MATH 1500: Introductory Calculus I Course Outline

Course Description

This course introduces students to the fundamental concepts of differential calculus. Topics include limits, continuity, derivatives of algebraic and transcendental functions, applications of derivatives, and an introduction to integration. The course emphasizes conceptual understanding, practical applications, and the development of problem-solving skills.

Course Learning Objectives

Upon successful completion of this course, students will be able to:

• Define and compute limits using algebraic techniques and interpret them graphically
• Determine continuity of functions and identify points of discontinuity
• Calculate derivatives of various functions using differentiation rules
• Apply differentiation techniques to solve related rates, optimization, and approximation problems
• Analyze functions using derivatives to determine increasing/decreasing intervals, concavity, and extrema
• Evaluate definite and indefinite integrals using basic integration techniques
• Apply the Fundamental Theorem of Calculus to solve problems involving rates of change
• Use technology appropriately to solve calculus problems and visualize concepts

Course Content

Module 1: Limits and Continuity

• Intuitive understanding of limits using tables and graphs
• Limit laws and algebraic techniques for evaluating limits
• One-sided limits and infinite limits
• Continuity of functions and types of discontinuities
• Intermediate Value Theorem

Module 2: Introduction to Differentiation

• Tangent lines and the derivative at a point
• The derivative as a function
• Differentiability vs. continuity
• Basic differentiation rules (power, constant, sum/difference rules)
• Product and quotient rules
• Chain rule for composite functions

Module 3: Differentiation of Transcendental Functions

• Derivatives of exponential functions
• Derivatives of logarithmic functions
• Derivatives of trigonometric functions
• Derivatives of inverse functions
• Applications involving transcendental functions

Module 4: Applications of Differentiation

• Related rates problems
• Linear approximation and differentials
• Mean Value Theorem and its applications
• Newton's Method
• Indeterminate forms and L'Hpital's Rule

Module 5: Analysis of Functions with Derivatives

• Critical numbers and local extrema
• Rolle's Theorem
• The first derivative test
• Concavity and inflection points
• The second derivative test
• Curve sketching
• Applied optimization problems

Module 6: Introduction to Integration

• Antiderivatives and indefinite integrals
• Area problem and Riemann sums
• Definite integrals and their properties
• The Fundamental Theorem of Calculus
• Techniques of integration: substitution, integration by parts
• Numerical integration methods

Assessment Structure

Assessment Component	Weight	Dates/Deadlines
Weekly Assignments	15%	Every Thursday at 11:59 PM
Quizzes (4 at 5% each)	20%	Weeks 3, 6, 9, 12
Midterm Examination	25%	Week 7 (2 hours)
Final Examination	40%	Exam period (3 hours)

Learning Resources

Required Textbook

• Stewart, J. (2022). Calculus: Early Transcendentals (9th ed.). Cengage Learning. ISBN: 978-0357434791

Recommended References

• Thomas, G. B., Weir, M. D., & Hass, J. (2019). Thomas' Calculus (14th ed.). Pearson.
• Larson, R., & Edwards, B. H. (2022). Calculus (12th ed.). Cengage Learning.
• Strang, G. (1991). Calculus. Wellesley-Cambridge Press.

Online Resources

• Khan Academy Calculus (www.khanacademy.org/math/calculus-1)
• Paul's Online Math Notes (tutorial.math.lamar.edu/classes/calcI/calcI.aspx)
• MIT OpenCourseWare Single Variable Calculus (ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010)
• Wolfram Alpha (www.wolframalpha.com) - for checking work

Course Schedule

Week	Topic	Readings
1	Introduction to Calculus; Limits and Rates of Change	Chapter 1, 2.1-2.2
2	Limit Laws and Calculating Limits	2.3-2.5
3	Continuity; Limits at Infinity	2.6-2.7
4	Derivatives and Tangent Lines; Rules of Differentiation	3.1-3.3
5	Derivatives of Trigonometric Functions	3.4-3.6
6	The Chain Rule; Implicit Differentiation	3.7-3.8
7	MIDTERM EXAM	N/A
8	Exponential and Logarithmic Functions	3.9-3.10
9	Related Rates; Linear Approximations	3.11-3.12
10	Maximum and Minimum Values	4.1-4.2
11	The Mean Value Theorem; Curve Sketching	4.3-4.5
12	Optimization Problems; Antiderivatives	4.7, 4.9, 5.3
13	Areas and Distances; The Definite Integral	5.1-5.4
14	The Fundamental Theorem of Calculus	5.5-5.6
15	Techniques of Integration; FINAL EXAM PREPARATION	5.7, Review

Policies and Expectations

Attendance Policy

Regular attendance is expected and necessary for success in this course. Lecture slides and supplementary materials will be available on the course website, but these are not a substitute for attending lectures. Students who miss more than 3 tutorial sessions without a valid documented reason may have their final grade reduced by 2% per additional absence.

Academic Integrity

All work submitted for assessment must be your own. Collaboration on assignments is encouraged, but the work you submit must reflect your understanding. Copying solutions or allowing others to copy your work constitutes academic dishonesty. All instances of academic dishonesty will be handled according to university policy and may result in a grade of zero on the assignment or course, or more severe penalties.

Grading Policy

Your final grade will be calculated based on the weighted components outlined above. There is no curve applied to grades. Final letter grades will be assigned as follows:

• A (85-100%): Exceptional performance
• B (70-84%): Good to very good performance
• C (55-69%): Satisfactory performance
• D (50-54%): Marginal performance
• F (0-49%): Unsatisfactory performance

Late Submission Policy

Assignments submitted late will be penalized 10% per day (or part thereof) of the maximum possible mark, up to a maximum of 3 days. After 3 days, late assignments will not be accepted and a mark of zero will be assigned. Extensions may be granted for reasons of illness or personal circumstances, provided appropriate documentation is submitted.

Technology Requirements

• Scientific calculator (non-programmable for exams)
• Access to course website and online resources
• Graphing software (GeoGebra or Desmos recommended)

Student Support Services

• Math Help Centre: Located in Room 325, Science Building. Open Monday-Friday, 9 AM-5 PM. No appointment necessary.
• Academic Skills Centre: Offers workshops and individual tutoring to improve study strategies and mathematical skills.
• Library Resources: Reserve desk contains copies of the textbook and solution manuals.