Канал: Learn Maths with Dr Alex

Proving an inequality involving integral.

Proving an inequality involving integral.

Cauchy Schwarz integral inequality, some clarifications in English.

Cauchy Schwarz integral inequality, some clarifications in English.

The function f=1/x.

The function f=1/x.

The sandwich theorem for evaluating limits.

The sandwich theorem for evaluating limits.

L hospital rule for limits.

L hospital rule for limits.

Timestables, an easy way to remember.

Timestables, an easy way to remember.

Area and length of a sector in a circle.

Area and length of a sector in a circle.

Converting degrees to radians.

Converting degrees to radians.

Newton's iterative algorithm, derivation.

Newton's iterative algorithm, derivation.

Cubic numbers

Cubic numbers

$Converting mixed numbers to improper fractions.$

Converting mixed numbers to improper fractions.

Multiplication of decimals (the easy way)

Multiplication of decimals (the easy way)

Square numbers

Square numbers

Powers of 10 to decimals

Powers of 10 to decimals

Decimals to powers of 10.

Decimals to powers of 10.

Tangent and normal line parabola y=x^2.

Tangent and normal line parabola y=x^2.

An elementary PDE Analysis problem.

An elementary PDE Analysis problem.

Warm up exercise, plotting a sequence

Warm up exercise, plotting a sequence

Warm up problem 2, loci of complex numbers.

Warm up problem 2, loci of complex numbers.

Warm-up problem 1, loci of complex numbers

Warm-up problem 1, loci of complex numbers

Truncated and infinite series, derivation of formulas.

Truncated and infinite series, derivation of formulas.

Homogeneous functions, warm up exercise.

Homogeneous functions, warm up exercise.

Symmetric functions, a warm up exercise.

Symmetric functions, a warm up exercise.

Solving a simple ODE

Solving a simple ODE

Potential gravitational energy, formula derivation and applications.

Potential gravitational energy, formula derivation and applications.

Integral of an even function, a simple exercise.

Integral of an even function, a simple exercise.

Elegant trigonometry question.

Elegant trigonometry question.

Free fall, derivation of the equations of motion.

Free fall, derivation of the equations of motion.

Cauchy Schwarz inequality, clarifications (Greek language)

Cauchy Schwarz inequality, clarifications (Greek language)

Solving a functional equation, problem 2

Solving a functional equation, problem 2

Solving a functional equation, problem 1

Solving a functional equation, problem 1

Vector analysis, a nice warm up exercise.

Vector analysis, a nice warm up exercise.

Solid mechanics, balancing a faceplate.

Solid mechanics, balancing a faceplate.

Temperature conversion.

Temperature conversion.

Monotonicity of a function, example.

Monotonicity of a function, example.

Finding differential of a function, example.

Finding differential of a function, example.

Functional analysis, warm up problem 2.

Functional analysis, warm up problem 2.

Functional analysis, warm up problem 1.

Functional analysis, warm up problem 1.

PDE problem, Laplacian operator of function u.

PDE problem, Laplacian operator of function u.

Proof of triangle inequality.

Proof of triangle inequality.

An elementary exercise in analysis 2.

An elementary exercise in analysis 2.

An elementary exercise in analysis 1

An elementary exercise in analysis 1

Proof of Hölder inequality.

Proof of Hölder inequality.

Pythagoras theorem, an algebraic problems.

Pythagoras theorem, an algebraic problems.

Properties of natural logarithms via calculus techniques.

Properties of natural logarithms via calculus techniques.

Function spaces, a nice exercise.

Function spaces, a nice exercise.

Some properties of a double indexed sequence.

Some properties of a double indexed sequence.

Limit of a sequence, exercise.

Limit of a sequence, exercise.

Derivation of kinetic energy of a moving body.

Derivation of kinetic energy of a moving body.

Invariance of lorenz equations under a particular transformation.

Invariance of lorenz equations under a particular transformation.

Calculation of 2 norm of a square matrix.

Calculation of 2 norm of a square matrix.

Formula for the density of the sphere

Formula for the density of the sphere

An equation on circular motion.

An equation on circular motion.

Calculation of a path integral.

Calculation of a path integral.

An elementary PDE problem.

An elementary PDE problem.

Calculating infinity norm of a square matrix.

Calculating infinity norm of a square matrix.

A Problem on separable ODE.

A Problem on separable ODE.

Compound interest, derivation of formula.

Compound interest, derivation of formula.

Formulas for area and perimeter of a compound shape.

Formulas for area and perimeter of a compound shape.

Condition number of symmetric 2x2 matrix

Condition number of symmetric 2x2 matrix

Size of the wound and exponential function.

Size of the wound and exponential function.

L2 space is a metric space

L2 space is a metric space

Complex numbers , rectangular to polar form.

Complex numbers , rectangular to polar form.

A problem involving the volume of the sphere and the volume of a cylinder.

A problem involving the volume of the sphere and the volume of a cylinder.

$Recurring decimal to fraction using infinite geometric series.$

Recurring decimal to fraction using infinite geometric series.

