# METHODES TOMIC - NUMWORKS
# Lignes < 32 car. Sans accent.

def ed():
  print("--- EQUA DIFF 1ER ORDRE ---")
  print("Forme: a(x)y' + b(x)y = f(x)")
  print("")
  print("ETAPE 1: FORME CANONIQUE")
  print("! CRUCIAL: Isolr y' !")
  print("Divise tout par a(x)")
  print("-> y' + P(x)y = Q(x)")
  print("Ex: xy' - 2y = ...")
  print("Devient: y' - (2/x)y = ...")
  print("Ici P(x) = -2/x")
  input("EXE pour suite...")
  
  print("ETAPE 2: SOL HOMOGENE (yh)")
  print("yh = K * exp(-Primitive(P))")
  print("Ex: Prim(-2/x) = -2ln(x)")
  print("yh = K*exp(2ln(x)) = K*x^2")
  print("")
  print("ETAPE 3: SOL PARTICULIERE")
  print("Chercher forme du 2nd membre")
  print("Si Q(x)=Polynome -> yp=Poly")
  print("Si Q(x)=Cst -> yp=Cst")
  input("EXE pour suite...")

  print("Si superposition (somme):")
  print("yp = yp1 + yp2")
  print("Injecter yp ds eq DEPART")
  print("pour trouver les cst.")
  print("")
  print("SOLUTION GENERALE")
  print("y(x) = yh(x) + yp(x)")
  input("EXE pour menu...")

def osc():
  print("--- OSCILLATEURS (2ND) ---")
  print("Type: x'' + w0^2 * x = f(t)")
  print("Identifier w0 (pulsation)")
  print("Ex: x'' + 4x = ... -> w0=2")
  print("")
  print("ETAPE 1: SOL HOMOGENE (xh)")
  print("Eq Carac: r^2 + w0^2 = 0")
  print("Racines: r = +/- i*w0")
  print("xh = A*cos(w0*t)+B*sin(w0*t)")
  input("EXE pour suite...")

  print("ETAPE 2: SOL PARTICULIERE")
  print("Meme forme que f(t)")
  print("Si f(t)=Cst -> xp=Cst")
  print("Si f(t)=at -> xp=At+B")
  print("Injecter xp ds eq diff")
  print("pour trouver A et B")
  print("")
  print("ETAPE 3: CONDITIONS INIT")
  print("x(t) = xh(t) + xp(t)")
  print("Calculer la derivee x'(t)")
  print("Resoudre systeme avec:")
  print("x(0)=... et x'(0)=...")
  print("pour trouver A et B finaux")
  input("EXE pour menu...")

def inv():
  print("--- INTEGRALES MULTIPLES ---")
  print("Aire = Double Int (dx dy)")
  print("Vol = Triple Int (dx dy dz)")
  print("")
  print("COORD CYLINDRIQUES")
  print("x = r * cos(th)")
  print("y = r * sin(th)")
  print("z = z")
  print("! JACOBIEN J = r !")
  print("dV = r dr dth dz")
  input("EXE pour suite...")
  
  print("BORNES (Ex: Cylindre)")
  print("z va de 0 a H")
  print("th (angle) de 0 a 2pi")
  print("r (rayon) de 0 a R")
  print("")
  print("CALCUL PRATIQUE")
  print("1. Separer les integrales")
  print("si bornes constantes")
  print("Int(r dr) * Int(dth)...")
  print("2. Primitives usuelles")
  print("Prim(r) = r^2 / 2")
  print("Prim(cst) = cst * x")
  input("EXE pour menu...")

def menu():
  while True:
    print("")
    print("=== MENU REVISIONS ===")
    print("1. Equa Diff")
    print("2. Oscillateurs")
    print("3. Integrales")
    print("4. Quitter")
    print("======================")
    c = input("Choix (1-4): ")
    if c == "1": ed()
    elif c == "2": osc()
    elif c == "3": inv()
    elif c == "4": break

# Lancement auto
menu()