Engineering↗
The Implied Domain of a Function
Which inputs a formula silently admits, the two conditions that restrict them, and how to state the answer in interval notation.
Content type
Guides
Structured, multi-part guides that take a subject from first principles to applied practice. 2916 pages.
Engineering↗
The Index Laws: a Complete Treatment
Why powers add on multiplication and multiply on nesting, how those two facts force the values of x0 and x-m, and why 00 is left undefined.
Engineering↗
The Pythagorean, Reciprocal and Quotient Identities
The one identity everything follows from, the two derived by division, and the reciprocal and quotient relations used to simplify expressions.
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The Quadratic Formula and the Discriminant
The formula that solves every quadratic, what b2 - 4ac tells you before you compute anything, and the three cases it distinguishes.
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The Real Number System and Its Subsets
How the counting numbers, integers, rationals, reals and complex numbers nest inside one another, why every recurring decimal is a fraction, and how to convert one.
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The Remainder and Factor Theorems
Why the remainder on dividing by x - a is exactly f(a), how that turns into a factor test, and how the two together factor a cubic without guesswork.
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The Unit Circle and the Six Trigonometric Functions
Defining sine and cosine as coordinates on the unit circle, the four functions derived from them, and why the definitions extend beyond acute angles.
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Vectors: Components, Magnitude and Direction
Quantities with both size and direction, how components turn them into pairs of numbers, and the rules for adding and scaling them.
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2D CAD Interface, Commands and Drafting Workflow: Boolean Operations
Engineering handbook for 2d cad interface, commands and drafting workflow, covering boolean operations, d modification, visual styles.
Engineering↗
2D CAD Interface, Commands and Drafting Workflow: Core Interface Elements
Engineering handbook for 2d cad interface, commands and drafting workflow, covering stage 1: interface and navigation, core interface elements, ribbon tabs.
Engineering↗
3D CAD Assembly Fundamentals and Workflow
Engineering handbook for 3d cad assembly fundamentals and workflow, covering the assembly environment, starting a new assembly, methods for inserting components.
Engineering↗
5S Workplace Organisation, Sustainment and Recovery: Enter the Six Tags
Engineering handbook for 5s workplace organisation, sustainment and recovery, covering the invisible wall between the people who see problems and the people who...
Engineering↗
5S Workplace Organisation, Sustainment and Recovery: The Real Competition You're Facing
Engineering handbook for 5s workplace organisation, sustainment and recovery, covering the real competition you're facing, your takeaway: changing thinking...
Engineering↗
Abstract Algebra Prerequisites: Number Theory, Set Theory and Linear Algebra
Abstract Algebra Prerequisites: Number Theory, Set Theory and Linear Algebra: core definitions, structural results and verification methods in abstract algebr
Engineering↗
Acme Power Threads: Geometry, Tolerances and Selection: Standard Abbreviations
Engineering handbook for acme power threads: geometry, tolerances and selection, covering standard abbreviations, designation examples, formulas for determining...
Engineering↗
Acme Power Threads: Geometry, Tolerances and Selection: Stub Acme Fit and Tolerances
Engineering handbook for acme power threads: geometry, tolerances and selection, covering stub acme fit and tolerances, formulas for determining stub acme...
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Acme Power Threads: Geometry, Tolerances and Selection: Verification Against Published Table 2b
Engineering handbook for acme power threads: geometry, tolerances and selection, covering verification against published table 2b, comparing classes: same...
Engineering↗
Acme Power Threads: Geometry, Tolerances and Selection: What Makes an Acme Thread an "Acme" Thread?
Engineering handbook for acme power threads: geometry, tolerances and selection, covering context and scope, what makes an acme thread an "acme" thread?, the...
Engineering↗
Adding and Subtracting Fractions with Common Denominators
Handbook guide to adding and subtracting fractions with common denominators, with rules, worked examples, verification, common errors and practical.
Engineering↗
Addition, Subtraction and Multiplication of Polynomials
Handbook guide to addition, subtraction and multiplication of polynomials, with formulas, methods, worked examples, checks and engineering-oriented applica.
Engineering↗
Advanced Algebra Notation and Reading Conventions
Handbook guide to advanced algebra notation and reading conventions, covering definitions, key results, methods, verification checks and worked examples.
Engineering↗
Advanced Assembly Constraints and Diagnostic Repair
Engineering handbook for advanced assembly constraints and diagnostic repair, covering advanced mate types, symmetric mate, width mate.
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Advanced CAD Sketching, Curves and Reference Geometry
Engineering handbook for advanced cad sketching, curves and reference geometry, covering advanced 2d shapes, polygons, ellipses.
