Remember to join us tonight!

Episode 38 - Trigonometric identities
In episode 38 today, I started from frame 35 of program F9 where I discussed trigonometric identities. The difference between equations and identities was explained, and I derived the fundamental trigonometric identity using Pythagoras' theorem. I derived several other identities from this fundamental identity that showed relationships between trigonometric ratios. In the last part of the video, I applied these concepts to compound angles, double angles, half angles, and finding the value of trigonometric ratios for angles different from the special angles of 30, 45, and 60 degrees. This concludes Program F9.


https://www.youtube.com/watch?v=H7-J5GGgyEE

Episode 39 - Functions | Domain | Codomain | Range

In episode 39 of the class, we began the next program, F.10, which covers functions on page 267. I introduced the concept of functions, types and explained how to find their domain, co-domain, and range.


https://www.youtube.com/watch?v=BM9Jqt0VrGw

Remember to join us tonight

Episode 40 - INVERSE OF A FUNCTION

In episode 40, I concluded program F10, which covered the topic of functions. Starting from frame 8 on page 272 of the book, I explained how to find the inverse of a function and gave examples of different ways functions can appear and how to find their inverses. I also discussed how to find the domain and range of a function algebraically. Furthermore, I covered the topic of the composition of functions and explained how to decompose them to find inverses of a function of functions.


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

📢 ANNOUNCEMENT
I regret to inform you that tonight's weekly session for the explanation of the book "KA Stroud Engineering Mathematics with Dexter Booth" has been cancelled. I apologize for any inconvenience caused and look forward to seeing you next week, God willing. Thanks for your understanding.

Remember to join us again tonight on zoom or Facebook at 9pm WAT on our weekly explanation of the book "KA Stroud Engineering Mathematics with Dexter Booth" in Yorùbá! It promises to be interesting. Thanks

Today, I continued exploring functions from Program F11, starting from frame 75 on page 307 of the book. I explained the concepts of odd and even functions and discussed their properties. I also explained how to identify whether a function is odd, even, or neither. Building upon these ideas, I derived the hyperbolic cosine and sine functions.


https://www.youtube.com/watch?v=nkS-4Nrtvmk

Remember to join us again tonight (and every Thursday) via zoom or Facebook at 9pm WAT on our weekly explanation of the book "KA Stroud Engineering Mathematics with Dexter Booth" in Yorùbá! It promises to be interesting. Thanks.

Episode 42 - The limits of functions

In tonight's episode (episode 42), I continued from Program F11 , specifically from frame 51 on page 309, to discuss the fundamental concept of limits in functions. I carefully explained the limits of functions and demonstrated different approaches to solving them with examples. I concluded the episode by presenting some properties of limits. This marks the completion of Program F11. Join us next week as we embark on Program F12, where we will explore the fascinating topic of differentiation.


https://www.youtube.com/watch?v=czzr4I6GWdM

Remember to join us again tonight (and every Thursday) via zoom or Facebook at 9pm WAT for our weekly explanation of the book "KA Stroud Engineering Mathematics with Dexter Booth" in Yorùbá! It promises to be interesting. Thanks.

In tonight's episode (episode 43), I began by introducing the topic of differentiation (Program F12, page 315). In the first part of the class, I focused on the concept of finding the gradient of functions, whether they are lines or curves. I explained the process of determining the gradient of a function using the first principle and derived the standard derivatives of various polynomial functions using this principle.


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

Thanks a lot for the shared lectures! If you find the round the decimal calculator at https://www.calculator.io/rounding-calculator/ to be reliable and user-friendly, I encourage you to give it a try. Your request for suggestions and personal experiences is a great way to gather insights from others in the community.

KA Stroud Engr Math 44 - Standard derivatives | Product rules

In tonight's episode (episode 44), I continued my exploration of differentiation. I derived the derivatives of special functions, including trigonometric and hyperbolic functions, using the first principle. Additionally, I derived the product rule of differentiation from first principles and illustrated its application through various examples.


https://www.youtube.com/watch?v=gMk3ZnNp4z0

KA Stroud Engr Math 45 - Quotient and chain rules

In tonight's episode (episode 45), I continued with Program F12, specifically starting from frame 33 on page 338 of our book. I delved into the topic of differentiating functions that appear as quotients, as well as composite functions. I provided a comprehensive explanation and demonstrated the differentiation process through a wide range of examples. Moreover, I shared helpful shortcuts to approach similar questions more efficiently.


https://www.youtube.com/watch?v=sh-NXuTDy6Q

Episode 46


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

In tonight's episode (episode 46), I continued from frame 49 of Program F12 (page 344), where the authors introduced one of the applications of differentiation in numerical analysis: the Newton-Raphson iterative method. I derived this scheme and explained how to utilize it to approximate solutions. Additionally, I reviewed some useful theorems of calculus, including the intermediate value theorem, the mean value theorem, and Rolle's theorem. This concludes Program F12, and we will be commencing Program F13 (Integration) next week.

