__About Me:__

My name is Ifan, I'm originally from North Wales and I have recently graduated from Imperial College London with a **1st class honours** masters degree in **Physics with Theoretical Physics**. I am **dedicated **to and** **have a **true passion** for the fields of science and mathematics; I am hoping to study for a PhD in physics next year. My tutoring style is **enthusiastic, creative and proactive**, and I'm certain that any student of mine will eventually share my enthusiasm! I truly believe with a **strong desire to learn **and** improve oneself**, alongside the **right guidance**, any student can achieve **great results**.

__My Experience__

I am a very **patient** and **friendly** tutor; personally, **I love teaching** and helping students **exceed their expectations**. I have **two years** of prior tutoring experience tutoring two different students of varying aptitude in A-Level mathematics and physics. I also currently tutor my younger cousin in GCSE mathematics weekly. I really enjoyed **passing on my knowledge** and getting to know my students, and also **achieved great results**.

**The Sessions**

My tuition is **tailored** to suit the student, accounting for their **long-term goals **(their desired career/profession) and **short-term goals** (__acing the exams!__). I then break the work down into **manageable steps** and focus on the specific areas of the subject that the student requires extra help with, working alongside them until they are **confident enough in their understanding **to complete the task alone. With physics/maths, **fundamental understanding** is key to achieving great results in practice, so I ensure students have a **thorough conceptual understanding** of the topic before focussing on exam techniques. I believe this improves results, as opposed to simply memorising certain methodology. I also try to **make learning fun** and to have a bit of rapport with my students, as I believe this facilitates improved interaction and promotes a more **relaxed** and **constructive** learning environment.

**What next?**

If you have any questions, send me a 'WebMail' or book a 'Meet the Tutor Session' (both accessible through this website). Remember to mention your **subject** and** what you're struggling with.**

Talk soon!

__About Me:__

My name is Ifan, I'm originally from North Wales and I have recently graduated from Imperial College London with a **1st class honours** masters degree in **Physics with Theoretical Physics**. I am **dedicated **to and** **have a **true passion** for the fields of science and mathematics; I am hoping to study for a PhD in physics next year. My tutoring style is **enthusiastic, creative and proactive**, and I'm certain that any student of mine will eventually share my enthusiasm! I truly believe with a **strong desire to learn **and** improve oneself**, alongside the **right guidance**, any student can achieve **great results**.

__My Experience__

I am a very **patient** and **friendly** tutor; personally, **I love teaching** and helping students **exceed their expectations**. I have **two years** of prior tutoring experience tutoring two different students of varying aptitude in A-Level mathematics and physics. I also currently tutor my younger cousin in GCSE mathematics weekly. I really enjoyed **passing on my knowledge** and getting to know my students, and also **achieved great results**.

**The Sessions**

My tuition is **tailored** to suit the student, accounting for their **long-term goals **(their desired career/profession) and **short-term goals** (__acing the exams!__). I then break the work down into **manageable steps** and focus on the specific areas of the subject that the student requires extra help with, working alongside them until they are **confident enough in their understanding **to complete the task alone. With physics/maths, **fundamental understanding** is key to achieving great results in practice, so I ensure students have a **thorough conceptual understanding** of the topic before focussing on exam techniques. I believe this improves results, as opposed to simply memorising certain methodology. I also try to **make learning fun** and to have a bit of rapport with my students, as I believe this facilitates improved interaction and promotes a more **relaxed** and **constructive** learning environment.

**What next?**

If you have any questions, send me a 'WebMail' or book a 'Meet the Tutor Session' (both accessible through this website). Remember to mention your **subject** and** what you're struggling with.**

Talk soon!

No DBS Check

(a) A frequency of 440 Hz means that a single trough and peak of the sound wave oscillates 440 times per second or equally that 440 sound waves are produced by the keyboard per second (This is because the SI unit of a Hz is inverse seconds s^-1)

(b) We first need the equation that relates the two given quantities we have (wave velocity and frequency) to the third unknown, desired quantity (wavelength). This is equation is a simple one, v = f lambda. We want the quantity lambda, so we have to divide both sides of the equation by f to get v / f = lambda. We then plug in the numbers to find lambda, the wavelength, which is lambda = 340 m /s / 440 /s = 340/440 m (as the /s units cancel out leaving just length which is the correct unit for a wavelength!)

