313.sagews

# MATHEMATICAL METHODS OF Science and Engineering

#http://www1.uprh.edu/rbaretti
# http://www1.uprh.edu/rbaretti/methodsoftheoreticalphysics.htm
# http://www1.uprh.edu/rbaretti/methodsoftheoreticalphysicsPart2.htm
# http://www1.uprh.edu/rbaretti/methodsoftheoreticalphysicsPart3.htm
# http://www1.uprh.edu/rbaretti/methodsoftheoreticalphysicsPart4.htm
# http://www1.uprh.edu/rbaretti/methodsoftheoreticalphysicsPart5.htm






# Lectures on Quantum Mechanics  http://www1.uprh.edu/rbaretti/LQMIntro.htm
# http://www1.uprh.edu/rbaretti/LQMch1.htm
#http://www1.uprh.edu/rbaretti/LQMch2.htm
# http://www1.uprh.edu/rbaretti/LQMch3.htm
# http://www1.uprh.edu/rbaretti/LQMch4.htm
# http://www1.uprh.edu/rbaretti/LQMch5.htm
#www.geocities.com/serienumerica4
#www.geocities.com/serienumerica3
#www.geocities.com/serienumerica2
#www.geocities.com/serienumerica
#www.geocities.com/fisicageneral2009



# example 1rst order DE dx/dt= -x+1
t = var('t')    # define a variable t
x = function('x',t)   # define x to be a function of that variable
DE = lambda y: diff(y,t) + y - 1
desolve(DE(x(t)), [x,t])

e^(-t)*(e^t + c)

# example 2nd order DE d^2x/dt^2= -x+1
t = var('t')    # define a variable t
x = function('x',t)   # define x to be a function of that variable
DE = lambda y: diff(y,t,2) + y - 1
desolve(DE(x(t)), [x,t])

k1*sin(t) + k2*cos(t) + 1

# example 2nd order DE d^2x/dt^2 + dx/dt +x =0
t = var('t')    # define a variable t
x = function('x',t)   # define x to be a function of that variable
DE = lambda y: diff(y,t,2) + diff(y,t) - y
desolve(DE(x(t)), [x,t])

k1*e^((sqrt(5) - 1)*t/2) + k2*e^((-sqrt(5) - 1)*t/2)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/sage/sagenb/sage_notebook/worksheets/reibaretti/28/code/10.py", line 7, in <module> x=k1*e**((sqrt(_sage_const_5 ) - _sage_const_1 )*t/_sage_const_2 ) + k2*e**((-sqrt(_sage_const_5 ) - _sage_const_1 )*t/_sage_const_2 ) NameError: name 'k1' is not defined