Equation of straight line passing through a point with a given gradient.

Equation of straight line passing through a point with a given gradient.

Volume of two cones interconnected with common circular base.

Volume of two cones interconnected with common circular base.

Finding height in the trapezium in an area problem.

Finding height in the trapezium in an area problem.

Volume of square based pyramid.

Volume of square based pyramid.

Infinite series, interval of convergence.

Infinite series, interval of convergence.

A nice geometric property on a triangle.

A nice geometric property on a triangle.

A nice geometry problem on areas of shapes.

A nice geometry problem on areas of shapes.

Finding inverse function, example.

Finding inverse function, example.

Volume of an elliptical cylinder

Volume of an elliptical cylinder

The identity tan(a+b)

The identity tan(a+b)

Indefinite integration, substitution method and examples.

Indefinite integration, substitution method and examples.

Solving trinomial using factorization (no formula)

Solving trinomial using factorization (no formula)

A beautiful problem on Laplace transform.

A beautiful problem on Laplace transform.

A nice vector analysis problem.

A nice vector analysis problem.

A nice integral (substitution and employing properties of gamma function)

A nice integral (substitution and employing properties of gamma function)

An application on volumes of spheres.

An application on volumes of spheres.

Matrix M as a sum of symmetric and skew symmetric matrix

Matrix M as a sum of symmetric and skew symmetric matrix

Pythagoras and linear systems

Pythagoras and linear systems

Complex analysis, another problem

Complex analysis, another problem

A problem in Complex analysis.

A problem in Complex analysis.

Ordinary differential equations, a nice problem.

Ordinary differential equations, a nice problem.

Electric circuit, energy of the capacitor

Electric circuit, energy of the capacitor

Electric circuits, energy of inductor L

Electric circuits, energy of inductor L

Trigonometry exercise

Trigonometry exercise

Stokes equation, weak formulation

Stokes equation, weak formulation

Differential calculus, physics problem

Differential calculus, physics problem

conservation of momentum, application

conservation of momentum, application

sinepsilon=epsilon for epsilon sufficiently small

sinepsilon=epsilon for epsilon sufficiently small

Solving linear system using inverse matrix

Solving linear system using inverse matrix

concentration of ions in water

concentration of ions in water

Concentration of ions in hydrochloric acid

Concentration of ions in hydrochloric acid

ODEs oscillation of vibrating spring

ODEs oscillation of vibrating spring

Population of bacteria, Linearization

Population of bacteria, Linearization

Richter scale logarithmic formula

Richter scale logarithmic formula

Parallel resistor formula

Parallel resistor formula

Normalized vector example

Normalized vector example

Solution of 3rd order homogeneous linear ode with constant coefficients

Solution of 3rd order homogeneous linear ode with constant coefficients

Solving 2x2 linear system using Cramer method

Solving 2x2 linear system using Cramer method

Solving trinomial inequality

Solving trinomial inequality

Roots of 3rd degree polynomial via horner method

Roots of 3rd degree polynomial via horner method

Fourier transform of unit step function

Fourier transform of unit step function

Problem on population of bacteria

Problem on population of bacteria

Lax Milgram for Poisson equation reupload

Lax Milgram for Poisson equation reupload

Laplace transform scaled function

Laplace transform scaled function

Laplace transform of periodic function

Laplace transform of periodic function

Laplace transform, second translation theorem

Laplace transform, second translation theorem

Laplace transform first translation theorem

Laplace transform first translation theorem

If f,g are in L2, then their linear combination is also in L2

If f,g are in L2, then their linear combination is also in L2

Abel's identity for ODEs

Abel's identity for ODEs

PDE Analysis Elementary exercise

PDE Analysis Elementary exercise

Intersection ponts between unit circle at the origin and parabola y=x^2

Intersection ponts between unit circle at the origin and parabola y=x^2

Jordan form of a square 2x2 matrix

Jordan form of a square 2x2 matrix

A classical inequality associating L1 and L2 norms of a function in a bounded 1d interval

A classical inequality associating L1 and L2 norms of a function in a bounded 1d interval

