Recall Key Points of MA 1505:
1. Fundamental Theorem in Calculus:
2. Integration by Parts:
3. Derivatives and Integration:
Hyperbolic Sine:
Hyperbolic Cosine:
MA 1506 Tutorials:
Ordinary Differential Equations:
1. Newton-Leibniz Formula
is a function with one variable with ordinary differential equation The solution is
with some constant .
2. Separable Equations
is a function with one variable with ordinary differential equation where is a function with one variable and is a function with one variable
The solution is with some constant
3. One Order Ordinary Differential Equations
is a function with one variable with one order ordinary differential equation The integrating factor is That means
and take the integration under x at the both sides,
for some constant
Sometimes, we need to make some substitution as or , since the following formulas:
If there is an initial condition for the first order ordinary differential equation then we must make use of the initial condition to calculate the constant C after we solved the equation.