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). ✔

Voltage ( V(t) ) for ( t \ge 0 ).

Errors are independent and normally distributed (for justification of least squares).

Dirichlet conditions hold (finite jumps, finite extrema).

On average, ( y ) increases by 1.35 units per unit increase in ( x ), with an intercept of 1.233. Example 3 – Fourier Series (Periodic Forcing) Given: ( f(t) = t ) for ( -\pi < t < \pi ), extended periodically with period ( 2\pi ).

Maths Solutions | Fundamental Applied

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). ✔

Voltage ( V(t) ) for ( t \ge 0 ).

Errors are independent and normally distributed (for justification of least squares). fundamental applied maths solutions

Dirichlet conditions hold (finite jumps, finite extrema). For ( n=1 ): coefficient ( 2 ) → matches sawtooth wave

On average, ( y ) increases by 1.35 units per unit increase in ( x ), with an intercept of 1.233. Example 3 – Fourier Series (Periodic Forcing) Given: ( f(t) = t ) for ( -\pi < t < \pi ), extended periodically with period ( 2\pi ). finite extrema). On average