Shear Force and Bending Moments

Shear Force and Bending Moments are one of the trickiest but also one of the easiest forms of physics in static level 4 engineering. If you can get your head around the physics then you'll be fine, looking at the directions however is not easy and it will all be cleared up when we solve a few solutions.

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.

Statics and Equilibrium - Forces and Moments

Whilst learning about forces and moments it is extremely important to always refer every single question you attempt to the global reference axis system. (This is shown in the figure 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 

Integration - The Basics

Integration is the reverse of differentiation, and it has to be said it is a lot harder in my opinion. Integration is known as finding the area under a curve and although you can use graphical software and calculators to avoid complex formula's, it does help to have the knowledge to integrate using the classic pen and pencil.

Shown below is a few of the most common integrals

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.