Course Overview

Calculus A introduces students to the foundational concepts of limits, differentiation, and the applications of derivatives. The course emphasizes multiple approaches—graphical, numerical, and analytical—to develop a well-rounded understanding of calculus and its role in advanced mathematics and real-world problem-solving.

Key Learning Focus

Students will learn to:

• Evaluate finite and infinite limits graphically, numerically, and analytically.
• Apply rules of differentiation, including the chain rule and implicit differentiation.
• Use the first derivative test and second derivative test to analyze and sketch functions.
• Solve problems involving derivatives through a variety of techniques, including substitution.

Instructional Approach

The course balances procedural fluency with conceptual depth, ensuring students understand not only how to compute but also why calculus works. Graphing calculators are an integral part of instruction, equipping students to visualize, test, and confirm results while strengthening problem-solving and analytical reasoning.

Applications and Connections

Students will apply differentiation to real-world contexts such as optimization, rates of change, and curve sketching. Instruction highlights connections across mathematics and science, reinforcing calculus as both a theoretical and applied discipline.

Outcome

By the end of Calculus A, students will have a strong foundation in limits and differentiation, preparing them for Calculus B and higher-level STEM coursework. They will leave the course equipped with the analytical tools necessary for both academic advancement and real-world applications.