Episode 64 - eigenvalues and eigenvectors

Today (Episode 64), I continued with Program 5 from Frame 47, Page 509. I explained the concept of eigenvalues and eigenvectors and demonstrated how to obtain the characteristic matrix, characteristic polynomial/determinant, characteristic root (eigenvalues), and their corresponding eigenvectors. I concluded the chapter by discussing Cayley Hamilton's theorem.


https://www.youtube.com/watch?v=fHPjpylcUDY

Episode 65


https://www.youtube.com/watch?v=2QA5jUaxyUM

In today's episode (Episode 65), I commenced the next Program (P2, Program 6, page 520) with the topic of vectors. I introduced vectors as quantities possessing both magnitude and direction and discussed how vectors can be represented on a straight line. In the second part of the video, I discussed types of vectors, including the concepts of equal vectors and the triangular laws of vectors.

Episode 67 - Cross product


https://www.youtube.com/watch?v=uLH5Ie5LSyM

Episode 68


In today's episode (Episode 68), the author continued his explanation of differentiation (remember, the topic was introduced as part of the foundational topics in Program F12 (Episode 42)). In this new program (Program 7, page 544), following the author's exposition, I reviewed derivatives and some standard derivatives, as well as methods of differentiating functions in their various forms. I concluded the video with an explanation of logarithmic functions - an easier method to differentiate more than two functions when the product/quotient rule might be longer to use.


https://www.youtube.com/watch?v=P7OFHm2LG84

https://www.youtube.com/watch?v=31zgoo4gbHw

In tonight's episode (Episode 69), I continued my explanation from Program 7, Frame 26, page 555, focusing on the topic of implicit function differentiation. I explained the difference between this type of function and the one we have been working with (explicit) and how to deal with functions of these types. In the second part of the class, I covered parametric equations and how to differentiate them, marking the end of Program 7.

Episode 70 - KA Stroud Engr Math 70 - Differentiation of inverse trigonometric and hyperbolic functions

In tonight's episode (Episode 70), I began the next program (Program from page 562 of the book, which focuses on differentiation applications. The first two topics covered in this program are the differentiation of inverse trigonometric and hyperbolic functions. I derived the derivatives of these functions and applied them to problems.


https://www.youtube.com/watch?v=xfrxpRC17Hc

Episode 72 - Sequences

Tonight, I began the next program (Program 10, page 605) covering the topic of sequences. I reviewed the meaning of sequences, discussing how they relate to and differ from sets. Additionally, I demonstrated how to graph sequences and explained some special sequences along with methods to obtain their nth terms.


https://www.youtube.com/watch?v=Clf4WfI27M0