The Deeply Recursive Neuralnet Not-So-Secret-Sauce of DRAIN.tips
What follows below is a high-level outline suggested by Claude AI for a 200-module syllabus for autodidactic immersive study of topics necessary for the engineering analysis of viscoelastic material flow, with a focus on anisotropic biological materials, especially human sewage which includes things like hair and all kinds of flushed surprises.
Developing this syllabus is essentially the first thing that an autodidact must learn how to do. This includes finding affordable resources such as Wolfram Alpha and Mathematic, but it also involves things like competing open-source resources, such as pre-print archives, online knowledge bases, and Wikipedia, to supplement the learning material. This means that the modern autodidact has to be comfortable being something of a polyglot … familiar with different affordable software tools, such as Mathematica (with a monthly subscription), Python libraries, and Jupyter notebooks … before moving on to more expensive multiphysics CAD tools for implementation and numerical simulations.
To gain hands-on experience, developing the syllabus will also involve searching for relevant projects or volunteer opportunities with organizations like Engineers Without Borders, focusing on the design, analysis, and improvement of systems involving viscoelastic flow and biological materials. The autodidact will use time as it’s availble to allow for loosely-structured, but self-paced learning, with a balance between theoretical concepts and practical applications. Self-assessments can include problem sets, coding assignments, case studies, and design projects, with an emphasis on developing a deep understanding of the subject matter and applying it to real-world challenges.
Throughout the syllabus, connections should be made between the various topics, exploring the interdisciplinary nature of the field and the importance of integrating knowledge from multiple domains to solve complex problems in the engineering analysis of viscoelastic material flow, particularly in the context of human sewage and biological materials.
I. Mathematical Foundations (40 modules)
This is a good opportunity to use BOTH Mathematica and Python libraries with Jupyter notebooks to explore the concepts of calculus and advanced calculus, including limits, derivatives, integrals, series, and sequences. This will also involve exploring multivariable calculus, vector calculus, and differential equations, with a focus on applications to engineering problems.
A. Calculus and Advanced Calculus (8 modules)
We start with Wolfram U’s Introduction to Calculus, in part, just to get familiar with Mathematica Notebooks and Wolfram Alpha.
Lesson 1: What Is Calculus … calculus is the science of change, originally developed to solve four main problems: 1) Finding a tangent line to a curve, 2) Calculating the area under a curve, 3) Investigating the velocity of a particle given either its position or acceleration, 4) Optimizing a process by finding the corresponding function’s maxima and minima.
Lesson 2: Functions is about showing how to precisely define change in quantity with respect to some other quantity (or quantities) using the Wolfram Language. A function f is a rule that assigns to each element x in a set A exactly one element, called f[x], in a set B. The value f[x] is called the value of f at x and is usually read as “f of x.”
Lesson 3: Elementary Functions Linear functions, polynomial functions, power functions, algebraic functions including rational functions and are created by adding, subtracting, multiplying, dividing and taking roots, trigonometric functions, exponential functions and their inverses, logarithmic functions.
Lesson 4: The Limit Of A Function Limits give the function value a function approaches as its input approaches some value. The function does not need to be defined at the value to have a limit there. As long as the right-hand limit and left-hand limit are equal at a point, the limit exists at the point. Tables are useful for finding limits
Lesson 5: The Laws Of Limits Limit laws give a way to find the limits of functions mathematically; they include situations for sums, differences, products and quotients and any polynomial. For rational and general algebraic functions, sometimes it is best to try factoring the function to calculate the limit. For piecewise functions, sometimes it is best to calculate the left and right limits of the function to calculate the limit. For a function that lies between two other functions, the squeeze theorem can be helpful when calculating the limit.
Lesson 6: Continuity A function f is continuous at a point a if f[a] equals the limit of f at a. A continuous function can be thought to have no gaps or breaks in its graph. Polynomials and root functions are continuous. Some rational functions and trigonometric functions are not continuous because of discontinuities. The intermediate value theorem is an interesting consequence of continuity, and helps you find roots of functions.
Lesson 7: Derivatives and Rates of Change The derivative of a function at a point lets you find the “slope” of the function at that point. The derivative is found by taking the limit of the slopes of secant lines that get closer and closer to the desired point.Derivatives are useful in many quantitative subjects, like physics and economics. The derivative can be approximated from a table of values. The next lesson will show how to express the derivative itself as a function.
Lesson 8: The Derivative As A Function The derivative of a function is itself a function. The derivative of a function at a point is the slope of the tangent line to the function at that point. The derivative of a function can be found by taking the limit of the slopes of secant lines that get closer and closer to the desired point. The derivative of a function can be approximated from a table of values.