Differential Equations and Linear Algebra – Textbook Review for Science and Engineering

Based on the supplied transcript. Punctuation and paragraph breaks have been added, with repeated fillers and false starts reduced for readability. Obvious name transcriptions have been corrected; unclear speech is marked where needed. The speaker’s commentary, opinions, and speculation are retained.

All right, kiddos. We’re going to take a look at Math Monthly—that monthly, monthly. The book from Gustavo Fring, the Chicken Brothers. In a land where the rich did not exist. Oh, flavor.

This is a 1,074-page book of mathematical equations, which means behind the scenes it’s probably like 10,000 pages. This is an ancient book from the archaic archives of intellect, my fellow people: Differential Equations and Linear Algebra: A Course for Science and Engineering.

This book isn’t necessarily just for engineers, but the theme of this month’s journal, Volume One, is engineering. Everything we’re doing has a hint of engineering in it, one way or another.

Just to review this book and show you how this works: this is not your traditional book. In other videos, I show you how to read a university physics, college algebra, or calculus textbook. This book takes a different approach.

This book is basically the accumulation of all those books in application form. If you don’t know how to read the algebra, trigonometry, precalculus, calculus, vector calculus, linear algebra, differential equations, and physics books, you won’t be reading this book. And if you aren’t reading this book, you’ll be dropping out.

That’s what happens junior year. You open a book like this and think, “Oh, crap. I was actually supposed to read the textbook.” Hello.

It’s funny that you think you’re smart and don’t make the connection that you’re supposed to read the book. Somebody who thinks they don’t have to read the textbook in college isn’t intelligent. You’re in the wrong place. You’re donating.

This is how it works: kids with money whose parents buy their way into college with tutors, then buy their way through junior year with tutors, are paying the college. That money is converted into grants for kids who can’t afford college and become successful using the textbooks. We thank you.

No truer words have been spoken on this day.

There’s not much to say about a book like this. In the research lessons, one of you little turd monkeys said, “You’re always at the beginning of the book.” I’m doing a lesson from start to finish, but I decided: why am I making lessons for you? You need to learn how to use the book.

I went to the back somewhere, to Jordan form and eigenanalysis, took a problem, and we solved it.

You have AI now. I didn’t. But AI isn’t correct. It’s wrong. You say, “What do you mean? It gave me the right answer.” I say, “How do you know?” You say, “It matches the book.” How do you know the book’s answer is right? How do you know they didn’t make the same mistake AI did?

“My mom bought me a tutor.” These are the responses you have: “I have a tutor.”

This is an advanced book. I don’t know how many schools would use it. I would use a book like this if I were a professor at a university, but only under the condition that I teach special topics.

I wouldn’t teach calculus, linear algebra, or differential equations. I wouldn’t deal with you at that level. I’d tell the dean, “If you put me in front of those kids, either they’re going to get a gun or I’m going to get a gun.” The dean would say, “I understand.”

I’d choose a different book every semester. The objective isn’t a free ride with a private tutor and AI. As a professor, I’d require you to use the book and screen-record yourself typing the entire solution so I could see your work. It would be valuable.

Let’s look here. Here’s a standard Cauchy–Euler situation. They probably don’t call it that in this book. It’s a scalar second-order Euler differential equation—a nonhomogeneous Cauchy equation, depending on the book.

If you looked at this equation, what method would you use? They’re doing the classic undetermined coefficients and variation of parameters. It repeats what you would do in a standard differential equations course, but goes into computer programs to finalize solutions because it’s designed for engineers.

Engineers aren’t operating in theory. They’re operating in approximation. I always say mathematics is the study of truth, physics is the application of truth, and engineering is the approximation of truth.

A book like this trains you to get solutions using computer technology because, for the most part, there aren’t definitive, straight-to-the-point solutions. It boils down to Euler’s method or—what’s the other one? It’ll come to me later. There are all kinds of approximation methods.

For example, if x plus five to the x equals zero, what is x? You won’t be able to solve something like that. Can you solve it? If you bring down the x—negative x—no. It isn’t solvable, but it’s approximable.

You have to use computer technology, or back in the day an abacus or whatever.

This book trains engineers. It’s different from a course a mathematician or physicist might take, where they study theory without calculators or MATLAB. They’re working with equations and theorems to reach precise answers.

Theory means absolutely true. Most people use those words incorrectly. When you say, “I have this theory,” what you mean is, “I hypothesize.” You have a thought.

At this level, not understanding the definitions of the words you use becomes a problem. These problems are based on theorems rooted in definitions, made of words with definitions.

You speak in slang and have no respect for English. You think it’s cool to disrespect it. You don’t belong in the university, but your parents are paying for other kids to go, so we thank you.

In the research program, we want to investigate things you’ve never heard of. The Cayley–Hamilton–Ziebur method—I’ve never heard of that. I’m interested and want to go through it.

We investigate exotic, unique things you might see in advanced jobs. This book explores that. Its author is doing what I’m doing: going through other books and collecting information.

It’s a rite of passage, a natural occurrence for people who evolve to this level of mathematics and physics. We research what other people have done in relation to what we’re trying to do so we can reach a conclusion.

