Fundamental Applied Maths Solutions May 2026

Best‑fit line ( y = a + bx ) in the least‑squares sense.

For ( n=1 ): coefficient ( 2 ) → matches sawtooth wave. ✔ At ( t=\pi/2 ): series gives ( 2 - 1 + 2/3 - 1/2 + \dots = \pi/2 ) (Leibniz series). ✔ fundamental applied maths solutions

Residuals: ( 2.1 - (1.233+1.35)= -0.483 ); ( 3.9 - (1.233+2.70)= -0.033 ); ( 5.8 - (1.233+4.05)= 0.517 ). Sum of residuals ≈ 0 (rounding). ✔ Best‑fit line ( y = a + bx ) in the least‑squares sense

Fourier series coefficients ( a_n, b_n ). ( 3.9 - (1.233+2.70)= -0.033 )

Ideal components, constant ( R, C, V_0 ).

Dirichlet conditions hold (finite jumps, finite extrema).