Finding a bound for an integral using the Cauchy Schwarz integral inequality

Finding a bound for an integral using the Cauchy Schwarz integral inequality

Partial Fourier transform in the y direction of the 2d Laplacian operator

Partial Fourier transform in the y direction of the 2d Laplacian operator

One analysis problem with 3 questions

One analysis problem with 3 questions

Variational form of biharmonic equation via energy functional

Variational form of biharmonic equation via energy functional

How to solve 1st order system of linear ODEs

How to solve 1st order system of linear ODEs

Mersennes numbers, proof of a basic identity

Mersennes numbers, proof of a basic identity

Voltage divider derivation of formulas

Voltage divider derivation of formulas

inequality in normed spaces associating L1 and L2 norms

inequality in normed spaces associating L1 and L2 norms

Analysis problem, integral over a given bounded interval

Analysis problem, integral over a given bounded interval

Average value of sum of trig functions on given interval

Average value of sum of trig functions on given interval

Average value of a simple trigonometric function on given interval

Average value of a simple trigonometric function on given interval

Resonant frequency in LC circuit

Resonant frequency in LC circuit

Resonant frequency in LC circuit

Resonant frequency in LC circuit

Law of sines, application

Law of sines, application

Calculation of Shannon Hentropy, example

Calculation of Shannon Hentropy, example

Integral representation of Riemann zeta function

Integral representation of Riemann zeta function

Divergence of n dimensional vector field

Divergence of n dimensional vector field

Dirichlet functional and variational form of Poisson equation

Dirichlet functional and variational form of Poisson equation

why 1 is not a prime number

why 1 is not a prime number

writing a positive integer as product of primes

writing a positive integer as product of primes

triangle inequality in L2 normed spaces -proof

triangle inequality in L2 normed spaces -proof

pythagoras theorem and trigonometry

pythagoras theorem and trigonometry

Coulomb's force electrostatics

Coulomb's force electrostatics

Regular hexagon area

Regular hexagon area

area of complex domain nice geometry problem

area of complex domain nice geometry problem

solving inhomogeneous ode example

solving inhomogeneous ode example

Fibonacci sequence -recurrence equation and closed formula

Fibonacci sequence -recurrence equation and closed formula

decimal con digito recurrente y series infinitas

decimal con digito recurrente y series infinitas

odd functions examples

odd functions examples

even functions- examples

even functions- examples

heat equation - energy method for uniqueness

heat equation - energy method for uniqueness

Set of complex numbers some properties

Set of complex numbers some properties

Kinematics basic equations of motion

Kinematics basic equations of motion

Generalization of Newton's 2nd law

Generalization of Newton's 2nd law

Kinematics problem comparing kinetic energies

Kinematics problem comparing kinetic energies

an interesting analysis exercise

an interesting analysis exercise

Opposite angles proof via analytical geometry

Opposite angles proof via analytical geometry

Indefinite integration problem 2

Indefinite integration problem 2

Indefinite integration -problem 1

Indefinite integration -problem 1

Harmonic series, integral test.

Harmonic series, integral test.

infinite series problem, comparison test.

infinite series problem, comparison test.

Integral calculus-problem 13

Integral calculus-problem 13

Area of a rectangle

Area of a rectangle

Vector analysis -finding the angle between vectors

Vector analysis -finding the angle between vectors

Singular matrices- example

Singular matrices- example

The sum 1+2+3+ ... +N

The sum 1+2+3+ ... +N

1d Biharmonic equation- example

1d Biharmonic equation- example

Nilpotent matrix example

Nilpotent matrix example

ODE for modelling population

ODE for modelling population

1d Helmholtz equation.

1d Helmholtz equation.

Integral Calculus-problem 12.

Integral Calculus-problem 12.

Integral Calculus-problem 11

Integral Calculus-problem 11

Integral Calculus-problem 10.

Integral Calculus-problem 10.

Integral Calculus-problem 9

Integral Calculus-problem 9

Pythagoras theorem- Differential Calculus problem.

Pythagoras theorem- Differential Calculus problem.

Integral Calculus-problem 8.

Integral Calculus-problem 8.

Parseval's theorem.

Parseval's theorem.

1d Poisson equation-exercise

1d Poisson equation-exercise

Integral calculus-problem 7.

Integral calculus-problem 7.

Integral calculus-problem 6.

Integral calculus-problem 6.

Integral calculus-problem 5.

Integral calculus-problem 5.

Integral calculus-problem 4.

Integral calculus-problem 4.

Integral calculus-problem 3.

Integral calculus-problem 3.

Integral calculus-problem 2.

Integral calculus-problem 2.

Integral calculus-problem 1.

Integral calculus-problem 1.

De Moivre's formula.

De Moivre's formula.

Trace of a matrix-problem 3

Trace of a matrix-problem 3

Trace of the matrix-problem 2

Trace of the matrix-problem 2

The trace of a matrix-problem 1.

The trace of a matrix-problem 1.

Cayley Hamilton theorem for a 2x2 matrix.

Cayley Hamilton theorem for a 2x2 matrix.

Skew-symmetric matrix-example

Skew-symmetric matrix-example

Symmetric matrix-example

Symmetric matrix-example

The trace of the sum of two matrices

The trace of the sum of two matrices

Young inequality-trivial case.

Young inequality-trivial case.

The derivative of the identity function.

The derivative of the identity function.

The derivative of f(x) =x^2.

The derivative of f(x) =x^2.

The derivative of a constant function.

The derivative of a constant function.

Triangle type inequality for integrals.

Triangle type inequality for integrals.

Proving inequalities-exercise 1

Proving inequalities-exercise 1

Laplace transform of the convolution of two functions.

Laplace transform of the convolution of two functions.

Hyperbolic and trigonometric functions-How are they associated?

Hyperbolic and trigonometric functions-How are they associated?

Double integration-example 1.

Double integration-example 1.