MathProblemsBank Math Problems Bank
  • Home
  • Forum
  • About Us
  • Contact Us
  • Login
  • Register
  • language
 MathProblemsBank banner

MathProblemsBank banner

Math Problems and solutions

Mathematics sections
  • Algebra
    • Vector Algebra
    • Determinant calculation
    • Permutation group
    • Matrix transformations
    • Linear transformations
    • Quadratic forms
    • Fields, Groups, Rings
    • Systems of algebraic equations
    • Linear spaces
    • Polynomials
    • Tensor calculus
    • Vector analysis
  • Analytic geometry
    • Curves of the 2-nd order
    • Surfaces of the 2-nd order
    • Lines on a plane
    • Line and plane in space
    • Tangents and normals
  • Complex analysis
    • Operations with complex numbers
    • Singular points and residues
    • Integral of a complex variable
    • Laplace transform
    • Conformal mappings
    • Analytic functions
    • Series with complex terms
    • Calculating integrals of a real variable using residues
  • Differential equations
    • Ordinary differential equations
      • First order differential equations
      • Second order differential equations
      • Higher order differential equations
      • Geometric and physical applications
    • Systems of ordinary differential equations
    • Stability
      • Stability of the equations
      • Stability of the systems of equations
    • Operating method
      • Differential equations
      • Systems of differential equations
  • Differential geometry
  • Discret mathematics
    • Boolean algebra
    • Set theory
    • Combinatorics
    • Graph theory
    • Binary relations
    • Propositional algebra
      • Propositional calculus
      • Sequent calculus
    • Predicate calculus
    • Theory of algorithms and formal languages
    • Automata theory
    • Recursive functions
  • Functional analysis
    • Metric spaces
      • Properties of metric spaces
      • Orthogonal systems
      • Convergence in metric spaces
    • Normed spaces
      • Properties of normed spaces
      • Convergence in normed spaces
    • Measure theory
      • Lebesgue measure and integration
      • Measurable functions and sets
      • Convergence (in measure, almost everywhere)
    • Compactness
    • Linear operators
    • Integral equations
    • Properties of sets
    • Generalized derivatives
    • Riemann-Stieltjes integral
  • Geometry
    • Planimetry
      • Transformations on the plane
      • Construction problems
      • Complex numbers in geometry
      • Various problems on the plane
      • Locus of points
    • Stereometry
      • Construction of sections
      • Various problems in the space
    • Affine transformations
  • Mathematical analysis
    • Gradient and directional derivative
    • Graphing functions using derivatives
    • Plotting functions
    • Fourier series
      • Trigonometric Fourier series
      • Fourier integral
    • Number series
    • Function extrema
    • Power series
    • Function properties
    • Derivatives and differentials
    • Functional sequences and series
    • Calculation of limits
    • Asymptotic analysis
  • Mathematical methods and models in economics
  • Mathematical physics
    • First order partial differential equations
    • Second order partial differential equations
      • d'Alembert method
      • Fourier method
      • With constant coefficients
      • With variable coefficients
      • Mixed problems
    • Convolution of functions
    • Nonlinear equations
    • Sturm-Liouville problem
    • Systems of equations in partial derivatives of the first order
  • Mathematical statistics
  • Numerical methods
    • Golden section search method
    • Least square method
    • Sweep method
    • Simple-Iteration method
    • Approximate calculation of integrals
    • Approximate solution of differential equations
    • Approximate numbers
    • Function Interpolation
    • Approximate solution of algebraic equations
  • Olympiad problems
    • Olympic geometry
    • Number theory
    • Olympic algebra
    • Various Olympiad problems
    • Inequalities
      • Algebraic
      • Geometric
    • Higher mathematics
  • Probability theory
    • One dimensional random variables and their characteristics
    • Theory of random processes
    • Markov chains
    • Queuing systems
    • Two-dimensional random variables and their characteristics
    • Definition and properties of probability
    • Limit theorems
  • Real integrals
    • Integrals of functions of a single variable
      • Indefinite integrals
      • Definite Integrals
      • Improper integrals
    • Double integrals
    • Triple integrals
    • The area of a region
    • Volume of a solid
    • Volume of a solid of revolution
    • Flux of the vector field
    • Surface integrals
    • Curvilinear integrals
    • Potential and solenoidal fields
    • Vector field circulation
    • Integrals depending on a parameter
  • Topology
  • USE problems
  • Variational calculus
Problem list Free problems

Attention! If a subsection is selected, then the search will be performed in it!

