University of Oxford Physics Year 1 - Linear Algebra and ODEs (CP3) Complete Lecture Notes & Revision Guide

Comprehensive handwritten lecture notes for the University of Oxford Year 1 Physics course "Linear Algebra and ODEs (CP3)". These notes provide a structured and detailed treatment of the material covered throughout the course, including derivations, worked examples, key formulas, diagrams, and explanations designed to support both understanding and revision. Topics covered include: • Vector algebra, scalar products, vector products, triple products, and geometric applications of vectors • Equations of lines, planes, spheres, intersections, distances, and coordinate representations in two and three dimensions • Matrix algebra, matrix multiplication, transpose, Hermitian conjugate, orthogonal and unitary matrices • Vector spaces, subspaces, span, basis vectors, dimension, linear independence, and coordinate systems • Linear maps, image and kernel, rank, invertibility, composition of mappings, and dimension theorems • Systems of linear equations, row reduction, echelon forms, matrix inversion, and solution methods • Determinants, multilinear forms, determinant properties, invertibility criteria, and determinant expansions • Scalar products, orthonormal bases, Hermitian operators, adjoints, dual vector spaces, and linear functionals • Eigenvalues, eigenvectors, diagonalisation, normal operators, Hermitian and unitary matrices, and spectral properties • Ordinary differential equations, integrating factors, second-order linear differential equations, complementary functions, and particular integrals • Applications to forced oscillations, resonant systems, damping, quality factor, bandwidth, and complex representations of oscillatory motion The document consists of carefully organised handwritten notes taken during the course and is suitable for lecture review, tutorial preparation, revision, and exam preparation. Ideal for Oxford Physics students and anyone studying introductory university-level linear algebra, differential equations, and mathematical methods.