# 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.