Plane Curves as Vector Functions and the Structure of a DNA Helix https://youtu.be/S94nUYS8Imc

In this video I discuss how plane curves can be represented as vector functions, and illustrate an example of a plane curve that spirals upwards into a helix.

#math #vectorfunctions #planecurves #biology #calculus

Space Curves: Tracing out the Tip of a Continuous Vector Function https://youtu.be/DHJnsmyG1LQ

In this video I show that a continuous vector function in 3D forms a curve in space when tracing out the point on the tip of the vector as it moves in time.

#math #vectofunctions #spacecurves #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

Exercise 4: Fibonacci's Original Rabbit Reproduction Sequence (and the Golden Ratio) https://youtu.be/NNNNKwGIKgI

In this video I go over the first appearance of the famous Fibonacci sequence and show that the limit of the ratio of two consecutive terms is equal to the Golden Ratio. The Italian mathematician Leonardo Bonacci, or more commonly known as Fibonacci (short for "filius Bonacci or "son of Bonacci"), first wrote the Fibonacci sequence in 1202 when analyzing the population growth of an idealized rabbit population. 

#math #sequences #fibonaccisequence #goldenratio #calculus

Exercise 3: Convergent Sequence inside a Continuous Function https://youtu.be/vdQa-zAA6w0

In this video I prove Theorem 3, which states that a convergent sequence with limit L can be plugged directly into a continuous function at L, thus obtaining f(L).

#math #sequences #limits #education #calculus