Engineering

Separability

Handbook guide to Separability, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.

Engineering Mathematics14 Aug 2026 · 12 min read

Separable and Normal Field Extensions

Handbook guide to separable and normal field extensions with core definitions, structural results, reasoning methods and verification checks.

Sequences and Series

Handbook guide to sequences and series, with formulas, methods, worked examples, checks and engineering-oriented applications.

Set Theory

Handbook guide to Set Theory, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.

Engineering Mathematics14 Aug 2026 · 10 min read

Sets, Functions, Relations and Equivalence Classes

Handbook guide to sets, functions, relations and equivalence classes, covering definitions, key results, methods, verification checks and worked examples.

Shaft Couplings and Clutches: Selection and Failure Control: Connecting Shafts

Engineering handbook for shaft couplings and clutches: selection and failure control, covering the complete engineering guide to connecting, transmitting, and...

Shaft Couplings and Clutches: Selection and Failure Control: Cutting Saw-Tooth Clutches

Engineering handbook for shaft couplings and clutches: selection and failure control, covering cutting saw-tooth clutches, dividing head angle formula...

Machine Design14 Aug 2026 · 17 min read

Shaft Couplings and Clutches: Selection and Failure Control: Engineering takeaway

Engineering handbook for shaft couplings and clutches: selection and failure control, covering engineering takeaway, your quick-reference cheat sheet, the two...

Machine Design14 Aug 2026 · 22 min read

Shafts, Keys, Keyseats, Circlips and Seals: ANSI B17.1 Depth Control Values (Selected)

Engineering handbook for shafts, keys, keyseats, circlips and seals, covering ansi b17.1 depth control values (selected), british standard metric keys and...

Machine Design14 Aug 2026 · 24 min read

Shafts, Keys, Keyseats, Circlips and Seals: Failure Mode 2

Engineering handbook for shafts, keys, keyseats, circlips and seals, covering failure mode 2: fatigue (the silent assassin), two approaches to shaft design,...

Shafts, Keys, Keyseats, Circlips and Seals: The Complete Shaft Design Checklist

Engineering handbook for shafts, keys, keyseats, circlips and seals, covering the complete shaft design checklist, phase 1: load analysis, phase 2: stress analysis.

Machine Design14 Aug 2026 · 22 min read

Shafts, Keys, Keyseats, Circlips and Seals: The Conveyor That Stopped a Factory

Engineering handbook for shafts, keys, keyseats, circlips and seals, covering the conveyor that stopped a factory, what exactly are keys and keyseats?, the...

Machine Design14 Aug 2026 · 20 min read

Shafts, Keys, Keyseats, Circlips and Seals: The Three Forces Trying to Destroy Your Shaft

Engineering handbook for shafts, keys, keyseats, circlips and seals, covering the three forces trying to destroy your shaft, why bending is the silent killer,...

Metrology14 Aug 2026 · 6 min read

SI Units, Prefixes and Coherent Engineering Measurement: From Chaos to Confidence

Engineering handbook for si units, prefixes and coherent engineering measurement, covering from chaos to confidence, master conversion reference, length.

Metrology14 Aug 2026 · 22 min read

SI Units, Prefixes and Coherent Engineering Measurement: IEC Standard Abbreviations (International...

Engineering handbook for si units, prefixes and coherent engineering measurement, covering iec standard abbreviations (international electrotechnical...

Metrology14 Aug 2026 · 22 min read

SI Units, Prefixes and Coherent Engineering Measurement: The Engineer's Complete Guide to Measurement Systems

Engineering handbook for si units, prefixes and coherent engineering measurement, covering the engineer's complete guide to measurement systems: from inches to...

Engineering Mathematics14 Aug 2026 · 14 min read

Signed Numbers: Addition and Subtraction

Handbook guide to signed numbers: addition and subtraction, with rules, worked examples, verification, common errors and practical engineering applications.

Simple and Semisimple Rings

Handbook guide to Simple and Semisimple Rings, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Engineering Mathematics14 Aug 2026 · 10 min read

Simple and Semisimple Rings, Matrix Rings and Endomorphisms

Simple and Semisimple Rings, Matrix Rings and Endomorphisms: core definitions, structural results and verification methods in abstract algebra.

Engineering Mathematics14 Aug 2026 · 14 min read

Simple Interest and Investment Allocation Problems

Handbook guide to simple interest and investment allocation problems, with rules, worked examples, verification, common errors and practical engineering.

