Tom Rocks Maths Courses

Oxford Calculus: How to Solve the Heat Equation

Learn to solve the Heat Equation, a fundamental PDE in calculus, with Oxford mathematician Dr Tom Crawford. Includes practice questions, interactive worksheets, and a free calculator app for comprehensive understanding.

• YouTube
• 35 minutes
• On-Demand
• Free Video

Oxford Linear Algebra - Eigenvalues and Eigenvectors Explained

Comprehensive tutorial on calculating eigenvalues and eigenvectors of matrices, featuring two worked examples. Covers the eigenvalue equation, characteristic polynomial, and step-by-step solutions for 2x2 and 3x3 matrices.

• YouTube
• 26 minutes
• On-Demand
• Free Video

Oxford Calculus - Separable Solutions to PDEs

Learn to solve partial differential equations using separable solutions with Oxford mathematician Dr Tom Crawford. Includes examples, practice worksheets, and links to a free calculator app for checking your work.

• YouTube
• 21 minutes
• On-Demand
• Free Video

Heisenberg's Uncertainty Principle

Derive Heisenberg's Uncertainty Principle in Quantum Mechanics, exploring Schrödinger's Equation, momentum and position operators, and the key proposition leading to this fundamental concept.

• YouTube
• 36 minutes
• On-Demand
• Free Video

Oxford Calculus - Heat Equation Derivation

Comprehensive derivation of the Heat Equation from physical principles, including Liebniz Rule and Fourier's Law. Extends to 2D and 3D applications with interactive exercises for practice.

• YouTube
• 25 minutes
• On-Demand
• Free Video

Oxford Linear Algebra - The Easiest Method to Calculate Determinants

Learn the easiest method to calculate determinants using Elementary Row Operations (ERO's). Includes a worked example for a 4x4 matrix and links to practice exercises and video solutions.

• YouTube
• 27 minutes
• On-Demand
• Free Video

What Is the Determinant Function for a Matrix?

Explore determinant calculation for 2x2 and 3x3 matrices, understand its origins, and learn key properties of the determinant function in this comprehensive linear algebra tutorial.

• YouTube
• 27 minutes
• On-Demand
• Free Video

Coding Fractals in HTML with JavaScript

Learn to create stunning mathematical art using HTML and JavaScript to generate Julia Fractals with Oxford mathematician Dr Tom Crawford. Explore the intersection of coding and mathematics.

• YouTube
• 37 minutes
• On-Demand
• Free Video

Oxford Calculus - Separation of Variables Integration Technique Explained with Examples

Learn to solve first order separable differential equations using the separation of variables method, with worked examples and practice exercises from an Oxford mathematician.

• YouTube
• 28 minutes
• On-Demand
• Free Video

Helmholtz Principle and Vortex Motion

Explore Helmholtz' Principle and vortex motion in 2D potential flow. Learn about complex potentials, velocity fields, and the Method of Images to understand fluid dynamics and vortex trajectories.

• YouTube
• 36 minutes
• On-Demand
• Free Video

Oxford Calculus - Jacobians Explained

Comprehensive explanation of Jacobians in 2D coordinate changes, focusing on polar coordinates. Includes derivation of general formula and practical applications with interactive exercises.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Amazing Pi Formula - Prime Numbers and Multiples of 4

Explore a fascinating pi formula involving prime numbers and multiples of 4. Learn step-by-step proofs, from geometric series to the Leibniz Formula, culminating in a remarkable relationship between pi and primes.

• YouTube
• 23 minutes
• On-Demand
• Free Video

Prime Reciprocal Series - Oxford Maths Interview Question

Explore the divergence of prime reciprocal sums using advanced mathematical concepts in this Oxford University admissions interview question, featuring collaboration between mathematicians.

• YouTube
• 22 minutes
• On-Demand
• Free Video

Potential Flow and Method of Images with 3Blue1Brown

Explore 2D incompressible fluid dynamics with Grant Sanderson, covering potential flow, common flow fields, and the method of images for various scenarios like sources near walls and in channels.

• YouTube
• 25 minutes
• On-Demand
• Free Video

Koch Snowflake Fractal - Area and Perimeter Calculation

Explore the fascinating Koch Snowflake fractal, calculating its infinite perimeter and constant area. Suitable for ages 14+, with step-by-step construction instructions and in-depth mathematical analysis.

• YouTube
• 29 minutes
• On-Demand
• Free Video