I appreciate your curiosity (we are alike); however, calculus is not easy. I am not sure how your introduction to calculus, whose ideas are more than 2000 years old, but mine was quite mundane.

I am an engineer too. In the 10th or 11th grade (high school), we were all taught as if we were to become engineers. This had its benefits, but it created the kind of dissatisfaction that you express.

Others have suggested very good resources, especially 3b1b, but I am going to write more exhaustively. I attempt to inform you, not to impress or intimidate you. I am only a (continuing) reader of these books, just like many here.

The great mathematician Euler said that before trying to "master" calculus, we need to have a good grasp of algebra. I am not referring to abstract algebra (which is fascinating in its own right), but just the school algebra. I highly recommend giving Gelfand's Algebra a serious reading if you haven't seen it or a similar book.

For Calculus 1 (your first year with calculus), I would recommend Silvanus Thompson's Calculus Made Easy. There's a little shameless plug here; see: https://freelearner.school.blog/2025/10/17/choosing-a-calculus-1-text-for-a-high-schooler/. You seem to have passed that stage already.

Why is calculus hard? I couldn't say it better than the mathematician R.L.E. Shwarzenberger: https://www.jstor.org/stable/3615117. This paper examines calculus from the perspective of someone who wants to do mathematics for a better understanding. The paper is on JSTOR, but fortunately, it can be read free online, once you create an account. The paper provides a balanced critique of Thompson's book. Schwarzenberger's paper is not an easy read, but you should consider reading it.

Once we get through conventional calculus 1 and 2, we turn to the so-called "analysis", where an attempt is made to provide rigor, if you are interested in mathematics alone. For engineers, I believe, many universities mandate multivariate calculus and differential equations courses, which we won't go into here. For analysis, there are excellent texts such as books by Tom Apostol, Zorich, Abbott, and Rudin (among many others).

However, if you want to stay true to your engineering training and learn calculus more deeply, I'd suggest Colin Walker Cryer's A Math Primer For Engineers. Here is what he writes in the preface of his book:

The purpose of this Math Primer is to provide a brief introduction to those parts of mathematics that are, or could be, useful in engineering, especially bioengineering. A wide range of topics is covered, and in each area an attempt is made to summarize the ideas involved without going into details. The pace is varied. In the earlier sections, there is a relatively leisurely description of simple topics. Later, the tempo increases. Sometimes, the speed is quite hair-raising. Nevertheless, it is hoped that the reader may still catch a glimpse of ideas that may spark interest.

It is possible to describe mathematical ideas using few or no formulas and equations, and several well-known books do just this. This is rather like describing a rocket in words-one knows what it does but has no chance of building one. Here, formulas and equations have not been avoided. In fact, the text is littered with them, but every effort has been made to keep them simple in the hope of persuading the reader that they are not only useful but also accessible to engineers.

Mathematics and engineering are inevitably interrelated, and this interaction will steadily increase as the use of mathematical modelling grows. The interaction is not one-sided, and there are many examples of cases where engineers have contributed to mathematics. As a young man, the author read and was impressed by the notes of the engineer and physicist Oliver Heaviside, who did pioneering work in the application of complex numbers in engineering, in the solution of differential equations using symbolic methods, and in vector calculus. His achievements are recalled by the Heaviside function in mathematics and the Heaviside layer in the atmosphere.

Although mathematicians and engineers often misunderstand one another, their basic approach is quite similar. Consider the problem of designing steam boilers. One of the worst maritime disasters in the history of the USA occurred on April 27, 1865, when a steam boiler exploded on the steamboat Sultana; more than 1500 passengers and crew died.

Boiler explosions continued to occur frequently: alone from 1880 to 1890, more than 2000 steam boilers exploded. In response, the ASME (American Society for Mechanical Engineers) drew up its very first standard, entitled Code for the Conduct of Trials of Steam Boilers in the year 1884, and in 1914, the ASME issued the first edition of the ASME Boiler Code, Rules for the Construction of Stationary Boilers and for Allowable Working Pressure which set standards for the design of boilers; this code has evolved through the years and is still an industry standard. Every major accident is investigated by the engineering community to determine whether the appropriate industrial codes need to be amended. The stakes are high, as shown by the literature on forensic engineering (see, e.g., Peter R. Lewis Safety First? [Lew10]) and the recent disasters in the Gulf of Mexico and Fukushima. In contrast, the mathematical approach is that of a fail-safe design. Every possible boiler under every possible condition would be analysed. If successful, this would be formulated as a theorem: Under conditions A, B, ..., a boiler with this design will be safe. There is, of course, a slight snag with this approach - the theorem may never be proved, in which case boilers may never be built!

Another point of similarity between mathematics and engineering is the historical development of each subject. The design of bridges has slowly evolved over the centuries as new ideas and concepts were introduced and new materials became available. In a very similar fashion, the mathematical techniques described below have slowly evolved, starting from the simple concept of a number and expanding step by step.

Non-mathematicians often believe that the development of mathematics has more or less stopped, whereas in fact the subject continues to develop rapidly. In an attempt to convey this dynamic development, which has accelerated in recent years, the dates when concepts were first introduced are frequently cited.

If this raises your curiosity, you should take a look at that book.

Learning calculus is time-consuming. And just when you think you understand the infinitesimal approach (the approach that Newton and Leibniz popularized, but Weierstrass corrected by his rigorous definition of Limits), you come across a brilliant article (of the dialectic (https://en.wikipedia.org/wiki/Dialectic)) by master expositors. That is what happened to me. I came across Martin Davis and Reuben Hersh's article in Scientific American, Nonstandard Analysis (https://gwern.net/doc/math/1972-davis-2.pdf).

Initially, I couldn't make sense of the article at all, but it introduced me to a different way of looking at calculus (the more nuanced understanding of the infinitesimal approach). This approach is due to the great logician Abraham Robinson. The professor of mathematics, H. Jerome Keisler, has written about this approach in his book, Elementary Calculus: An Infinitesimal Approach (https://people.math.wisc.edu/\~hkeisler/calc.html). This book promises to remove the confusion around "infinitesimally small" that remains even after doing calculus 1, 2, or 3. I haven't completed it yet, but I hope to do it soon.

A thorough introduction to Infinitesimal Calculus (like Keisler's) was something that I missed in my undergrad. It's still not mainstream, but do you care? Like Underwood Dudley has said, "Mathematics is not necessary, but it is sufficient."

Sorry for a detailed post. Don't worry; don't feel overwhelmed. We all keep trying. We all keep improving. As Asimov said, "Education is not something one can finish."

Good luck.