Definition of Derivative for Vector Functions https://youtu.be/LAXaiYA5p1k

In this video I go over the definition of derivative for a vector function, which is very similar to the definition for real valued functions. The derivative of a vector function is defined as the limit as h approaches zero of the secant vector (difference of two vectors separated by incrementing the parameter t by h) divided h. As h approaches zero the secant vector approaches a vector that is parallel to the tangent vector to the curve.

#math #science #calculus #vectorfunctions #geogebra

Derivatives and Integrals of Vector Functions https://youtu.be/YT4QJczx8KI

In this video I go further into vector functions and this time show how to obtain their derivatives and integrals. The definition of derivative for a vector function is much the same as with a real valued function, but the difference is that we apply this definition to each component of the vector function. Likewise, integration is also similar to real valued functions but the integral of each component is solved. This will be the basis for future videos when I cover velocity and acceleration of planetary bodies so stay tuned for that!

#math #science #calculus #vectorfunctions #education

MES Livestream 106: Dr. Tony Cicoria Discusses his Near Death Experience (NDE) Lightning Strike https://youtu.be/gwyKv42EvPE

Dr. Tony Cicoria joins the show to discuss getting struck by lightning while standing next to a public telephone in Albany, New York in 1994, seeing his own body on the ground while his consciousness floated upwards surrounded by a bluish-white light, then waking up back in his own body a few minutes later. And a few days later, at the age of 42, he had the insatiable desire to listen and learn to play to piano music, thus becoming an "accidental" pianist and composer! 

August 30, 2025 SATURDAY at 1 PM PST / 3 PM CST / 4 PM EST / 10 PM CAT / 21:00 GMT (UK)

#nde #neardeathexperience #lightningstrike #consciousness #piano

Ecology: Ecosystems https://youtu.be/IiXjAiAEybw

Ecology is the study of the distribution of living organisms and their interactions with the environment. An ecosystem is the community of living or biotic organisms with their nonliving or abiotic components of their environment. The topography, shape, and tilt of the Earth leads to a wide variety of terrestrial biomes, such as tundras, forests, deserts, and rainforests.

#science #biology #ecosystems #ecology #environment

Animal Form and Function: Animal Behavior https://youtu.be/T5ZHDEn6QRA

In this video I go over animal behavior, which is central to how animals interact with other animals and their environment such as through foraging, mating, and migration. Some actions are genetically determined and occur without learning, such as kelp gull (and other seagull) chicks pecking at the red dot on their mother's beak when they want food. Dutch scientist Niko Tinbergen won a Nobel Prize in part for his discovery that this seagull peaking was instinctive from birth and not learned. 

#science #biology #animalbehavior #animals #nature

Animal Form and Function: Immune System https://youtu.be/xEffS5ZV47M

In this video I go over the mainstream theory of the immune system, which is a network of biological processes that detects and responds pathogens entering an organism. Nearly all organisms have some sort of immune system, while jawed vertebrates (including humans) have sophisticated defense mechanisms and the ability to adapt to recognize previously encountered pathogens. The innate immune system is a rapid and broad defense mechanism, which includes phagocytosis to engulf large foreign particles. The adaptive immune system involves specialized white blood cells (killer cells and T / B lymphocytes) which can recognize unique molecules on pathogens (called antigens) via Y-shaped proteins called antibodies. This immunological memory is the basis of vaccination.

#science #biology #ImmuneSystem #animals #vaccine