in-depth review of functions and an introduction to differential calculus. In particular, limits, continuity and derivatives are introduced as tools used to analyze the behavior algebraic, exponential, logarithmic and trigonometric functions.
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Objectives: Upon successful completion of this course, the student is expected to: 1. Grasp a thorough knowledge and understanding of functions, limit and continuity. 2. Determine the derivative of algebraic and transcendental functions 3. Apply the derivative in real-life situations. 4. Solve some mathematical problems using the differentials. 5. Find the derivatives n parametric form 6. Be familiar with partial differentiation.
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Course Content
First Grading TOPICS Orientation I. Functions, Limits and Continuity
Time Allotment 6 hours
A. Functions B. Functional Notation C. The Algebra of Function D. Composition of Functions E. Limits F. Limits and Infinity G. Continuity II. The Derivative
6 hours
A. Average Rate of Change B. Instantaneous Rate of Change C. Slope of Secant and Tangent line D. Techniques of Differentiation E. Chain Rule F. Implicit Differentiation
III. Differentiation of Algebraic Functions
5 hours
A. Review of the Techniques of Differentiation B. Implicit Functions C. Parametric equations D. The derivative of a function E. Inverse Function F. Higher Derivative IV. Applications
5 hours
A. Tangents and Normal to Plane Curves B. Polynomial Functions C. Maxima and Minima Problems D. Related Rates E. Rectilinear Motion V. The Differential
5 hours
A. Definition, The Differential B. Formulas for Differential C. Applications of Differential VI. Trigonometric Functions
5 hours
A. The Sine and cosine Functions B. Derivatives of Trigonometric Functions C. Applications of Trigonometric D. Graphs of Trigonometric Functions VII. Inverse Trigonometric Functions
5 hours
A. Definitions and Limitations B. Derivatives of Inverse Trigonometric Functions C. Application of Trigonometric Functions VIII. Logarithmic and Exponential Functions
5 hours
A. The Exponential Functions B. The logarithmic Functions C. Derivative of Exponential Functions D. Derivative of Logarithmic Functions E. Applications F. Hyperbolic Functions G. Inverse hyperbolic Functions IX. Indeterminate Forms
5 hours
X. Partial Differentiation
5 hours
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Strategies
1. Lecture Method 2. Board work 3. Seat work/Homework 4. Cooperative Learning 5. Brainstorming
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Course Requirement Assignments Board works Seat works Participation/Recitation Quizzes Midterm and Final Examinations
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Reference Feliciano and Uy, Differential and Integral Calculus, Merriam and Webster Bookstore Inc., 1983 Love, C. et. al., Differential and Integral Calculus, 6th ed., Fadrigalan, et.al., Differential Calculus, 2002 Leithold, L, The Calculus with Analytic Geometry, 7th ed., Harper and Row, Publishers Inc.
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Grading System
1 Final Grade =
1 (First Grade) +
2
(Second Grade) 2
Where: 2 First Grade =
1 (Class Standing before ME) +
3
(Midterm Examination); 3
2 Second Grade =
1 (Class Standing after ME) +
3
(Final Examination) 3