(a) A frequency of 440 Hz means that a single trough and peak of the sound wave oscillates 440 times per second or equally that 440 sound waves are produced by the keyboard per second (This is because the SI unit of a Hz is inverse seconds s^-1)

(b) We first need the equation that relates the two given quantities we have (wave velocity and frequency) to the third unknown, desired quantity (wavelength). This is equation is a simple one, v = f lambda. We want the quantity lambda, so we have to divide both sides of the equation by f to get v / f = lambda. We then plug in the numbers to find lambda, the wavelength, which is lambda = 340 m /s / 440 /s = 340/440 m (as the /s units cancel out leaving just length which is the correct unit for a wavelength!)

Firstly, we note that z being a complex number can be expressed in the form z = a + bi. If we then take the complex conjugate of this expression, the real numbers remain the same (as they are their own c conjugates) but the c conjugate of i is -i, therefore z* = a - bi. We then insert these expressions into the given equation, so

5 i (a + bi) + 3 (a - bi) + 16 = 8 i

We then expand the brackets and rearrange, remebering that i^{2} = -1, such that

5 i a - 5 b + 3 a - 3 b i + 16 = 8i.

We can then split the equation up into real and complex parts (i.e the terms that are not functions of i and are functions of i respectively) and treat each equation seperately, so we have

-5 b + 3 a + 16 = 0, 5a - 3b - 8 = 0

This is a simple simultaneous equation to solve, and we this find that

16b = 104, 16a = 88

so z is thus given by z = 11/2 + 13/2 i

QED

Firstly, we note that z being a complex number can be expressed in the form z = a + bi. If we then take the complex conjugate of this expression, the real numbers remain the same (as they are their own c conjugates) but the c conjugate of i is -i, therefore z* = a - bi. We then insert these expressions into the given equation, so

5 i (a + bi) + 3 (a - bi) + 16 = 8 i

We then expand the brackets and rearrange, remebering that i^{2} = -1, such that

5 i a - 5 b + 3 a - 3 b i + 16 = 8i.

We can then split the equation up into real and complex parts (i.e the terms that are not functions of i and are functions of i respectively) and treat each equation seperately, so we have

-5 b + 3 a + 16 = 0, 5a - 3b - 8 = 0

This is a simple simultaneous equation to solve, and we this find that

16b = 104, 16a = 88

so z is thus given by z = 11/2 + 13/2 i

QED

So we initially have the relationship y = ln(sin(3x)). As the left hand side is a function of the variable y and the right hand side is a function of the variable x i.e they are implicitly related, we need to use implicit differentiation. This means we differentiate each side of the equation seperately with respect to the functional variable, in this case x. Now differentiate the LHS, which is simple enough

d/dx(y) = dy/dx = f'(x)

To differentiate the RHS, we note that the differential of a logarithm ln(g(x)) is given by g'(x) / g(x), a relationship that can be found easily by integrating. So in this example we have that g(x) = sin(3x), therefore we need to use the chain rule to differentiate it. The differential of sin(3x) is thus cos(3x) multiplied by the differential of 3x which is 3, therefore g'(x) = 3cos(3x) and so the differential of the RHS is 3cos(3x)/sin(3x) = 3cot(3x)

We thus have dy/dx = 3cot(3x)

So we initially have the relationship y = ln(sin(3x)). As the left hand side is a function of the variable y and the right hand side is a function of the variable x i.e they are implicitly related, we need to use implicit differentiation. This means we differentiate each side of the equation seperately with respect to the functional variable, in this case x. Now differentiate the LHS, which is simple enough

d/dx(y) = dy/dx = f'(x)

To differentiate the RHS, we note that the differential of a logarithm ln(g(x)) is given by g'(x) / g(x), a relationship that can be found easily by integrating. So in this example we have that g(x) = sin(3x), therefore we need to use the chain rule to differentiate it. The differential of sin(3x) is thus cos(3x) multiplied by the differential of 3x which is 3, therefore g'(x) = 3cos(3x) and so the differential of the RHS is 3cos(3x)/sin(3x) = 3cot(3x)

We thus have dy/dx = 3cot(3x)