Math 210 (Calculus I): Syllabus and Course Overview

Course Description

This course provides an introduction to the study of the real number system, functions and graphs, continuity, and differentiation and their applications. The material is foundational for students pursuing mathematics, science, or engineering, and covers both theoretical and applied aspects of calculus.

Course Goals

• Prepare students for further study in mathematics, science, or engineering.

• Introduce differential calculus techniques and their applications.

• Develop problem-solving skills and the ability to analyze mathematical models.

Learning Outcomes

By the end of the course, students should be able to:

• Limits and Continuity: Understand and compute limits, analyze continuity, and interpret the behavior of functions graphically and analytically.

• Derivative Analysis Techniques: Use derivative rules to perform symbolic and graphical analysis of functions, including applications to rates of change and optimization problems.

• Derivative Formulas and Interpretation: Apply standard derivative formulas and interpret the meaning of derivatives in various contexts.

• Applications of Differentiation: Solve problems involving maxima, minima, related rates, and curve sketching using derivatives.

Major Topics Covered

• Functions: Definitions, types of functions, domain and range, function notation, and transformations.

• Limits: Concept of a limit, one-sided and two-sided limits, properties of limits, and techniques for evaluating limits.

• Continuity: Definition of continuity at a point and on an interval, and the Intermediate Value Theorem.

• Derivatives: Definition of the derivative, interpretation as a rate of change, and basic differentiation rules.

• Applications of Derivatives: Tangent lines, velocity and acceleration, optimization, related rates, and curve sketching.

Key Formulas and Theorems

• Limit Definition of the Derivative:

• Power Rule:

• Product Rule:

• Quotient Rule:

• Chain Rule:

Textbook

• Calculus: Early transcendentals by William Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz (ISBN: 9780134763644)

Assessment and Grading

• Weekly quizzes, online homework, group project, midterm exams, and a cumulative final exam.

• Grading breakdown includes MyMathLab (15%), Attendance (10%), Class Work (10%), Midterm exams (15% each, total 45%), and Final exam (20%).

Course Policies and Support

• Attendance and participation are expected.

• Academic integrity is strictly enforced.

• Tutoring and support services are available for students who need assistance.

• Accommodations are provided for students with documented disabilities.

Study Tips for Success in Calculus I

• Attend all lectures and actively participate in class discussions.

• Complete all assigned homework and review solutions to understand mistakes.

• Form study groups to discuss challenging concepts and solve problems collaboratively.

• Utilize office hours and tutoring resources for additional help.

• Read the textbook before and after lectures to reinforce understanding.