Mathematics Master Sheet – Algebra, Calculus, ODE/PDE, Probability & More (8-Page PDF)

The complete mathematics handbook I wish I had in my first years of university.

This 8-page master sheet condenses the core tools of calculus, probability, and applied analysis into a clean, printable reference – perfect for fast revision before exams or while solving problem sets.

What’s inside

Organized in clearly labeled sections for quick lookup:

• Algebra & Fundamentals – groups, complex numbers, triangle inequality, Bernoulli’s inequality, De Moivre, series rules, special sequences and series.
• Single-Variable Calculus – limits, differentiation rules, special functions, Taylor & Maclaurin expansions with remainder forms, binomial series, basic integrals, substitution, integration by parts, rational functions & partial fractions.
• Fourier Analysis – Fourier series, special cases, convergence conditions, complex form, Fourier transform.
• Ordinary Differential Equations – first-order equation types (separable, exact, linear, Bernoulli, Riccati, Clairaut), linear second-order ODEs with constant coefficients, stability, Laplace method, power-series solutions.
• Special Functions – Hermite, Laguerre, Bessel and Legendre polynomials with their ODEs, recurrences and orthogonality.
• Linear Algebra & Vector Calculus – vector norms, scalar & cross product, determinants, eigenvalues/eigenvectors, linear systems, linear programming, gradient, divergence, curl, line & surface integrals, Gauss & Stokes theorems.
• Multivariable Calculus – Taylor expansion in several variables, implicit functions, tangent lines/planes, arc length, parametric curves.
• Partial Differential Equations – separation of variables, product ansatz, heat, wave and potential equations, plus the time-dependent and time-independent Schrödinger equation structure.
• Probability & Statistics – combinatorics, binomial / Poisson / normal / χ² distributions, expectations, variance, CLT, correlation, error propagation, confidence intervals and χ² hypothesis test.
• Numerical Methods – interpolation (Newton & Lagrange), trapezoidal / Simpson rules, regula falsi, Newton’s method, Picard iteration and Runge–Kutta for ODEs.

Who is this for?

• Engineering, physics, math and CS students taking higher mathematics / math methods.
• Students preparing for exams in Analysis, Linear Algebra, Differential Equations, Probability, Numerical Methods.
• Anyone who wants a single compact reference instead of flipping through multiple textbooks.

💡 Why it works

• All the core formulas and methods are condensed onto 8 dense pages, grouped by topic so you can find what you need in seconds.
• Focuses on definitions, key theorems, standard forms and solution recipes, not long explanations.
• Ideal as a desk companion, exam warm-up sheet or quick refresher when working on problem sets or projects.

Format

• PDF, 8 pages, optimized for A4/Letter printing or tablet viewing.
• Can be printed as a folded booklet or kept as a digital reference.