Problem: Find all the values of \( \beta \), for which there is a linear transformation of variables \( (x, y) \rightarrow(z, t) \), bringing the equation to the following canonical form: a) \( u_{t t}= \) \( =u_{z z} \), b) \( u_{t}=u_{z z} \). \[ u_{x x}+4 u_{x y}-\beta u_{y y}-\beta u_{x}+\beta^{2} u_{y}=0 . \]

11.5.4.4 With constant coefficients

6.42 $

Problem: Let \( f(x)=e^{-|x|} \cos \omega x \). Calculate the integral: \[ F(y)=\frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{+\infty} f(x) e^{i y x} d x \text {. } \]

2.6.1.6 Fourier integral

3.08 $

Problem: Does function \( f_{n}(x)=\cos \frac{x}{n} \cdot \cos x \) uniformly converge in a) \( [0, \pi] \), b) \( \mathbb{R} \).

2.9.4 Functional sequences and series

2.06 $

Problem: Find the solution of the comparison: \[ x^{8} \equiv 62(\bmod 169) \text {. } \]

12.2.14 Number theory

3.08 $

Problem: Find the solution of the comparison: \[ 355 x \equiv 257 \cdot 156(\bmod 338) . \]

12.2.13 Number theory

3.08 $

Problem: Let \( a_{n} \) be a sequence of positive numbers, for which the following inequality holds. \[ a_{n}^{2}

12.3.1.4 Algebraic

3.85 $

Problem: Prove the equivalence of the formulas: \[ \int_{0}^{a} t^{\beta-1} e^{-\lambda t} d t \sim \Gamma(\beta) \lambda^{-\beta}, \quad \lambda \rightarrow+\infty, \quad a, \beta>0 . \]

2.12.1 Asymptotic analysis

3.08 $

Problem: Let function \( f(x) \in C(0 ; 1] \) be such that \[ f(x) \sim x^{a-1}(x \rightarrow+0), 0

2.12.2 Asymptotic analysis

6.42 $

Problem: Write down the asymptotic formula for the function: \[ f(x)=\left(\frac{e^{x}-1}{x}\right)^{\frac{1}{x}}, \quad x \rightarrow 0 . \]

2.12.3 Asymptotic analysis

3.85 $

Problem: Write down the asymptotic formula for the function: \[ \begin{array}{l} f(x)=\sqrt{x^{4}+2 x^{2}-2 x}-x^{2} \cos \frac{x}{x^{2}+1}, \\ x \rightarrow+\infty . \end{array} \]

2.12.4 Asymptotic analysis

4.37 $

Problem: Find the asymptotics of the roots of the equation: \[ \cos x=\frac{1}{x}, \quad x>0 . \]

2.12.5 Asymptotic analysis

7.71 $

Problem: Write down the asymptotic representation of the function: \[ F(x)=\int_{x}^{+\infty} \frac{e^{-t}}{\sqrt{t^{3}+2}} d t, \quad x \rightarrow+\infty . \]

2.12.6 Asymptotic analysis

6.42 $

Problem: Write down the asymptotic representation of the function: \[ F(x)=\int_{1}^{x} \sqrt{t^{3}+t} d t, \quad x \rightarrow+\infty . \]

2.12.7 Asymptotic analysis

6.42 $

Problem: Let \( (M, \cdot) \) - be a group, and \( \alpha \) and \( \beta \) - mappings from \( M \) to \( M \). Let's define an operation * on \( M \) by the rule: \( x * y=\alpha(x) \beta(y) \forall x, y \in M \). Prove that the conditions are equivalent: (1) \( (M, *) \) - a group; (2) \( \exists a, b \in M: \alpha(g)=g a, \beta(g)=b g \quad \forall g \in M \).

1.6.9 Fields, Groups, Rings

6.42 $

Problem: Prove that \( \mathbb{Q}(p) / \mathbb{Z}^{+} \cong \mathbb{Z}_{p^{\infty}} \).

1.6.10 Fields, Groups, Rings

4.37 $

  • ‹
  • 1
  • 2
  • ...
  • 38
  • ...
  • 116
  • 117
  • ›

mathproblemsbank.net

Terms of use Privacy policy

© Copyright 2025, MathProblemsBank

Trustpilot
Order a solution
Order a solution to a problem?
Order a solution
Order a solution to a problem?
home.button.login