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Reference/Formula Sheets

Engineering Formulas & Governing Equations

Standardized equations, theoretical constants, and mathematical derivations across all core engineering disciplines.

Mechanics of Materials & Structures4 Equations

Flexural Bending Stress (Navier)
Euler Column Buckling Load
2D Mohr's Principal Stresses
Von Mises Equivalent Stress (Plane Stress)

Fluid Mechanics & Hydraulics4 Equations

Darcy-Weisbach Head Loss
Colebrook-White Friction Factor
Hydraulic Pump Power
Reynolds Number

Machine Design & Torsion3 Equations

Circular Shaft Torsional Shear
Angle of Torsional Twist
Bolt Tightening Torque

Electrical & Heat Transfer2 Equations

3-Phase AC Voltage Drop
Fourier 1D Conduction (Multi-Layer)

Algebra, Polynomials & Series4 Equations

Quadratic Formula & Roots
Binomial Theorem Expansion
Logarithm Change of Base Rule
Taylor & Maclaurin Series

Calculus & Differential Equations4 Equations

Integration by Parts
Fundamental Theorem of Calculus
Simpson's 1/3 Rule Quadrature
First-Order Linear ODE Integrating Factor

Trigonometry & Complex Numbers4 Equations

Euler's Formula & Identity
Pythagorean & Double Angle Identities
Law of Cosines (General Triangles)
Hyperbolic Function Definitions

Linear Algebra & Vector Calculus4 Equations

Cramer's Rule for Linear Systems
2×2 & 3×3 Matrix Determinants
Vector Dot & Cross Product
Gradient, Divergence & Curl (Del Operator)

Geometry, Mensuration & Section Properties4 Equations

Circle & Sphere Mensuration
Rectangle Moment of Inertia (Centroidal)
Solid Circular Section Polar Inertia (J)
Parallel Axis Theorem