Course Outline: Calculus I (HMAT131)
Course Description
This course introduces the fundamental concepts of differential and integral calculus. It
covers limits, continuity, derivatives, applications of derivatives, definite and indefinite
integrals, and real-world applications, particularly in science and engineering fields.
Emphasis is placed on conceptual understanding, analytical reasoning, and solving
practical problems. The course also introduces students to sequences and series,
focusing on arithmetic and geometric sequences and tests for convergence.
Course Objectives
• Understand basic concepts of functions
• Compute limits and investigate continuity of functions.
• Differentiate functions using standard rules and techniques.
• Apply derivatives in real-world contexts such as motion, optimization, and curve
sketching.
• Compute definite and indefinite integrals using appropriate techniques.
• Use integration to solve problems involving area, volume, and other physical
applications.
• Understand the basic concepts of sequences and series, and apply convergence tests
to determine their behavior.
Chapter 1: Functions
• - Functions and their properties
• - Domain and range
• - Inverse functions
• - Exponential and logarithmic functions
• - Trigonometric functions
Chapter 2: Limits and Continuity
• - Understanding limits graphically and numerically
• - Limit laws
• - One-sided limits
• - Infinite limits and vertical asymptotes
• - Continuity and types of discontinuities
• - Limits at infinity and horizontal asymptotes
• - Infinite limits at finite points
Chapter 3: Definition of the Derivative
• - Derivative as a limit
• - Differentiability and continuity
• - Basic differentiation rules (Power rule, Constant rule, etc.)
• - Product rule and quotient rule
• - Derivatives of trigonometric functions
• - Derivatives of exponential and logarithmic functions.
• - Higher-order derivatives
• - Chain rule
• - Derivatives of inverse functions
• - Implicit differentiation
Chapter 4: Applications of Derivatives I
• - Related rates
• - Linear approximation and differentials
• - Mean Value Theorem
• - Increasing/decreasing functions
• - Critical points
• - First and second derivative tests
• - Concavity and inflection points
• - Solving applied max/min problems
• - Sketching graphs of functions
• - Asymptotes, intercepts, behavior at infinity
Chapter 5: Integration
• - Introduction to integration
• - Antiderivatives and basic integration rules
• - Definite integral
• - Properties of definite integrals
• - Substitution method
• - Change of variables
• - Integrals involving exponential and trigonometric functions
Chapter 6: Applications of Integration
• - Area between curves
• - Arc length
• - Volumes of solids of revolution (disk and washer methods).
• - Arc length and average value of a function.
Chapter 7: Infinite Sequences and Series
• - Definition and notation for sequences.
• - Arithmetic and geometric series.
• - Convergence and divergence of series.
• - Simple convergence tests (n-th term test, geometric series test).
OTHER IMPORTANT INFORMATION
1. Methods of facilitation of learning
a. Lectures
b. written assignments.
c. group work
d. class discussions
e. Presentations
2. Assessment strategy
a. Continuous assessment 40% (minimum 2 tests)
b. Final examination 30% (1 x 3-hour paper)
PRESCRIBED TEXT
1. Thomas, G. B., Weir, M. D., & Hass, J. (2018). *Thomas’ Calculus*. 14th Edition. Pearson.
RECOMMENDED TEXTS
2. Stewart, J. (2021). *Calculus: Early Transcendentals*. 9th Edition. Cengage Learning.
3. Larson, R., & Edwards, B. (2019). *Calculus*. 11th Edition. Cengage.
4. Adams, R. A., & Essex, C. (2013). *Calculus: A Complete Course*. 8th Edition. Pearson.