A book like James Stewart’s Calculus was written for a step-by-step plan of showing calculus in colleges and universities. This book may have started while the author was doing a PhD, learning the material needed for an original contribution.

That’s what we’re doing in the research program. You might think this person sat down and wrote the book. Instead, the book accumulated through research, learning, writing papers, and developing knowledge.

Then the author organized it into a tool for passing on knowledge. It’s the same thought process I’m using. People have done this for thousands of years.

This is the kind of book you encounter junior or senior year. You won’t understand a book like this if you’re using AI, and AI won’t help you understand it at this level.

Professors with integrity who care about the sciences won’t allow AI. We’ll give you a book and find a way to prevent its use. If you use it, we’ll remove you from class and pray you don’t get a gun and shoot us, because that’s what you crazy kids do.

You should see the stalking and harassment. A kid is asking why it’s wrong to use a tutor as an engineer. I ask, “Did you read your syllabus and code of conduct?” He says, “I’m asking why it’s wrong.”

Are you following the code you agreed to? If you agree and don’t follow it, you’re dishonest and unreliable. You ask why it’s wrong to cheat and lie. I don’t want a lying, cheating plagiarizer working for my company.

“How is it lying and cheating?” I can’t explain English to you. Go back to preschool and start over.

I emphasize this because a book like this is what you’ll encounter junior or senior year. It will scare you, AI won’t help, and it could end your education.

Some of you are capable, though. You’ve been cheating, but you realize it. I had a student over the summer, a good young man I liked. I’m sad he isn’t still part of the program, but he got the message.

He said meeting me was a godsend. He had been doing everything I described. He had to retake the course, turned off the internet, and used the textbook.

He emailed to thank me and said I’d shown him the light. He wasn’t a liar, but he had been lying without realizing it. I told him to look up the definitions of liar, cheat, and plagiarizer, then read his code of conduct and syllabus.

Some of you won’t do that. You respond with another question. When someone tells you what you need to do and you respond with a question, it’s a pathetic form of communication.

Young lady, if you’re watching, responding to my question with a question at your level of education, especially in an unedited blob of gibberish, is the communication of a child. That needs to be broken.

A book like this will destroy you. I don’t know whether this particular book is still used, but it’s similar to others at this level.

Its objective is to show questions you can’t answer without a computer or thousands of pages of calculations to obtain an approximation. It shows you how to rearrange, solve, and enter the result into a computer.

There are things in this book you’ve never heard of and won’t hear of if you don’t read. You cheat and plagiarize, then ask how it’s cheating and plagiarizing. Do you know the definitions of the words?

Some take it to continuous harassment because they don’t understand or don’t want to acknowledge what they’re doing. You don’t want to read the definitions because you’ll learn it’s true.

The young man over the summer had the courage to read them. He said, “I’m not a lying cheat.” He was grateful, changed his approach, and is on the right track. I can’t wait to see what he does.

Otherwise, he could have failed and lived with his parents for six years before realizing it himself. Those are what we call adults returning to college: they fail, realize what happened, and return ready to read.

Some of this book is a basic differential equations review, such as series solutions. Then it gets into products, summations, and notation that may look overwhelming.

It seems crazy, but it isn’t. Take the staircase of learning one step at a time, and it becomes fluent.

The objective is to lead to a solution you can’t finish directly, then use a computer to find an approximation. That’s engineering. Mathematics is the study of truth, physics its application, and engineering its approximation.

The real world isn’t exact. Everything is off balance, but we can get close and build precise things. Their precision depends on previous precision, and the first precision was imprecise. We get more precise every year.

The Frobenius theory—remember that video? We did a very long lesson. I wish I’d kept the video, but I still have the written solution. It’s in the first journal.

Here, the author shows a solution using the Frobenius theorem. That’s cool, but it’s complicated and tedious. What you see is only about 10% of the work behind it.

The amount of typing would have been extensive. Do I still have the Frobenius question? Yes, there it is.

I show all the arithmetic behind the scenes because it’s easier to type in Microsoft Word. The author shows the method in a page or two. I work through every detail, and you can see all the material missing between the textbook’s steps.

This is where your AI education will crumble. You won’t be able to type something like this if you use AI to learn freshman- and sophomore-year material.

You look at a page and think it’s simple. You’re missing the point. These 10 pages of calculations are behind that one piece of the explanation.

If you’re an engineer who hasn’t started reading the textbook and typing mathematics in Microsoft Word, junior year will be a wake-up call. It could separate you from college or make you retake courses and add years to your degree.

That’s why I wrote my books: to help you recover. I’m not discouraging you from continuing. I’m warning those who haven’t started college what happens if they cheat, and showing those who have been cheating what they need to change.

You may have to retake a semester, but changing your approach can speed up recovery rather than leaving you to figure it out alone.

This is an interesting book. We enjoyed going through it, and I’ll probably return to it. I have it stored for the research program, whose theme this month is engineering.

Here’s the question we did. I completed Part One and made a typo. The solution process is correct, but we need to fix the typo.

