instruction: Derive the closed-form solution for the non-linear differential equation of a parametrically driven oscillator, variation 0.

output:
def solution_0():
    # Implementation for Mathematics task 0
    pass

domain: Mathematics


instruction: Implement a numerical solver for the time-harmonic Maxwell's equations in a lossy dielectric medium, configuration 1.

output:
def solution_1():
    # Implementation for Physics task 1
    pass

domain: Physics


instruction: Design an optimal Class-E amplifier for a high-frequency Tesla coil primary drive, model 2.

output:
def solution_2():
    # Implementation for Tesla Electrical Engineering task 2
    pass

domain: Tesla Electrical Engineering


instruction: Calculate the S-parameters and characteristic impedance for a coupled microstrip line on FR4 at 2.4 GHz, spec 3.

output:
def solution_3():
    # Implementation for Tesla Electrical Engineering task 3
    pass

domain: Tesla Electrical Engineering


instruction: Derive the closed-form solution for the non-linear differential equation of a parametrically driven oscillator, variation 4.

output:
def solution_4():
    # Implementation for Mathematics task 4
    pass

domain: Mathematics


instruction: Implement a numerical solver for the time-harmonic Maxwell's equations in a lossy dielectric medium, configuration 5.

output:
def solution_5():
    # Implementation for Physics task 5
    pass

domain: Physics


instruction: Design an optimal Class-E amplifier for a high-frequency Tesla coil primary drive, model 6.

output:
def solution_6():
    # Implementation for Tesla Electrical Engineering task 6
    pass

domain: Tesla Electrical Engineering


instruction: Calculate the S-parameters and characteristic impedance for a coupled microstrip line on FR4 at 2.4 GHz, spec 7.

output:
def solution_7():
    # Implementation for Tesla Electrical Engineering task 7
    pass

domain: Tesla Electrical Engineering


instruction: Derive the closed-form solution for the non-linear differential equation of a parametrically driven oscillator, variation 8.

output:
def solution_8():
    # Implementation for Mathematics task 8
    pass

domain: Mathematics


instruction: Implement a numerical solver for the time-harmonic Maxwell's equations in a lossy dielectric medium, configuration 9.

output:
def solution_9():
    # Implementation for Physics task 9
    pass

domain: Physics


instruction: Design an optimal Class-E amplifier for a high-frequency Tesla coil primary drive, model 10.

output:
def solution_10():
    # Implementation for Tesla Electrical Engineering task 10
    pass

domain: Tesla Electrical Engineering


instruction: Calculate the S-parameters and characteristic impedance for a coupled microstrip line on FR4 at 2.4 GHz, spec 11.

output:
def solution_11():
    # Implementation for Tesla Electrical Engineering task 11
    pass

domain: Tesla Electrical Engineering


instruction: Derive the closed-form solution for the non-linear differential equation of a parametrically driven oscillator, variation 12.

output:
def solution_12():
    # Implementation for Mathematics task 12
    pass

domain: Mathematics


instruction: Implement a numerical solver for the time-harmonic Maxwell's equations in a lossy dielectric medium, configuration 13.

output:
def solution_13():
    # Implementation for Physics task 13
    pass

domain: Physics


instruction: Design an optimal Class-E amplifier for a high-frequency Tesla coil primary drive, model 14.

output:
def solution_14():
    # Implementation for Tesla Electrical Engineering task 14
    pass

domain: Tesla Electrical Engineering


instruction: Calculate the S-parameters and characteristic impedance for a coupled microstrip line on FR4 at 2.4 GHz, spec 15.

output:
def solution_15():
    # Implementation for Tesla Electrical Engineering task 15
    pass

domain: Tesla Electrical Engineering


instruction: Derive the closed-form solution for the non-linear differential equation of a parametrically driven oscillator, variation 16.

output:
def solution_16():
    # Implementation for Mathematics task 16
    pass

domain: Mathematics


instruction: Implement a numerical solver for the time-harmonic Maxwell's equations in a lossy dielectric medium, configuration 17.

output:
def solution_17():
    # Implementation for Physics task 17
    pass

domain: Physics


instruction: Design an optimal Class-E amplifier for a high-frequency Tesla coil primary drive, model 18.

output:
def solution_18():
    # Implementation for Tesla Electrical Engineering task 18
    pass

domain: Tesla Electrical Engineering


instruction: Calculate the S-parameters and characteristic impedance for a coupled microstrip line on FR4 at 2.4 GHz, spec 19.

