Integrals of Trigonometric Functions and Exponentials
13. Aug. 2026NachschlagewerkSergey
Reference table of indefinite integrals of products of exponentials with sine and cosine.
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290
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Integrals with Radicals
13. Aug. 2026NachschlagewerkSergey
Reference table of indefinite integrals of expressions containing square roots and other radicals.
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260
Integrals of Rational Functions
13. Aug. 2026NachschlagewerkSergey
Reference table of indefinite integrals of rational functions, including quadratic denominators and partial-fraction forms.
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290
Integrals with Logarithms
13. Aug. 2026NachschlagewerkSergey
Reference table of indefinite integrals of expressions containing the natural logarithm.
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230
Integrals of Hyperbolic Functions
13. Aug. 2026NachschlagewerkSergey
Reference table of indefinite integrals of the hyperbolic sine, cosine, tangent and cotangent.
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260
Integrals with Exponentials
13. Aug. 2026NachschlagewerkSergey
Reference table of indefinite integrals of the exponential function and its products with powers of x.
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290
Table of Derivatives
13. Aug. 2026NachschlagewerkSergey
Reference table of the derivatives of the elementary functions: power, exponential, logarithmic, trigonometric and their inverses.
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240
Table of Basic Integrals
13. Aug. 2026NachschlagewerkSergey
Reference table of the basic indefinite integrals of the elementary functions: power, exponential, logarithmic and trigonometric.
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270
Векторное произведение
5. Aug. 2026SonstigesSergey
Ориентация тройки векторов, определение векторного произведения через длину, перпендикулярность и правую тройку, геометрический смысл (площадь параллелограмма), свойства с доказательствами и полный вывод формулы через определитель.
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90
Базис, координаты и проекция вектора
5. Aug. 2026TheorieSergey
Разложение вектора по базису на плоскости и в пространстве, ортонормированный базис и декартова система координат, координаты вектора и линейные операции над ними, проекция вектора на ось, её линейность и проекция на вектор.
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60
The torsion component of the Picard scheme
29. Juli 2026SonstigesBogdan Zavyalov
Every finite flat commutative group scheme over a noetherian local ring is the torsion component of the Picard scheme of a smooth projective scheme with 3-dimensional fibers, built as a quotient of a complete intersection. An application: Hodge numbers that jump in a smooth projective family.
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510
Fun example: empty colimit does not commute with empty limit
29. Juli 2026NotizenBogdan Zavyalov
Why the definition of a filtered category insists on non-emptiness: the empty colimit fails to commute with the empty limit, and that is the only failure.
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310
A non-Noetherian local ring with finitely generated maximal ideal
29. Juli 2026NotizenBogdan Zavyalov
A complete local ring with a finitely generated maximal ideal is Noetherian. Drop completeness and it fails: an ultraproduct construction gives a non-Noetherian local ring whose maximal ideal is principal.
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340