Comprehensive Vector Notes Comprehensive Guide to Vectors 1. Vector Basics Vectors are mathematical objects that have both magnitude (size) and direction. They are used to represent physical quantities like velocity,
Let’s explore areas in polar coordinates. In the rectangular coordinate system, we use definite integrals to calculate the area under a curve. For instance, if we have a function (y
When describing a curve using polar coordinates, it remains a curve in the (x-y) plane. The relationship between polar and rectangular coordinates is given by (x = r\cos\theta) and (y
A vector-valued function, also known as a vector function, is a mathematical function that maps one or more variables to a set of multidimensional vectors or infinite-dimensional vectors. Let’s explore
Arc Length (Distance Traveled Along a Curve) in Parametric Form If a curve C is given by the parametric equations x = f (t) and y = g (t) such
Let’s explore slopes and tangents for parametric curves. When we work with parameterized curves, we often encounter questions like: How can we calculate the slope of a tangent line to