Academy
Level 1 - Math I (Physics)
The core maths toolkit for physics: algebra, functions, graphs, trigonometry, vectors, units, and introductory calculus.
Questions available
Exam papers available
Course Purpose
Level 1 - Math I (Physics) builds the mathematical language needed for calculus-based physics. It focuses on the skills that turn physical statements into usable equations: manipulating real and complex numbers, reasoning with functions, taking limits and derivatives, integrating, working with series, and using matrices and vector spaces.
The course is written as a physics support course rather than as a pure mathematics survey. Definitions, theorems, and proof methods are included where they improve modelling, estimation, approximation, and problem solving in physics.
What You Will Study
- Real numbers and functions: algebraic manipulation, summation notation, induction, the binomial theorem, inverse functions, trigonometry, exponentials, logarithms, and hyperbolic functions.
- Limits and differentiation: formal limit language, practical limit methods, continuity, derivatives, inverse-function derivatives, and L'Hopital's Rule.
- Integration: definite and indefinite integrals, the fundamental theorem of calculus, integration by parts, substitution, partial fractions, and trigonometric integrals.
- Complex numbers: arithmetic, modulus, conjugates, polar form, arguments, De Moivre's theorem, complex equations, complex functions, and transcendental equations.
- Groups and symmetry: group axioms, symmetry groups, cyclic groups, group tables, subgroups, and maps between groups.
- Series and linear algebra: numerical series, power series, Taylor series, matrices, Gaussian elimination, determinants, inverse matrices, vector spaces, linear maps, eigenvalues, diagonalisation, and matrix groups.
How The Course Works
Topic pages combine compact explanations, the notation needed to use each idea, the main methods, worked examples, and checks that prevent common mistakes.
Use the topic pages for lesson content, question mode for practice, worked answers for feedback, and exam papers for timed revision.