Applied Mathematics

Applied mathematics guides covering single and multivariable calculus, ordinary and partial differential equations, linear algebra, probability theory, statistical methods, and mathematical modeling.

Articles in this section

Calculus Basics Guide: Limits, Derivatives, and Integrals Learn calculus fundamentals — limits, derivatives, integrals, the Fundamental Theorem, and real-world applications … 10 min Multivariable Calculus: Functions of Several Variables Explore multivariable calculus — partial derivatives, multiple integrals, vector fields, gradient, divergence, curl, and … 8 min Ordinary Differential Equations: Concepts and Solution Methods Master ordinary differential equations — first-order ODEs, linear systems, numerical methods, and applications in … 8 min Partial Differential Equations: Heat, Wave, and Laplace Equations Explore partial differential equations — classification, solution methods for heat, wave, and Laplace equations, … 8 min Applied Linear Algebra: Vectors, Matrices, and Transformations Study applied linear algebra — vector spaces, matrix operations, eigenvalues, linear transformations, and computational … 8 min Probability Theory Guide: Foundations of Randomness Understand probability theory — sample spaces, random variables, distributions, expectation, variance, limit theorems, … 7 min Statistics Guide: Data Analysis and Inference Methods Learn statistics — descriptive statistics, sampling distributions, hypothesis testing, confidence intervals, regression … 9 min Numerical Analysis: Algorithms for Approximate Solutions Explore numerical analysis — root finding, interpolation, numerical integration, solving linear systems, and … 8 min Mathematical Modeling: Building Predictive Frameworks Explore mathematical modeling — model formulation, parameter estimation, validation, simulation, and applications in … 8 min Optimization Theory: Finding Optimal Solutions Study optimization theory — unconstrained optimization, constrained optimization, convexity, gradient methods, linear … 8 min Fourier Analysis: Decomposing Signals into Frequencies Explore Fourier analysis — Fourier series, Fourier transforms, convolution, spectral analysis, and applications in … 7 min Vector Calculus: Fields, Flux, and Circulation Study vector calculus — gradient, divergence, curl, line and surface integrals, Green's theorem, Stokes' theorem, and … 8 min Linear Programming: Optimizing with Linear Constraints Learn linear programming — simplex method, duality theory, sensitivity analysis, integer programming, and real-world … 9 min Differential Equations in Modeling: Real-World Dynamics Explore differential equations modeling — population dynamics, chemical kinetics, mechanical vibrations, circuit … 8 min Computational Mathematics: Algorithms for Scientific Computing Explore computational mathematics — algorithm design, complexity analysis, numerical linear algebra, Monte Carlo … 8 min Game Theory Guide: Strategic Decision Making Learn game theory — Nash equilibrium, zero-sum games, prisoner's dilemma, evolutionary game theory, and applications in … 8 min Information Theory: Entropy, Compression, and Communication Explore information theory — entropy, mutual information, channel capacity, source coding, error-correcting codes, and … 8 min Data Science Mathematics: Foundations for Analytics Explore data science mathematics — linear algebra, calculus, probability, optimization, dimensionality reduction, and … 8 min