Episode 47

In last night's episode (episode 47), we began Program F13 (integration). I introduced integration as the reverse process of differentiation and explained how we encounter the constant of integration after integrating a function. Additionally, I differentiated between general and particular solutions.


https://www.youtube.com/watch?v=u8ZPL_Uydf0

Episode 48


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

In tonight's episode 48, I continued my explanation from frame 12 (page 360) of Program F13. I discussed how to integrate functions of a linear function of x. Using this concept, I introduced the u-substitution approach to integration. From this approach, I derived two rules of integration. I then concluded the video with integration by partial fractions.

In this video, I discussed two important u-substitution rules of integral. The video is an excerpt from my weekly Thursday session (ep. 48)


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

In today's episode (Episode 49), I commenced my explanation from the second part of the book, specifically Program 1 (Complex Numbers - page 385), after having covered all the foundational topics in the first 13 programs. I provided a comprehensive explanation of complex numbers and the "i" symbol. Additionally, I delved into operations involving complex numbers, encompassing addition, subtraction, and multiplication.


https://www.youtube.com/watch?v=Ltubeq1wu4U

In this short excerpt from the last session of my weekly Thursday explanation of the book "KA Stroud Engineering Mathematics with Math," I explained the concept of complex numbers and addressed some controversies surrounding the square root of a negative number.


https://www.youtube.com/watch?v=x8itOXyksEw

In tonight's episode (Episode 50), I continued my explanation from Program F1, specifically starting from frame 28 on page 395. Following the authors' presentation, I demonstrated how to perform division operations with complex numbers, working with complex numbers and representing complex numbers on the Argand diagram.


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

Episode 51 - Complex Numbers 3: representing complex numbers in polar and Euler form

Tonight's session (Episode 51) was engaging. I continued with Program P2, specifically from F1, frame 46 on page 401. During this episode, I illustrated the various ways we can represent complex numbers, including rectangular, polar, and Euler forms. I also worked through several examples to demonstrate these representations, thereby completing Program P2, F1 of the book.


https://www.youtube.com/watch?v=dnELK-LF02g

Tonight (Episode 54), I continued my explanation from frame 40 (P2, Program F2) on page 427. Following the authors's expositions, I demonstrated how to solve trigonometric identities involving multiple angles using De Moivre's theorem. I concluded the program by solving loci problems involving complex numbers, marking the end of our program on complex numbers.


https://www.youtube.com/watch?v=75JXtWcSehY

Tonight (episode 56), I continued my explanation from frame 19 (page 445). I demonstrated how to evaluate hyperbolic functions, hyperbolic inverse functions, including the logarithmic method. I concluded the program with hyperbolic identities and illustrated the relationship between hyperbolic and trigonometric functions.


https://www.youtube.com/watch?v=bGfxVpXo1vg

Episode 57


https://www.youtube.com/watch?v=ts34OUlO1Pk

In today's episode (episode 57), I began a new program, Program 4 (Determinants). I initiated the program by explaining why the author chose to cover determinants before matrices, which is the topic of the next program. I then proceeded to demonstrate how to expand a 2 x 2 determinant and derive formulas to find solutions to systems of linear equations involving 2 x 2 determinants.

In today's episode (episode 52), I continued from program 4, frame 28 on page 470. I demonstrated how to expand a 3 x 3 determinant and derive formulas to find solutions to systems of linear equations involving 3 x 3 determinants.


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

https://www.youtube.com/watch?v=UboAORT0V_Y

In today's episode (Episode 59), I continued from Program 4, Frame 52 on page 478. I explained how to determine the consistency of sets of simultaneous linear equations. In the second part, I demonstrated how to use the properties of determinants to solve equations written in determinant form, marking the end of Program 4.

Episode 60

Tonight (episode 60), I started the next program - where the authors explained matrices (Program 5, frame 1, page 489). I introduced the concept of matrices and highlighted the distinctions from determinants, which we covered in the previous session. I provided an explanation of what a matrix entails, including terms such as row and column. The video concluded with a demonstration of how matrices can be added, subtracted, and multiplied.


https://www.youtube.com/watch?v=YnluJokh5gw

https://www.youtube.com/watch?v=VvWqrDeMbK4

Tonight (Episode 61), I continued with Program 5, specifically from Frame 12, Page 493 of the book. I demonstrated how two matrices are multiplied and explained some special matrices and their usage. I concluded the episode by explaining how to find the determinant of a matrix.

Tonight (Episode 62), I continued with Program 5, specifically from Frame 26, Page 500 of the book. I explained how to obtain the adjoint and inverse from a square matrix. In the last part of the video, I demonstrated that the product of the inverse of a matrix and the matrix itself results in an identity matrix.



https://www.youtube.com/watch?v=a28s276f_Ds

Today (Episode 63), I continued with Program 5, specifically from Frame 35, Page 504 of the book. I revised how inverses of matrices are found via adjoint and applied these to solve some systems of linear equations. In the second part of the session, I demonstrated how to use the Gaussian elimination method for solving a set of linear equations.


https://www.youtube.com/watch?v=d5w0oRgRyJE