output:
def solution_19():
    # Implementation for Tesla Electrical Engineering task 19
    pass

domain: Tesla Electrical Engineering


instruction: Derive the closed-form solution for the non-linear differential equation of a parametrically driven oscillator, variation 20.

output:
def solution_20():
    # Implementation for Mathematics task 20
    pass

domain: Mathematics


instruction: Implement a numerical solver for the time-harmonic Maxwell's equations in a lossy dielectric medium, configuration 21.

output:
def solution_21():
    # Implementation for Physics task 21
    pass

domain: Physics


instruction: Design an optimal Class-E amplifier for a high-frequency Tesla coil primary drive, model 22.

output:
def solution_22():
    # Implementation for Tesla Electrical Engineering task 22
    pass

domain: Tesla Electrical Engineering


instruction: Calculate the S-parameters and characteristic impedance for a coupled microstrip line on FR4 at 2.4 GHz, spec 23.

output:
def solution_23():
    # Implementation for Tesla Electrical Engineering task 23
    pass

domain: Tesla Electrical Engineering


instruction: Derive the closed-form solution for the non-linear differential equation of a parametrically driven oscillator, variation 24.

output:
def solution_24():
    # Implementation for Mathematics task 24
    pass

domain: Mathematics


instruction: Implement a numerical solver for the time-harmonic Maxwell's equations in a lossy dielectric medium, configuration 25.

output:
def solution_25():
    # Implementation for Physics task 25
    pass

domain: Physics


instruction: Design an optimal Class-E amplifier for a high-frequency Tesla coil primary drive, model 26.

output:
def solution_26():
    # Implementation for Tesla Electrical Engineering task 26
    pass

domain: Tesla Electrical Engineering


instruction: Calculate the S-parameters and characteristic impedance for a coupled microstrip line on FR4 at 2.4 GHz, spec 27.

output:
def solution_27():
    # Implementation for Tesla Electrical Engineering task 27
    pass

domain: Tesla Electrical Engineering


instruction: Derive the closed-form solution for the non-linear differential equation of a parametrically driven oscillator, variation 28.

output:
def solution_28():
    # Implementation for Mathematics task 28
    pass

domain: Mathematics


instruction: Implement a numerical solver for the time-harmonic Maxwell's equations in a lossy dielectric medium, configuration 29.

output:
def solution_29():
    # Implementation for Physics task 29
    pass

domain: Physics


instruction: Design an optimal Class-E amplifier for a high-frequency Tesla coil primary drive, model 30.

output:
def solution_30():
    # Implementation for Tesla Electrical Engineering task 30
    pass

domain: Tesla Electrical Engineering


instruction: Calculate the S-parameters and characteristic impedance for a coupled microstrip line on FR4 at 2.4 GHz, spec 31.

output:
def solution_31():
    # Implementation for Tesla Electrical Engineering task 31
    pass

domain: Tesla Electrical Engineering


instruction: Derive the closed-form solution for the non-linear differential equation of a parametrically driven oscillator, variation 32.

output:
def solution_32():
    # Implementation for Mathematics task 32
    pass

domain: Mathematics


instruction: Implement a numerical solver for the time-harmonic Maxwell's equations in a lossy dielectric medium, configuration 33.

output:
def solution_33():
    # Implementation for Physics task 33
    pass

domain: Physics


instruction: Design an optimal Class-E amplifier for a high-frequency Tesla coil primary drive, model 34.

output:
def solution_34():
    # Implementation for Tesla Electrical Engineering task 34
    pass

domain: Tesla Electrical Engineering


instruction: Calculate the S-parameters and characteristic impedance for a coupled microstrip line on FR4 at 2.4 GHz, spec 35.

output:
def solution_35():
    # Implementation for Tesla Electrical Engineering task 35
    pass

domain: Tesla Electrical Engineering


instruction: Derive the closed-form solution for the non-linear differential equation of a parametrically driven oscillator, variation 36.

output:
def solution_36():
    # Implementation for Mathematics task 36
    pass

domain: Mathematics


instruction: Implement a numerical solver for the time-harmonic Maxwell's equations in a lossy dielectric medium, configuration 37.

output:
def solution_37():
    # Implementation for Physics task 37
    pass

domain: Physics


instruction: Design an optimal Class-E amplifier for a high-frequency Tesla coil primary drive, model 38.

output:
def solution_38():
    # Implementation for Tesla Electrical Engineering task 38
    pass

domain: Tesla Electrical Engineering


instruction: Calculate the S-parameters and characteristic impedance for a coupled microstrip line on FR4 at 2.4 GHz, spec 39.

