Hi, I'm Peter. I am currently studying Aerospace Engineering at Queen's in Belfast; a Russell Group university with a great reputation. Maths and Physics have always been my passion, so I've worked hard at them and can offer not only knowledge on the subjects, but perhaps new ways of thinking about them as well. With experience in tutoring these subjects at both GCSE and A-Level, I have developed some great techniques in tutoring, whether for someone who is struggling with concepts or wants to get ahead of the game. If you're studying Maths and looking towards an Engineering course, then I'm your guy for helping to get ahead in visualising how your mathematical techniques and equations can be applied in real life; a key ability in any Engineering course. I try to work around a student's strengths to begin with, then use those to help with the harder aspects. I also like to mix up the session, using different teaching methods every time to try to keep it interesting, and to help see things from a different aspect. If you're going for Aerospace Engineering, or anything in Aviation, I'm also a qualified pilot, so I can once again offer a more practical view of things. I know how frustrating these subjects can be sometimes, particularly when "but, why?" comes into it, but I firmly believe that we can get there together so you have the confidence to face anything the examiners can throw at you. I look forward to meeting you soon!

Hi, I'm Peter. I am currently studying Aerospace Engineering at Queen's in Belfast; a Russell Group university with a great reputation. Maths and Physics have always been my passion, so I've worked hard at them and can offer not only knowledge on the subjects, but perhaps new ways of thinking about them as well. With experience in tutoring these subjects at both GCSE and A-Level, I have developed some great techniques in tutoring, whether for someone who is struggling with concepts or wants to get ahead of the game. If you're studying Maths and looking towards an Engineering course, then I'm your guy for helping to get ahead in visualising how your mathematical techniques and equations can be applied in real life; a key ability in any Engineering course. I try to work around a student's strengths to begin with, then use those to help with the harder aspects. I also like to mix up the session, using different teaching methods every time to try to keep it interesting, and to help see things from a different aspect. If you're going for Aerospace Engineering, or anything in Aviation, I'm also a qualified pilot, so I can once again offer a more practical view of things. I know how frustrating these subjects can be sometimes, particularly when "but, why?" comes into it, but I firmly believe that we can get there together so you have the confidence to face anything the examiners can throw at you. I look forward to meeting you soon!

Tutorials with me will be very much focussed around the student. This will be apparent in two ways. The first is that I would like students to be able to assess themselves, either from the outset or to learn that skill as we go one. Knowing your own limits is the first step to going beyond them. The second student-focussed aspect is constant engagement. I will ask you for what you **think** the answer could be or what kind of approach we might take. This is to help build a deeper understanding of the whys and hows from the outset, which I believe is a much better way to ensure the knowledge stays in your head. Obviously I won't let you get it wrong, but unlike a lot of tutors, I really strive to take a guiding approach, as opposed to others who might just end up talking at you. This also serves to keep tutorials interesting, rather than it being just another lesson.

Tutorials with me will be very much focussed around the student. This will be apparent in two ways. The first is that I would like students to be able to assess themselves, either from the outset or to learn that skill as we go one. Knowing your own limits is the first step to going beyond them. The second student-focussed aspect is constant engagement. I will ask you for what you **think** the answer could be or what kind of approach we might take. This is to help build a deeper understanding of the whys and hows from the outset, which I believe is a much better way to ensure the knowledge stays in your head. Obviously I won't let you get it wrong, but unlike a lot of tutors, I really strive to take a guiding approach, as opposed to others who might just end up talking at you. This also serves to keep tutorials interesting, rather than it being just another lesson.

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he was patient and explained in a very concise and understandable manner

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a very productive tutorial session

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Peter has been a fantastic tutor for my daughter in the run up to her exams. Very knowledgeable and supportive.

Argand diagrams are, like graphs, a visual representation. Instead of representing an equation though, Argand diagrams represent numbers.

Any number can be represented on an Argand diagram, be it real, imaginary or complex. Mostly, though, it is used to show complex numbers.

As you probably know, complex numbers are made up of a combination of real and imaginary numbers. For example **3+2i**.

