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Phase 1 · Months 1–4
Math Foundations
Build the math every later subject depends on. Don't rush this phase.
Algebra & Trigonometry
Every engineering calculation is algebra. Trig resolves forces into components.
- Solving linear & quadratic equations; quadratic formula x = (−b ± √(b²−4ac)) / 2a
- Systems of equations (2–3 unknowns): substitution and elimination
- Exponents, logarithms, and unit-consistent rearranging of formulas
- SOH-CAH-TOA; Fx = F cos θ, Fy = F sin θ
- Law of sines & law of cosines (surveying & truss geometry)
- Radians vs degrees; π rad = 180°
Extra resources
Calculus I & II
Derivatives give slopes and rates (deflection, flow). Integrals give areas, centroids, and moments of inertia.
- Limits and derivatives: power, product, quotient, chain rule
- Maxima/minima: set f′(x) = 0 (e.g., where bending moment is maximum, shear V = 0)
- Integrals: area under a curve, ∫xⁿ dx = xⁿ⁺¹/(n+1)
- Centroid x̄ = ∫x dA / ∫dA; moment of inertia I = ∫y² dA
- Series and Taylor approximations (used in numerical methods)
Extra resources
Checklist
learn~45 h
learn~45 h
practice~3 h
Multivariable Calculus
Needed for fluids, stress in 3D, and understanding the derivations in textbooks.
- Partial derivatives and gradients
- Double & triple integrals (areas, volumes, mass)
- Vectors: dot product (work, projections), cross product (moments M = r × F)
Extra resources
Linear Algebra
Structural analysis software solves [K]{d} = {F} — huge systems of linear equations.
- Matrices, determinants, inverses
- Solving Ax = b with Gaussian elimination
- Eigenvalues/eigenvectors (vibration modes of buildings)
Extra resources
Checklist
learn~4 h
practice~25 h
Differential Equations
Beam deflection (EI y″ = M), consolidation of soils, and flow are all differential equations.
- First-order ODEs: separable and linear
- Second-order linear ODEs with constant coefficients
- Beam equation: EI d²y/dx² = M(x) — integrate twice with boundary conditions
Extra resources
Checklist
practice~2 h
Probability & Statistics
Material strength testing, load factors, traffic, and rainfall are all statistical. It's also on the FE.
- Mean, median, mode, standard deviation, variance
- Normal distribution, z-scores, confidence intervals
- Linear regression and correlation
- Probability: combinations, independent events, binomial distribution