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Differential Equations
Getting started
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Introduction to differential equations
introduction to differential equations
sketching direction fields (8:21)
Euler's method
euler's method (17:41)
Separable differential equations
separable differential equations (7:22)
change of variable for separable differential equations (4:51)
separable differential equations initial value problems (6:00)
mixing problems (10:58)
orthogonal trajectories (14:34)
Logistic models
population growth (5:34)
logistic growth model for a population (6:10)
predator-prey systems (13:22)
equilibrium solutions and stability (16:34)
Exact differential equations
exact differential equations (16:39)
exact differential equations initial value problems (9:47)
Linear differential equations
linear differential equations (8:48)
linear differential equations for circuits (7:22)
linear differential equations initial value problems (9:52)
Homogeneous
distinct real roots (8:16)
equal real roots (4:32)
complex conjugate roots (8:15)
initial value problems (39:42)
boundary value problems with distinct real roots (9:17)
boundary value problems with equal real roots
boundary value problems with complex conjugate roots (7:43)
working backwards (4:43)
method of power series
method of power series, initial value problems
reduction of order
linear dependence and independence
fundamental sets of solutions and the Wronskian
Nonhomogeneous
undetermined coefficients (60:44)
variation of parameters, system of equations (18:44)
variation of parameters, cramer's rule (27:25)
nonhomogeneous initial value problems (13:40)
how to guess the particular solution
Laplace transforms basics
laplace transforms using the table (4:10)
laplace transforms using the definition (14:32)
Methods of Laplace transforms
laplace transforms and initial value problems (17:02)
laplace transforms and integration by parts (23:59)
inverse laplace transforms (11:13)
inverse laplace transforms
nonconstant coefficients initial value problems
step functions
step functions initial value problems
Advanced Laplace transforms
dirac delta functions
convolution integrals and initial value problems (17:23)
gamma and beta functions
Final exam
differential equations final exam
fundamental sets of solutions and the Wronskian
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