Engineering Mathematics14 Aug 2026 · 6 min read

Simple Rings, Left and Right Ideals, and Matrix Structure

Noncommutative rings require side-sensitive ideals and lead to simple rings whose internal structure is closely connected with endomorphism and matrix algebras.

Simple Rings, Matrix Rings and Endomorphisms

Handbook guide to Simple Rings, Matrix Rings and Endomorphisms, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Engineering Mathematics14 Aug 2026 · 13 min read

Simplifying Monomials and Algebraic Powers

Handbook guide to simplifying monomials and algebraic powers, with rules, worked examples, verification, common errors and practical engineering applications.

Engineering Mathematics14 Aug 2026 · 13 min read

Simplifying Radicals and Rational Exponents

Handbook guide to simplifying radicals and rational exponents, with rules, worked examples, verification, common errors and practical engineering.

Simplifying Square Roots and Radicals

Understand radical notation, perfect squares and systematic simplification of numerical and algebraic square roots.

Engineering Mathematics14 Aug 2026 · 7 min read

Smith Normal Form

Handbook guide to Smith Normal Form, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.

Engineering Mathematics14 Aug 2026 · 7 min read

Smith Normal Form and Module Structure

Handbook guide to smith normal form and module structure with core definitions, structural results, reasoning methods and verification checks.

Engineering Mathematics14 Aug 2026 · 7 min read

Snake Lemma

Handbook guide to Snake Lemma, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.

Welding14 Aug 2026 · 21 min read

Soldering and Brazing: Process and Joint Selection: Aggressive Fluxes (Corrosive Residue)

Engineering handbook for soldering and brazing: process and joint selection, covering aggressive fluxes (corrosive residue), the residue problem: why cleanup is...

Soldering and Brazing: Process and Joint Selection: Chemical Compounds in Brazing Fluxes

Engineering handbook for soldering and brazing: process and joint selection, covering chemical compounds in brazing fluxes, the master flux selection guide,...

Soldering and Brazing: Process and Joint Selection: Forms Available

Engineering handbook for soldering and brazing: process and joint selection, covering forms available, properties of soft solder alloys, tin-lead solder alloys...

Soldering and Brazing: Process and Joint Selection: How Metal Joining Actually Works

Engineering handbook for soldering and brazing: process and joint selection, covering how metal joining actually works, soldering — the precision of...

Soldering and Brazing: Process and Joint Selection: Porosity and Worm Track Prevention

Engineering handbook for soldering and brazing: process and joint selection, covering porosity and worm track prevention, fcaw shielding gas selection,...

Engineering Mathematics14 Aug 2026 · 6 min read

Soluble Groups, Derived Series and Extension Logic

Guide to soluble groups, repeated derived subgroups, commutative layers, extensions, subgroups, quotients and direct products.

Solvability by Radicals

Handbook guide to Solvability by Radicals, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.

Solvable and Nilpotent Groups

Handbook guide to Solvable and Nilpotent Groups, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Solving Basic Linear Equations

Use inverse operations to isolate a variable in one-step and basic two-step equations, then verify solutions by substitution.

Solving Exponential and Logarithmic Equations

Handbook guide to solving exponential and logarithmic equations, with formulas, methods, worked examples, checks and engineering-oriented applications.

Engineering Mathematics14 Aug 2026 · 13 min read

Solving Linear Equations Step by Step

Handbook guide to solving linear equations step by step, with rules, worked examples, verification, common errors and practical engineering applications.

Solving Linear Inequalities

Solve one-variable linear inequalities, including the sign-reversal rule for multiplication or division by negative quantities.

Engineering Mathematics14 Aug 2026 · 14 min read

Solving Linear Inequalities and Threshold Problems

Handbook guide to solving linear inequalities and threshold problems, with rules, worked examples, verification, common errors and practical engineering.

Solving Multi-Step Linear Equations

Solve linear equations requiring several transformations, including distribution, combining terms and fractional coefficients.

Solving Quadratic Equations by Factoring

Solve quadratic equations by arranging them equal to zero, factoring completely and applying the zero-product property.

Solving Radical Equations

Solve equations containing variables under square roots by isolating the radical, squaring both sides and checking for extraneous solutions.

Solving Systems by Elimination and Substitution

Solve systems of linear equations algebraically using elimination and substitution, with method selection and verification guidance.

Solving Trigonometric Equations

Handbook guide to solving trigonometric equations, with formulas, methods, worked examples, checks and engineering-oriented applications.

Splines and Serrations for Shaft-Hub Connections: Failure Mode 4

Engineering handbook for splines and serrations for shaft-hub connections, covering failure mode 4: bursting stress on internal splines, estimating spline size:...