I put it on the website and encouraged members to write the solution themselves in LaTeX. You can type using dollar signs or brackets in the comment box. I had an issue this morning and am still adjusting it, but it’s working.

You can communicate with each other here. I wanted you to finish the solution. I made a mistake: this negative one should be here, and the zero should be there. The calculation is wrong because of it.

Do you understand? The solution approach is correct for the question, but the answer is wrong because of the typo. I want you to correct it because this is an interactive research program.

There’s no point in me going back and fixing everything. I’m not trying to get a course grade. This is an interactive journal for you to contemplate and participate in.

It’s to help you build your résumé, gain exposure, improve written and oral communication, and experience different software and books.

If you attended the session, you learned a little about Maple. You can put some familiarity with Maple on your résumé. More accomplishments and exposure can help you get an interview senior year. That’s my primary objective.

You need to separate your emotions, frustration, and anger from the work. If you have temper tantrums, you won’t succeed in a degree like this.

Be like a Buddhist monk. When you can’t solve a problem, calm yourself and say it’s okay. When someone says something that irritates you or that you disagree with, calm yourself. You won’t function in the workforce if you can’t.

You’re wrong about everything. That’s why you’re in college. You don’t know anything, have no experience, and aren’t employable. The sooner you acknowledge it, the sooner you can work toward becoming employable.

It’s difficult for many of you. Some hold on to anger and ego to the point of failure. I’ve watched it for nearly 20 years.

This is Differential Equations and Linear Algebra: A Course for Science and Engineering, Volumes One and Two. We used Volume Two, Chapter 11, I believe.

Most of you would have taken the assigned equation and sat with pencil and paper, like a kid coloring with chocolate milk, trying to solve it without understanding that you need the book’s instructions, which lead to computer input.

A mathematician or physicist might approach it differently, but this problem is from this book. If you don’t follow the assigned instructions, you aren’t doing the task correctly.

Why pay $50,000 for a professor to guide you through a textbook, then disagree, use AI, and tell the professor how school should work? You’re throwing tens of thousands of dollars at people to tell them they’re wrong.

“Here’s $50,000. You’re wrong. I’m right.” There’s a thing called the psych ward. I recommend checking that out. Or send me the money. For $50,000, I’ll listen to you tell me I’m wrong all day.

That’s Gustavo Fring. Sorry, Grant. Gustafson. By Grant B. Gustafson, who is now forever Gustavo Fring. The Chicken Brothers.

It appears this book was written by someone with no credentials listed. What are your credentials? You’d imagine a PhD, but I don’t see credentials. I don’t know his education. I see a name and a lot of information.

However, it’s a container of rules, and everything here can be shown, verified, or proved. Thus, it’s worth reading because it’s trustworthy. Understand?

This is November 2026. Engineering is the focus for our research team. I’m live while recording this, and you can join when I go live. Log in, find the link, and join.

You may be muted while I record, depending on what we’re doing. I’m not here to do your homework or be your private tutor. I’m not here to answer your pathetic, whiny, little-baby questions.

I’m here to engage in a complicated martial arts dojo situation of intense mathematics. Have a nice—[unclear closing remark].

Professor Jonathan D. Tullis reviews Differential Equations and Linear Algebra: A Course for Science and Engineering as part of the November 2026 engineering focus for Math Monthly. The review emphasizes reading the source carefully, reconstructing omitted calculations, and understanding the purpose of the textbook’s computational methods.

Connecting Earlier Coursework

Professor Tullis presents the text as a setting in which earlier work in algebra, calculus, linear algebra, differential equations, and physics comes together. He emphasizes that familiarity with definitions and notation helps readers navigate the more compact explanations found in advanced material.

Analytical & Computational Methods

Topics mentioned include Euler-type differential equations, undetermined coefficients, variation of parameters, series solutions, the Frobenius method, Jordan form, and eigenanalysis. The review also discusses numerical approximation and the use of Maple code in the textbook’s workflow.

The Work Between the Lines

A comparison with a detailed Frobenius solution illustrates the central study point: a short published derivation can omit extensive intermediate arithmetic and explanation. Professor Tullis contrasts the textbook’s compact presentation with his own expanded, typed solution.

Verification Beyond Matching an Answer

The discussion challenges treating agreement with an answer key or AI output as sufficient verification. The emphasis is on understanding the steps and checking whether the result satisfies the original problem and its conditions.

Correcting the Matrix Calculation

Professor Tullis revisits an earlier matrix calculation in which misplaced entries affected the final answer. He describes the intended method as sound while acknowledging that the calculation requires correction. Members are invited to complete and verify the work, then discuss it through the website’s mathematical comment interface.

Research Participation & Communication

The interactive journal is presented as an opportunity to practice mathematical reading, written explanations, software-related workflows, and collaboration. Professor Tullis also stresses remaining calm when calculations fail or a correction is needed.

This summary focuses on the textbook discussion and the program’s stated activities. The transcript retains the speaker’s personal judgments and speculation about the author’s background; the absence of credentials on a displayed page does not establish that the author lacks credentials.