Week 1: Foundations of Calculus
Topics: Understanding functions, domain, range, and the concept of a limit.
Activities: Interactive examples on evaluating limits, and discussion of continuity.
Assignments: Practice problems on limits and continuity.
Week 2: Derivatives – The Basics
Topics: Introduction to derivatives, the concept of slope, and the derivative as a rate of change.
Activities: Step-by-step differentiation examples, real-world applications of rates.
Assignments: Simple differentiation exercises.
Week 3: Rules of Differentiation
Topics: Product, quotient, and chain rules.
Activities: Guided practice applying differentiation rules to various functions.
Assignments: Problems on applying differentiation rules.
Week 4: Applications of Derivatives
Topics: Understanding critical points, maxima, minima, and optimization problems.
Activities: Problem-solving sessions on optimization and curve sketching.
Assignments: Optimization problems and graphing tasks.
Week 5: Introduction to Integrals
Topics: Antiderivatives, definite and indefinite integrals, and the Fundamental Theorem of Calculus.
Activities: Hands-on activities to find areas under curves.
Assignments: Basic integral problems.
Week 6: Applications of Integrals
Topics: Applications of integration in physics and economics (e.g., areas, volumes, and accumulated change).
Activities: Group discussions on real-world integral applications and practice solving applied problems.
Assignments: Applied integral problems and reflection on course learnings.
Throughout this course, we will also focus on preparing for the AP Calculus AB exam by aligning our lessons with key topics tested on the exam. Learners will gain both the foundational understanding and the problem-solving skills needed to succeed, with opportunities to understand the topics and fill any knowledge gaps.
At the end of each class, learners are encouraged to ask questions to clarify concepts and seek additional help. For further support, individual sessions can be scheduled to address specific challenges or dive deeper into topics of interest. This ensures every learner gets personalized guidance and maximizes their understanding of calculus.
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