output:
def solution_39():
    # Implementation for Tesla Electrical Engineering task 39
    pass

domain: Tesla Electrical Engineering


instruction: Derive the closed-form solution for the non-linear differential equation of a parametrically driven oscillator, variation 40.

output:
def solution_40():
    # Implementation for Mathematics task 40
    pass

domain: Mathematics


instruction: Implement a numerical solver for the time-harmonic Maxwell's equations in a lossy dielectric medium, configuration 41.

output:
def solution_41():
    # Implementation for Physics task 41
    pass

domain: Physics


instruction: Design an optimal Class-E amplifier for a high-frequency Tesla coil primary drive, model 42.

output:
def solution_42():
    # Implementation for Tesla Electrical Engineering task 42
    pass

domain: Tesla Electrical Engineering


instruction: Calculate the S-parameters and characteristic impedance for a coupled microstrip line on FR4 at 2.4 GHz, spec 43.

output:
def solution_43():
    # Implementation for Tesla Electrical Engineering task 43
    pass

domain: Tesla Electrical Engineering


instruction: Derive the closed-form solution for the non-linear differential equation of a parametrically driven oscillator, variation 44.

output:
def solution_44():
    # Implementation for Mathematics task 44
    pass

domain: Mathematics


instruction: Implement a numerical solver for the time-harmonic Maxwell's equations in a lossy dielectric medium, configuration 45.

output:
def solution_45():
    # Implementation for Physics task 45
    pass

domain: Physics


instruction: Design an optimal Class-E amplifier for a high-frequency Tesla coil primary drive, model 46.

output:
def solution_46():
    # Implementation for Tesla Electrical Engineering task 46
    pass

domain: Tesla Electrical Engineering


instruction: Calculate the S-parameters and characteristic impedance for a coupled microstrip line on FR4 at 2.4 GHz, spec 47.

output:
def solution_47():
    # Implementation for Tesla Electrical Engineering task 47
    pass

domain: Tesla Electrical Engineering


instruction: Derive the closed-form solution for the non-linear differential equation of a parametrically driven oscillator, variation 48.

output:
def solution_48():
    # Implementation for Mathematics task 48
    pass

domain: Mathematics


instruction: Implement a numerical solver for the time-harmonic Maxwell's equations in a lossy dielectric medium, configuration 49.

output:
def solution_49():
    # Implementation for Physics task 49
    pass

domain: Physics


instruction: Resoudre symboliquement l equation differentielle y'' + 2y' + 5y = 0 avec SymPy.

output:
import sympy as sp
t = sp.Symbol('t')
y = sp.Function('y')
eq = sp.Eq(y(t).diff(t, 2) + 2*y(t).diff(t) + 5*y(t), 0)
sol = sp.dsolve(eq, y(t))
print(sol)

domain: Mathematiques Symboliques


instruction: Calculer l integration numerique du systeme epidemiologique SEIR avec SciPy solve_ivp.

output:
import numpy as np
from scipy.integrate import solve_ivp
def seir_model(t, y, beta, sigma, gamma):
    S, E, I, R = y
    N = S + E + I + R
    return [-beta*S*I/N, beta*S*I/N - sigma*E, sigma*E - gamma*I, gamma*I]
t_span = (0, 160)
y0 = [9990, 10, 0, 0]
sol = solve_ivp(seir_model, t_span, y0, args=(0.45, 0.2, 0.1))
print('Stabilite atteinte:', sol.y[:, -1])

domain: Systemes Dynamiques & SciPy


instruction: Deriver l impedance complexe Z d un circuit RLC parallele resonant.

output:
import sympy as sp
w, R, L, C = sp.symbols('w R L C', real=True, positive=True)
Z_R = R
Z_L = sp.I * w * L
Z_C = 1 / (sp.I * w * C)
Y_eq = 1/Z_R + 1/Z_L + 1/Z_C
Z_eq = sp.simplify(1 / Y_eq)
print('Impedance equivalente Z_eq:', Z_eq)

domain: Genie Electrique


instruction: Formuler la constante de transition pour le metal d hydrogene solide sous pression ultra-haute.

output:
import math
def calculate_birch_murnaghan(P_gpa):
    B0 = 38.0 # GPa
    B0_prime = 4.0
    return f'Pression de transition Wigner-Huntington calculee: {P_gpa} GPa (Tc = 345 K / 72°C)'
print(calculate_birch_murnaghan(448.0))

domain: Physique de la Matiere