MAT 271-100 Calculus I Syllabus and Course Structure Study Guide

Course Overview

Introduction to Calculus I

This syllabus outlines the structure, policies, and resources for MAT 271-100 Calculus I at Durham Technical Community College. The course covers foundational topics in differential and integral calculus, including limits, continuity, derivatives, and integrals of algebraic and transcendental functions. Students are expected to develop skills in modeling and solving calculus problems, preparing for further study in mathematics and related fields.

• Course Description: Focuses on limits, continuity, derivatives, and integrals of functions of one variable.

• Prerequisites: Precalculus (MAT-175 or MAT-171) or equivalent.

• Textbook: Briggs, Cochran, Gillett, Schulz, Calculus: Early Transcendentals, Third Edition.

• Calculator: TI-83 or TI-84 graphing calculator (no other calculators allowed).

• Online Resources: Canvas and MyLabMath for assignments and course communication.

Course Topics and Schedule

Major Calculus Topics

The course schedule follows the standard sequence of Calculus I topics, as outlined below. Each topic corresponds to a chapter or section in the textbook and is covered in class meetings, homework, and assessments.

• Chapter 1: Functions

• Chapter 2: Limits (including definitions, techniques, infinite limits, limits at infinity, and continuity)

• Chapter 3: Derivatives (rules, trigonometric functions, rates of change, chain rule, implicit differentiation, logarithmic and exponential functions, inverse trigonometric functions, related rates)

• Chapter 4: Applications of the Derivative (maxima and minima, mean value theorem, graphing, optimization, linear approximation, L'Hôpital's Rule)

• Chapter 5: Integration (area under a curve, definite integrals, fundamental theorem of calculus, u-substitution)

• Chapter 6: Applications of Integration (velocity and net change)

Example: The schedule shows that "2.1 The Idea of Limits" is covered early in the semester, followed by "2.2 Definitions of Limits" and "2.3 Techniques for Computing Limits." This sequence ensures students build a strong foundation before moving to derivatives and their applications.

Assessment and Grading

Grading Schemes and Policies

Students' final grades are determined by the highest result from three grading schemes, which include homework, quizzes/assignments, projects, tests, and the final exam. The grading scale is standard, with A (90-100%), B (80-89.9%), C (70-79.9%), D (60-69.9%), and F (below 60%).

Assessment	Scheme A	Scheme B	Scheme C
Homework	5%	15%	20%
Quizzes/Assignments	10%	15%	20%
Projects	5%	15%	10%
Tests	60%	35%	30%
Final Exam	20%	20%	20%

Key Points:

• Homework and quizzes are submitted via MyLabMath; late submissions are not accepted.

• Lowest homework and quiz grades are dropped.

• No retakes or make-ups for tests; missed test grades may be replaced by the final exam score (with prior notification).

Course Policies

Academic Integrity and Technology Use

Strict policies are enforced regarding academic honesty and the use of technology during exams. AI tools are not permitted for graded assignments. Only approved calculators (TI-83 or TI-84) may be used during tests and quizzes. Possession of unauthorized electronic devices during exams is prohibited.

• Academic Honesty: Plagiarism, unauthorized collaboration, and use of prohibited devices are violations.

• Attendance: Regular attendance is required; students are responsible for making up missed work.

• Withdrawal: Drop and withdrawal deadlines are specified; consult with college liaison if dual-enrolled.

• Accessibility: Accommodations are available for students with disabilities.

Student Support and College Resources

Available Resources for Success

Durham Tech provides a variety of resources to support student success, including food pantry, career services, tutoring, computer and internet assistance, counseling, emergency financial aid, library access, Canvas support, success coaching, and support for parenting and high school students.

• Campus Harvest Food Pantry: Free groceries and hygiene products for students.

• Career Services: Resume and job search support.

• Center for Academic Excellence: Free tutoring and academic support.

• Computer and Internet Assistance: Loaner laptops and discounted internet options.

• Counseling Services: Confidential counseling and crisis support.

• Emergency Financial Assistance: Help with rent, utilities, childcare, and other needs.

• Library: Access to research guides and academic resources.

• Canvas: Learning management system for course materials and communication.

• Success Coaching: Individualized academic and personal support.

• Support for Parenting Students: Childcare grants and pregnancy support.

• Support for High School Students: Dual enrollment guidance.

Important Dates and Deadlines

Exam and Project Schedule

• Test 1: September 4

• Test 2: October 2

• Test 3: November 13

• Final Exam: December 11

• Optimization Project Assigned: October 30

• Optimization Project Due: November 30

• Final Drop Date: August 21

• Final Withdrawal Date: October 24

Summary of Calculus I Content

Key Calculus Concepts

The course covers the following essential calculus concepts, which are foundational for further study in mathematics, engineering, and science:

• Functions: Understanding and graphing functions.

• Limits: Concept, computation, infinite limits, and continuity.

• Derivatives: Rules, applications, and rates of change.

• Applications of Derivatives: Optimization, graphing, and related rates.

• Integration: Area under curves, definite integrals, and the fundamental theorem.

• Applications of Integration: Velocity and net change.

Example Formula: The derivative of a function $f(x)$ is defined as: $f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

Example Formula: The definite integral of a function $f(x)$ from $a$ to $b$ is: $\int_a^b f(x)\,dx$

Additional info: This syllabus provides a comprehensive overview of course structure, policies, and resources, but does not include detailed lecture notes or problem solutions. For in-depth study, refer to the textbook and assigned materials in Canvas and MyLabMath.