
Calculus is a foundational course that explores the concepts of change and motion through the study of limits, derivatives, and integrals. This course provides a rigorous introduction to differential and integral calculus, emphasizing both theoretical understanding and practical application.
Key Topics:
- Limits: Understanding the concept of limits, continuity, and the behavior of functions as they approach specific points or infinity.
- Derivatives: Introduction to the derivative as a measure of instantaneous rate of change. Techniques for differentiation, including the product, quotient, and chain rules. Applications of derivatives in real-world problems, such as motion and optimization.
- Integrals: Understanding the definite and indefinite integrals as the accumulation of quantities. Fundamental Theorem of Calculus, techniques of integration, and applications to area under curves.
- Applications: Real-world applications of calculus in fields such as physics, engineering, and economics. Problem-solving strategies involving rates of change and optimization.
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