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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]
The official titles of the course are Studies in Algebra and Group Theory (Math 55a) [1] and Studies in Real and Complex Analysis (Math 55b). [2] Previously, the official title was Honors Advanced Calculus and Linear Algebra. [3] The course has gained reputation for its difficulty and accelerated pace.
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.
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 ...
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 ...