(MC13) Vector Function Fundamentals

We begin with an introduction to the graphical representations of vector functions, providing a visual foundation for understanding their behavior. We then explore limits, derivatives-including scalar, dot product, and cross product rules-with a detailed proof of the dot product rule. Moving forward, we discuss the integration of vector functions and key concepts such as unit tangent vectors, velocity vectors, norms, curvature, and arc length. Each topic is broken down with clear explanations and practical examples, demonstrating how these mathematical tools are used to analyze the properties and trajectories of vector functions in space.
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