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<!DOCTYPE html>
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<title>James Moore: Physics</title>
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<h1>James Moore: Researcher in Particle Physics</h1>
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<ul class="nav">
<li class="button"><a href="index.html">Home</a></li>
<li class="button"><a href="research.html">Research</a></li>
<li class="button"><a href="physics_notes.html">Physics Notes</a></li>
<li class="button"><a href="notes.html">Maths Notes</a></li>
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<p> <br>On this page, notes for the Cambridge Natural Sciences Tripos will slowly appear...</p>
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<h2> <img src="exponentials.png" alt="Exponential functions" style="float: left; width: 300px; margin-left:5px; height: auto; padding:60px; margin-top:-60px; padding-bottom:20px;">Lucy Cavendish Bridging Week </h2>
<p> As part of the Lucy Cavendish Bridging Week, I ask students to complete a preparatory examples sheet on exponential functions, given below.</p>
<p>❧ <a href="preparatory_examples_sheet.pdf">Preparatory mathematics examples sheet</a><br></p>
<p>To do one of the starred (difficult and optional) questions, it will be useful to look up the <i>Gaussian integral</i>, described <a href="https://en.wikipedia.org/wiki/Gaussian_integral">here</a>.</p>
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Part IA Mathematics for Natural Sciences<img src="ExSheets/NatSciMaths/scalar_triple_product.png" alt="Scalar triple product" style="float: right; width: 300px; margin-left:5px; height: auto; padding:60px; margin-top:-60px; padding-bottom:20px;"> </h2>
<p><i>Course theme music: <a href="https://open.spotify.com/track/0fxUGOzBYJGKgs5ZKw1Em5?si=0527e3ada2104850">12345, by Em Beihold</a></i><br><br>
In 2024-2025, I supervised the Part IA Mathematics for Natural Sciences course, and will be doing so again in 2025-2026. For my Lucy Cavendish students, I have my own problem sheets which are given below.<br><br>
<a href="ExSheets/NatSciMaths/ia_maths_faqs.pdf">Here</a> is a useful document detailing some frequently asked questions about first-year maths; I would advise you to read it before our first supervision.
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<h3>Mathematics A and B</h3>
<p>0. <a href="ExSheets/NatSciMaths/maths_sheet_0.pdf">Basic skills</a></p>
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<h3>Mathematics A</h3>
<p>1. <a href="ExSheets/NatSciMaths/maths_a_sheet_1.pdf">Basics of vector geometry, and the scalar product</a><br>
2. <a href="ExSheets/NatSciMaths/maths_a_sheet_2.pdf">The vector product, and triple products of vectors</a><br>
3. <a href="ExSheets/NatSciMaths/maths_a_sheet_3.pdf">Vector area, polar coordinate systems, and complex numbers</a><br>
4. <a href="ExSheets/NatSciMaths/maths_a_sheet_4.pdf">More complex numbers, and hyperbolic functions</a><br>
5. <a href="ExSheets/NatSciMaths/maths_a_sheet_5.pdf">Differential calculus, Riemann sums, and basic integrals</a><br>
6. <a href="ExSheets/NatSciMaths/maths_a_sheet_6.pdf">Methods of integration</a><br>
7. <a href="ExSheets/NatSciMaths/maths_a_sheet_7.pdf">Taylor series, and Newton-Raphson iteration</a><br>
8. <a href="ExSheets/NatSciMaths/maths_a_sheet_8.pdf">Probability spaces, conditional probability, and combinatorics</a><br>
9. <a href="ExSheets/NatSciMaths/maths_a_sheet_9.pdf">Discrete and continuous random variables, and functions of random variables</a><br>
❧ <i>Michaelmas revision sheet</i><br>
10. <a href="ExSheets/NatSciMaths/maths_a_sheet_10.pdf">First-order ordinary differential equations</a><br>
11. <a href="ExSheets/NatSciMaths/maths_a_sheet_11.pdf">Linear ordinary differential equations</a><br>
12. <a href="ExSheets/NatSciMaths/maths_a_sheet_12.pdf">Partial differentiation, and the chain rule for multivariable functions</a><br>
