Single Variable Calculus

Welcome to Single Variable Calculus, Impart’s in-depth exploration of one of the most profound and beautiful subjects in mathematics. This course is designed for self-study and can be used to prepare for the AP Calculus BC exam or a complete Calculus I/II sequence in college.

Whether you’re encountering calculus for the first time or returning with fresh eyes, this course is built to develop your mathematical thinking and intuition. To do this, we emphasize problem solving throughout the course.

Course Structure

The course is organized into 11 units, each containing a series of lessons. For every topic, you’ll have the option to read the material or watch the math lesson. Lessons are designed to be concise, concept-driven, and practical.

Each lesson includes strategic practice problems that help you internalize key ideas as you learn. At the end of every unit, you’ll complete a problem set that challenges you to synthesize what you’ve learned and apply it creatively.

This course aligns with the following curriculum breakdowns:

• AP Calculus AB: Units 0–8
• AP Calculus BC: Units 0–10
• College Calculus I/II: Units 0–5 (Calc I), Units 6–10 (Calc II) (Note: This breakdown may vary by institution.)

Prerequisites

You should be comfortable with precalculus. Although calculus introduces many new ideas, solving problems often comes down to algebraic manipulation. If you struggle with simplifying expressions, factoring, or working with equations, we strongly recommend reviewing these skills before or alongside this course.

You can find helpful resources by clicking on Algebra or Precalculus in our Mathematics Roadmap.

Looking Forward

In the upcoming unit, we’re going to go over limits and continuity. This unit will form the bedrock of everything we’ll learn in calculus, so it’s important to make sure you have a solid understanding of it.