Math Monthly — Inside the Book
Inside The Ultimate Crash Course for STEM Majors — Algebra, Calculus & Beyond
Take a look inside The Ultimate Crash Course for STEM Majors with Author Jonathan David. This walkthrough previews the algebra review, detailed calculus solutions, and introductory material on vectors, physics, linear algebra, differential equations, and index notation.
Watch the inside-the-book preview on YouTube ↗
See the Explanations, Calculations & Written Solutions
Jonathan demonstrates the book’s student-oriented presentation and compares it with the more formal layout of his mathematical journals.
- Review algebraic manipulation, exponential expressions, and notation.
- Preview calculus examples through sequences and series.
- Explore introductory vector calculus, physics, and index notation.
- See the accompanying library of recordings showing the books being written.
Original Transcript (punctuated)
Based on the supplied transcript. Punctuation and paragraph breaks have been added, with repeated fillers and false starts reduced for readability. Obvious transcription errors have been corrected, and unclear speech is marked where necessary. The speaker’s opinions and product descriptions are retained.
Okay, boys and girls. This is going to be a look inside The Ultimate Crash Course for STEM Majors that I wrote.
Let me show you: if you buy the Triple Play, it comes with access to upward of 900 or 1,000 videos of me writing the book.
Let’s go from oldest to newest. You can look back at when I started this mission to get you to change your ways.
As you go through it, you’ll find videos of me writing the books and going through the textbook. There are something like a thousand videos here. It doesn’t tell me the count, but there’s a lot.
You can type in whatever—[unclear speech]—and see what comes up. Here’s me adding a section to the book, a recap of a live tutoring session. That was a live session I did.
There are lots of videos of me writing this book, and they’re included if you purchase the Triple Play. It’s $99.
This is about 400 pages. It contains a plethora of information that is world-class, written from your point of view.
First, I give you a preview of what you need from algebra. Then I went through James Stewart’s calculus book, used the outline, took a question from every section, and answered it.
It follows the same general material as Stewart’s Calculus or Thomas’ Calculus. I cover the situations, but I didn’t just take easy problems.
I chose questions that cover what you need and include the tricks students miss because they skip lecture, use AI and Khan Academy, and don’t do the research.
That’s why I wrote this: to help repair the damage that Khan Academy, AI, Wyzant tutoring, and teacher solution manuals did to your education.
It isn’t necessarily for someone currently in calculus, although it could be beneficial. It would be a violation of your syllabus, just so you know.
The way I look at it, if you need help after Calculus Two, you’re in the wrong place. Physics, math, and engineering aren’t for you if you need assistance after Calculus Two.
I used that stuff in Calculus One and Two, too. Then I tutored for 15 years, and I know because I watched students fail. I’m not making it up.
Here, I show how to take notes from a physics book. The How to Study guide is in here. I show that material, then get into solution writing.
I show simple algebraic things students miss, including notation they misunderstand, before starting calculus.
There isn’t much you need from algebra or trigonometry before calculus. I put the arithmetic you need here, show how to do it, then move on.
The problems demonstrate tedious arithmetic because you’ll do that kind of work in calculus, along with much more. It becomes increasingly tedious as you progress into mathematics.
I prepare you by reviewing what you need from algebra. Here’s exponential material. I choose the craziest examples and show how to solve them.
We’re still in the algebra section. Let me jump to calculus. There are some linear algebra things, more material, and here we are at limits.
My journals are written differently, very professionally. This is written as you would write it as a student, not like a professional scholarly paper. That’s why I wrote it this way.
It’s more of a centered arrangement instead of an elegant page filled from corner to corner. Let me show you the difference.
Some people are confused about why the book is written this way. Look at this other one. It’s structured differently.
That’s something we do together as a group, with a lot of information I’m pointing out. I fill the pages as much as I can, top to bottom and left to right.
In this book, I write the way you think as a student. I worked one-on-one with students for 15 years and wrote it the way you think.
The calculus material goes through sequences and series. I show how to do the questions you’ll see in calculus exams.
I didn’t write it to help you cheat. I wrote it to show what you’re missing. I took the questions I’d seen on exams and solved them in detail from your perspective.
There’s a lot of integration material, the squeeze theorem, and more. Then we get into physics and vector calculus.
If you’re in Calculus Two doing sequences and series, the material you need is in this book. It’ll save your life. It’s worth purchasing and inexpensive.
I drastically reduced the price, and it comes with the videos because I’m moving on to the journal.
For $99, you get all my work, all my books, and the videos at the website I showed you. It’s a one-time fee.
Here’s where I introduce engineers and physicists to tensor index notation before tensor analysis.
I show the backbone because textbooks don’t always show the proofs behind these objects or why they work. They give you the objects, and you think, “What is this, and why does it work that way?”
I show that here. For example, the cross product: physics and engineering books may give you an expression without all the background.
I show the proofs and how it happened, on a basic scale rather than in a super-intense way.
Then I get into physics problem-solving. There’s written explanation, and I show vector addition properly.
I introduce physics, vector calculus, linear algebra, differential equations, and higher math because, if you need help after Calculus Two, you’re in the wrong place.
This is The Ultimate Crash Course. Check it out. It’s a great book and resource. I highly recommend it.
If you read ratings from kids, remember that I tell them to stop cheating, lying, and stealing, and they go destroy my business. They’re going to burn in hell. They’re sick.
Don’t believe the things you read online. This is the book. You can see it here and watch the videos of me writing it live. It’s quality material.
Have a nice day.
AI Summarization
Author Jonathan David provides a screen-recorded preview of The Ultimate Crash Course for STEM Majors and its accompanying lesson library. He explains the organization, choice of examples, and deliberate use of a student-oriented writing style.
Algebra Review Before Calculus
The walkthrough begins with algebraic manipulation, exponential expressions, and notation. Jonathan describes choosing examples that expose common misunderstandings and prepare readers for lengthy calculations in later coursework.
Calculus Through Sequences & Series
Jonathan describes using the section progression of James Stewart’s calculus textbook to organize worked examples. The preview includes limits, integration, sequences and series, and problems selected for details students frequently overlook.
A Student-Oriented Presentation
The book’s layout and explanations are intended to resemble a student’s detailed working notes. Jonathan contrasts this presentation with the more formal, densely arranged pages of his collaborative mathematical journals.
Introductions to Later Topics
Later material introduces vector calculus, linear algebra, differential equations, physics problem-solving, and index notation. Cross products and vector addition are mentioned as examples where the book explores the reasoning behind expressions and procedures.
Recordings of the Writing Process
Jonathan also demonstrates the accompanying library, describing hundreds of recordings of the books being written and textbook material being explored. He notes that he does not have an exact count of the videos.
The price and bundle contents mentioned in the recording reflect the offer described at that time. Consult the linked product pages for purchase details. Whether a supplementary resource is permitted in a course depends on that course’s instructions.
Books, PDF Bundle & Lesson Library
Explore my books and PDF bundle, which include access to a library of lessons.
Hardcover purchasers: Send me your purchase receipt to receive lesson library access.
Continue Exploring with Math Monthly
Explore mathematics, physics, and their connections to engineering with Author Jonathan David. Discover the available Math Monthly memberships and follow the development of new lessons and journal material.
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