Shear Force Example (Intermediate - Hard)

This example for Shear Force and Bending Moments is going to be a lot more complex than the previous with the addition of calculating the Maximum Bending Moment. This is all fitted on a single piece of paper so the working out can be a lot less than shown.

First Order Differential Equations.

First order differential equations are a lot more complex than ordinary differentials, the best way to identify a first order is shown below.

Integration by Parts

Integration by parts the easiest and probably the most popular method for integration components and finding the area under the curve. This can get very complex, very fast. 

It is important when looking at an equation to try and work out what you want to be your u and v. The best way for this is to use LogAlgTrigExp. You may see the connection, you may not. When initially looking at the equation if the equation contains a logarithm then make that your u, if not use an algebraic expression, if this again doesn't exist use a trigonometric expression and finally use an exponential function. 

Shown below is the integration by parts equation as well as a quick example 

Differential Calculus - Examples

As promised here are some examples of differentiation which should clear up any confusion from the first topic "Diffential Calculus - The Basics" 

These first examples do not require any rules as they are simple equations and not combinations of functions. They can be solved by simply using the basic functions in the previous chapter.

Differential Calculus - The Basics

Welcome to the first differential calculus topic, shown below are some of the basic functions in differentiation which will be required to complete the unit.