Limit of a Vector Function https://youtu.be/z48K6YRJ3Jc

In this video I go over the definition of the limit of a vector function, which involves taking the limit of each of its component functions. If the limit exists, then so does the limit of each component function.

#math  #limits #vectorfunctions #education #calculus

Introduction to Vector Functions https://youtu.be/Qi2hVnKN-5c

In this video I introduce vector functions and show how they differ from the real-value functions that we are used to. Vector functions have domain of real numbers and a range of vectors. Compare this with real-valued functions which have both domain and range being single values, aka numbers.

#math #science #vectorfunctions #education #calculus

Vector Functions and Space Curves https://youtu.be/Qi2hVnKN-5c

In this video I deep dive nearly 5 hours into vector functions and space curves. A vector function has a domain (or input) of real numbers and a range (or outputs) of vectors. Compare this with the real-valued functions that we are used to, which have inputs of real numbers (typically x) and the outputs are also real numbers (typically y = f(x)).

#math #science #education #vectorfunctions #calculus

True-False Quiz Questions 22: Cauchy–Schwarz Inequality https://youtu.be/5SF6JokcFUY

In this video I show that the absolute value of the dot product has a maximum value of the lengths of each vector multiplied by each other. This relation is known as the Cauchy-Schwarz Inequality.

#math #science #STEM #vectors #education

True-False Quiz Questions 19 to 21: When Dot and Cross Products Equal Zero https://youtu.be/naNwDZdYSZY

In this video I show that if the dot or cross products are zero then neither vector has to be zero, but if BOTH the dot and cross products are zero then at least one of the vectors has to be zero.

True-False Quiz Questions 15 and 16: Perpendicular Vectors to a Plane https://youtu.be/_PcU6fKN0sc

In this video I quickly show that a vector is perpendicular to a plane if it is a multiple of the normal vector obtained from the plane's linear equation.