13. <a href="ExSheets/NatSciMaths/maths_a_sheet_13.pdf">Exact differentials, algebra of differentials, and applications in thermodynamics</a><br>
14. <a href="ExSheets/NatSciMaths/maths_a_sheet_14.pdf">Gradient, directional derivatives, and contour sketching</a><br>
15. <a href="ExSheets/NatSciMaths/maths_a_sheet_15.pdf">Multivariable integration and Gaussian integrals</a><br>
16. <a href="ExSheets/NatSciMaths/maths_a_sheet_16.pdf">Scalar and vector fields, and line integrals</a><br>
17. <a href="ExSheets/NatSciMaths/maths_a_sheet_17.pdf">Surface integrals and the integral theorems</a><br>
❧ <i>Lent revision sheet</i><br>
18. Matrix algebra I<br>
19. Matrix algebra II<br>
20. Fourier series
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<h3>Mathematics B</h3>
<p>1. <a href="ExSheets/NatSciMaths/maths_b_sheet_1.pdf">Basics of vector geometry, and the scalar and vector products</a><br>
2. <a href="ExSheets/NatSciMaths/maths_b_sheet_2.pdf">Further vector geometry, triple products, vector area, and polar coordinate systems</a><br>
3. <a href="ExSheets/NatSciMaths/maths_b_sheet_3.pdf">Complex numbers and hyperbolic functions</a><br>
4. <a href="ExSheets/NatSciMaths/maths_b_sheet_4.pdf">Differential calculus, limits and continuity</a><br>
5. <a href="ExSheets/NatSciMaths/maths_b_sheet_5.pdf">Infinite series and Taylor series</a><br>
6. <a href="ExSheets/NatSciMaths/maths_b_sheet_6.pdf">Single-variable integration</a><br>
7. <a href="ExSheets/NatSciMaths/maths_b_sheet_7.pdf">Multivariable integration and Gaussian integrals</a><br>
8. <a href="ExSheets/NatSciMaths/maths_b_sheet_8.pdf">Probability spaces, conditional probability, and combinatorics</a><br>
9. <a href="ExSheets/NatSciMaths/maths_b_sheet_9.pdf">Discrete and continuous random variables, and functions of random variables</a><br>
❧ <i>Michaelmas revision sheet</i><br>
10. <a href="ExSheets/NatSciMaths/maths_b_sheet_10.pdf">First-order ordinary differential equations</a><br>
11. <a href="ExSheets/NatSciMaths/maths_b_sheet_11.pdf">Linear ordinary differential equations</a><br>
12. <a href="ExSheets/NatSciMaths/maths_b_sheet_12.pdf">Partial differentiation, differentials, and the single-variable chain rule with multivariable functions</a><br>
13. <a href="ExSheets/NatSciMaths/maths_b_sheet_13.pdf">The multivariable chain rule, exact differentials, and applications in thermodynamics</a><br>
14. <a href="ExSheets/NatSciMaths/maths_b_sheet_14.pdf">Contour sketching and conditional optimisation</a><br>
15. <a href="ExSheets/NatSciMaths/maths_b_sheet_15.pdf">Scalar and vector fields, conservative vector fields, and line integrals</a><br>
16. <a href="ExSheets/NatSciMaths/maths_b_sheet_16.pdf">Surface integrals and the integral theorems</a><br>
17. Fourier series<br>
❧ <i>Lent revision sheet</i><br>
18. Matrix algebra I<br>
19. Matrix algebra II<br>
20. Partial differential equations
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<img src="ExSheets/NatSciMaths/vector_area_projection.png" alt="Vector area projection" style="display: block; margin-left: auto; margin-right: auto; width: 50%">
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<h2>Part IB Physics B: Electromagnetism</h2>
<p> From 2024-2025 I supervised the Physics B Electromagnetism course, and I will be doing so again in 2025-2026. Here are my examples sheets for 2025-2026.</p>
<p>1. <a href="ExSheets/PhysBEM/em_sheet1.pdf">Electrostatic force and potential, electric dipoles, and Gauss’ law</a><br>
2. <a href="ExSheets/PhysBEM/em_sheet2.pdf">Poisson’s equation and the method of images</a><br>
3. <a href="ExSheets/PhysBEM/em_sheet3.pdf">Capacitors, electrostatic energy, virtual work, and dielectrics</a><br>
4. <a href="ExSheets/PhysBEM/em_sheet4.pdf">The Biot-Savart law, magnetic dipoles, and Ampère’s law</a><br>
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