Mathematics
Mathematics provides the analytical tools used throughout every other FE topic. The exam covers calculus, differential equations, linear algebra, and analytic geometry.
Calculus
The derivative measures rate of change; the power rule d/dx(x^n) = n·x^(n-1) handles polynomials. The definite integral gives area and is evaluated with the Fundamental Theorem of Calculus using an antiderivative at the limits.
Linear Algebra
Matrices represent systems of linear equations. A 2x2 determinant is ad - bc; a nonzero determinant means the system has a unique solution. Matrix operations and eigenvalues appear in vibration and structural analysis.
Differential Equations and Geometry
First- and second-order differential equations model growth, decay, and oscillation. Analytic geometry and trigonometry support vector work, while numerical methods approximate roots and integrals when closed-form answers are unavailable.