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Learn Mathematics, earn certificates with free online courses from Harvard, Stanford, MIT, University of Pennsylvania and other top universities around the world. Read reviews to decide if a class is right for you.
Comprehensive proof of five fundamental sequence limit laws in real analysis, covering sum, difference, constant multiple, product, and quotient of convergent sequences with practical applications.
Detailed solution to IMO 1962 Problem 2, exploring a complex square root inequality through mathematical analysis, intermediate value theorem, and algebraic manipulation.
Step-by-step solutions for simple interest word problems using I = prt formula. Practice with five diverse scenarios to master calculating interest earned or owed in various financial situations.
Learn to simplify, divide, and solve problems with ratios and rates, building foundational skills for more advanced mathematical concepts.
Learn essential index notation, laws, and calculations using spreadsheets. Master multiplication, division, and power operations for indices, enhancing your mathematical skills.
Explore measurement applications: scientific notation, significant figures, metric units, errors, rounding, perimeter, area, volume, similar objects, and surface area. Practical examples enhance understanding.
Explore advanced vector concepts in 3D space, including coordinate systems, dot products, vector equations, and applications to geometric shapes, enhancing your understanding of multidimensional mathematics.
Explore the fascinating Basel Problem through a step-by-step mathematical journey, covering recurrence relations, integration techniques, and the squeeze theorem.
Comprehensive exploration of equation theory, covering roots, transformations, and advanced solution methods for cubic and biquadratic equations.
Comprehensive exploration of Bessel's functions and Legendre polynomials, covering recurrence relations, proofs, and applications in partial differential equations.
Comprehensive exploration of numerical analysis techniques, covering interpolation, integration, differentiation, and equation-solving methods with practical examples and applications.
Comprehensive exploration of Laplace and Fourier transforms, covering theory, applications, and problem-solving techniques for differential equations and signal processing.
Comprehensive exploration of series solutions for differential equations, covering Legendre polynomials, Frobenius method, Bessel's functions, and partial differential equations.
Explore graph theory fundamentals, adjacency matrices, and efficient algorithms like Kruskal's and Prim's for solving network optimization problems.
Explore delta functions, their properties, and applications in signal sampling, including Fourier transforms and practical exam scenarios.
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