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A branch of calculus that goes beyond multivariable calculus; for this, see Calculus on Euclidean space Topics referred to by the same term This disambiguation page lists articles associated with the title Advanced calculus .
Problems in Mathematical Analysis, by Boris Demidovich [48] Problems and Theorems in Analysis (2 volumes), by George Pólya, Gábor Szegő [49] [50] Mathematical Analysis: A Modern Approach to Advanced Calculus, by Tom Apostol [51] Principles of Mathematical Analysis, by Walter Rudin [52]
Fundamental theorem of calculus; Integration by parts; Inverse chain rule method; Integration by substitution. Tangent half-angle substitution; Differentiation under the integral sign; Trigonometric substitution; Partial fractions in integration. Quadratic integral; Proof that 22/7 exceeds π; Trapezium rule; Integral of the secant function ...
The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Halting problem. insolubility of the halting problem; Harmonic series (mathematics) divergence of the (standard) harmonic series; Highly composite number; Area of hyperbolic sector, basis of hyperbolic angle; Infinite series. convergence of the geometric series with first term 1 and ratio 1/2; Integer partition; Irrational number. irrationality ...