Calculus in Action: Mathematics and Applications

Far beyond textbook problems, this course dives into the powerful applications of calculus in the real world — from engineering and physics to economics, biology, and data science. Students will explore key concepts such as limits, derivatives, integrals, and differential equations while learning how these tools model and solve real-world challenges. With a strong focus on individual exploration and collaborative problem-solving, students will analyze changing systems and simulate natural and technological processes using both analytical and computational methods. Through guided projects, experiments, and group challenges, students will see how abstract concepts translate into meaningful solutions, preparing them for advanced study and inspiring careers in STEM.

*Gifted course, see Admissions Criteria for eligibility requirements.

Example Activities & Projects:

• Rate of Change Labs: Model and graph physical motion, such as a rolling ball or a changing water level, using derivatives.
• Optimization Challenge: Design the most efficient container or structure by applying principles of maxima and minima.
• Area Under the Curve Exploration: Use Riemann sums and integrals to analyze data from real-world sources like population growth or velocity-time graphs.
• Applied Economics Simulation: Examine marginal cost and revenue to determine profit-maximizing strategies using calculus tools.

Course Outcomes:

By the end of the program, students will be able to:

1. Understand and apply foundational calculus concepts
2. Solve real-world problems using calculus-based modeling and critical thinking.
3. Understand how technology is used to visualize and analyze mathematical behavior.
4. Make connections between calculus and diverse fields such as physics, biology, economics, and engineering.
5. Develop confidence in communicating complex mathematical ideas clearly and effectively.

Prerequisites:

• To be successful in this course, students should have completed Advanced Algebra and Geometry courses.
• Prior coursework in pre-calculus and computer science strongly recommended.