An Argand diagram has two axes, like a regular cartesian graph. However, in this case the horizontal axis represents real number, just like an ordinary number line you learnt about in primary school. The vertical axis represents imaginary rumbers. The axes cross at zero, again just like in a cartesian graph.

To plot **3+2i** on an Argand diagram, you plot the point where the value on the real axis reads 3 and the value on the imaginary axis reads 2i. Then, extend a line from 0 to the point you just plotted. That line is the visual representation of the number **3+2i**.

Some other properties are represented by the line on the Argand diagram. The length of the line represents the modulus of the number: √(3^{2}+2^{2}) = √13

The line also forms an angle with the positive side of the real axis. This angle, measured in radians, is known as the argument, and is important when representing complex numbers in polar form. For many aspects of dealing with complex numbers, this form can be a lot more useful.

So you can see, just from one line on an Argand diagram, you can learn a lot of the information you need to manipulate a complex number.

Argand diagrams are, like graphs, a visual representation. Instead of representing an equation though, Argand diagrams represent numbers.

Any number can be represented on an Argand diagram, be it real, imaginary or complex. Mostly, though, it is used to show complex numbers.

As you probably know, complex numbers are made up of a combination of real and imaginary numbers. For example **3+2i**.

An Argand diagram has two axes, like a regular cartesian graph. However, in this case the horizontal axis represents real number, just like an ordinary number line you learnt about in primary school. The vertical axis represents imaginary rumbers. The axes cross at zero, again just like in a cartesian graph.

To plot **3+2i** on an Argand diagram, you plot the point where the value on the real axis reads 3 and the value on the imaginary axis reads 2i. Then, extend a line from 0 to the point you just plotted. That line is the visual representation of the number **3+2i**.

Some other properties are represented by the line on the Argand diagram. The length of the line represents the modulus of the number: √(3^{2}+2^{2}) = √13

The line also forms an angle with the positive side of the real axis. This angle, measured in radians, is known as the argument, and is important when representing complex numbers in polar form. For many aspects of dealing with complex numbers, this form can be a lot more useful.

So you can see, just from one line on an Argand diagram, you can learn a lot of the information you need to manipulate a complex number.

Practical applications of calculus occur more often than you would think. The most common example of them being applied to real world problems is through the relationship between distance and time. The distance an object will travel in a certain time is it's velocity. If we differentiate an equation for distance travelled with respects to time, it will give an equation for velocity.

However this is only useful if the objects velocity is constant; it could be speeding up (acccelerating). The acceleration of a body is it's change in speed over time. So, if we differentiate an equation for velocity with respects to time, it will give an equation for acceleration.

You can differentiate again to give the rate of change of acceleration, but this is a less useful figure to be given.

Conversely, if you have an equation for an object's acceleration, you can integrate it (the opposite of differentiating it) with respects to time to give an equation for it's velocity at a certain time.

Integrating again will give the distance it has travelled after a certain time.

Calculus can be used in this way in loads more equations including force-energy-power, and circumference-area in a circle.

All of these values can be plotted on graphs, and different features of a particular graph (such as the gradient of the line and the area under it) will give you these values. Remember, a graph is just a visual representation of an equation, so that's where they come into it.

Practical applications of calculus occur more often than you would think. The most common example of them being applied to real world problems is through the relationship between distance and time. The distance an object will travel in a certain time is it's velocity. If we differentiate an equation for distance travelled with respects to time, it will give an equation for velocity.

However this is only useful if the objects velocity is constant; it could be speeding up (acccelerating). The acceleration of a body is it's change in speed over time. So, if we differentiate an equation for velocity with respects to time, it will give an equation for acceleration.

You can differentiate again to give the rate of change of acceleration, but this is a less useful figure to be given.

Conversely, if you have an equation for an object's acceleration, you can integrate it (the opposite of differentiating it) with respects to time to give an equation for it's velocity at a certain time.

Integrating again will give the distance it has travelled after a certain time.

Calculus can be used in this way in loads more equations including force-energy-power, and circumference-area in a circle.

All of these values can be plotted on graphs, and different features of a particular graph (such as the gradient of the line and the area under it) will give you these values. Remember, a graph is just a visual representation of an equation, so that's where they come into it.