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Advanced Factoring Strategies for Quadratic Expressions
Factor trinomials with a leading coefficient other than one, select methods systematically and apply more than one factoring stage.
Engineering↗
Affine Varieties
Handbook guide to Affine Varieties, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.
Engineering↗
Affine Varieties and Finite Generation
Handbook guide to affine varieties and finite generation with core definitions, structural results, reasoning methods and verification checks.
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Affine Varieties and Polynomial Zero Sets
Handbook guide to affine varieties and polynomial zero sets, covering definitions, key results, methods, verification checks and worked examples.
Engineering↗
Algebra as Coordinatisation: Objects, Operations and Mathematical Structure
An introduction to algebra as a method of coordinatising mathematical and physical objects with abstract quantities and operations, rather than treating algebra merely as symbol…
Engineering↗
Algebra Glossary and Quick Reference
A consolidated quick-reference handbook for core algebra vocabulary, notation, graphing terms, polynomial language, radicals and equation-solving rules.
Engineering↗
Algebra of Functions and Difference Quotients
Handbook guide to algebra of functions and difference quotients, with formulas, methods, worked examples, checks and engineering-oriented applications.
Engineering↗
Algebra Study Workflow: Diagnose, Practise and Verify
A structured handbook method for learning algebra through diagnosis, worked steps, deliberate practice, checking and targeted review.
Engineering↗
Algebraic Closures
Handbook guide to Algebraic Closures, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.
Engineering↗
Algebraic Expressions and Order of Operations
Learn algebraic notation, simplify expressions, apply grouping and exponent rules, and evaluate expressions by substitution.
Engineering↗
Algebraic K-Theory: K0, K1, K2 and Arithmetic Connections
Algebraic K-theory assigns groups to rings using projective modules and stable linear groups. The first K-groups connect module classification, determinants, symbols and arithme…
Engineering↗
Analysing Graphs of Quadratic Functions
Handbook guide to analysing graphs of quadratic functions, with formulas, methods, worked examples, checks and engineering-oriented applications.
Engineering↗
Applications of Right Triangles
Handbook guide to applications of right triangles, with formulas, methods, worked examples, checks and engineering-oriented applications.
Engineering↗
Applications of Sylow Theory
Handbook guide to Applications of Sylow Theory, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.
Engineering↗
Applying Lean Principles Beyond Manufacturing
Engineering handbook for applying lean principles beyond manufacturing, covering how a manufacturing principle born in japanese car plants became healthcare's...
Engineering↗
Arithmetic in Dedekind Domains
Handbook guide to Arithmetic in Dedekind Domains, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.
Engineering↗
Arithmetic Sequences and Series
Handbook guide to arithmetic sequences and series, with formulas, methods, worked examples, checks and engineering-oriented applications.
Engineering↗
Assembly Structures, Subassemblies and Configurations
Engineering handbook for assembly structures, subassemblies and configurations, covering assembly structure and organization, creating sub-assemblies, flexible...
Engineering↗
Base Change in Tensor Products
Handbook guide to Base Change in Tensor Products, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.
Engineering↗
Basic Geometry for Algebra and Trigonometry
Handbook guide to basic geometry for algebra and trigonometry, with formulas, methods, worked examples, checks and engineering-oriented applications.
Engineering↗
Basics of Equation Solving
Handbook guide to basics of equation solving, with formulas, methods, worked examples, checks and engineering-oriented applications.
Engineering↗
Belt Drives and Pulleys: Rating, Selection and Maintenance: Belt Length Traversing Three Pulleys
Engineering handbook for belt drives and pulleys: rating, selection and maintenance, covering the deep problem: a three-pulley belt nobody could measure, belt...
Engineering↗
Belt Drives and Pulleys: Rating, Selection and Maintenance: Belt Width Factor
Engineering handbook for belt drives and pulleys: rating, selection and maintenance, covering belt width factor, selection of flanged pulleys, belt storage and...
Engineering↗
Belt Drives and Pulleys: Rating, Selection and Maintenance: Double V-Belts (ANSI/RMA IP-21)
Engineering handbook for belt drives and pulleys: rating, selection and maintenance, covering double v-belts (ansi/rma ip-21): power from both sides, cross...
Engineering↗
Belt Drives and Pulleys: Rating, Selection and Maintenance: How Power Transmission Actually Works in a...
Engineering handbook for belt drives and pulleys: rating, selection and maintenance, covering every cross section, dimension, and correction factor you need to...