Канал: KeysToMaths

Greatest Common Divisor Proofs

Greatest Common Divisor Proofs

Proof of Euclid's Division Lemma

Proof of Euclid's Division Lemma

Loop Analysis Example

Loop Analysis Example

Negative Feedback Loop and Initial and Final Value Theorems

Negative Feedback Loop and Initial and Final Value Theorems

Transfer Function, Time Constant and Initial and Final value Theorems

Transfer Function, Time Constant and Initial and Final value Theorems

Laplace Transforms - Differential Equation Solution

Laplace Transforms - Differential Equation Solution

Z Transform Properties - Right Shift Theorems

Z Transform Properties - Right Shift Theorems

Z Transforms - Left Shift Theorems

Z Transforms - Left Shift Theorems

Z Transforms - First Order Difference Equations

Z Transforms - First Order Difference Equations

Z Transforms and Second Order Difference Equations - Fibonacci Sequence

Z Transforms and Second Order Difference Equations - Fibonacci Sequence

Z Transforms - Unit Impulse and Geometric Sequences

Z Transforms - Unit Impulse and Geometric Sequences

Z Transforms - Linearity Property, Hyperbolic and Trigonometric Functions

Z Transforms - Linearity Property, Hyperbolic and Trigonometric Functions

Z Transform Properties - Multiplication of a Sequence by the Ramp and Geometric Sequences

Z Transform Properties - Multiplication of a Sequence by the Ramp and Geometric Sequences

ANOVA Example

ANOVA Example

Uniform Circular Motion - Geometrical Derivation of Centripetal Acceleration

Uniform Circular Motion - Geometrical Derivation of Centripetal Acceleration

Triple Integration - The Centre of Mass of a Tetrahedron

Triple Integration - The Centre of Mass of a Tetrahedron

Triple Integration - Volume of a Curved region

Triple Integration - Volume of a Curved region

Triple Integration - Volume of a Triangular Prism

Triple Integration - Volume of a Triangular Prism

Triple Integration - Introduction and Example

Triple Integration - Introduction and Example

Double Integration using Polar Coordinates

Double Integration using Polar Coordinates

Double Integration and the order of integration

Double Integration and the order of integration

Double Integration over Non - Rectangular Regions 2

Double Integration over Non - Rectangular Regions 2

Double Integration over Non - Rectangular Regions 1

Double Integration over Non - Rectangular Regions 1

Double Integration - Centre of Pressure Derivation and Example

Double Integration - Centre of Pressure Derivation and Example

Double Integration - Introduction and Examples

Double Integration - Introduction and Examples

Double Integration - Order of Integration

Double Integration - Order of Integration

Double Integration - Examples

Double Integration - Examples

Convolution Example using Graphs

Convolution Example using Graphs

The Mean Value Theorem with Proof

The Mean Value Theorem with Proof

The Extreme Value Theorem

The Extreme Value Theorem

Rolle's Theorem with Proof

Rolle's Theorem with Proof

Fermat's Theorem with Proof

Fermat's Theorem with Proof

The Squeeze Theorem with Proof

The Squeeze Theorem with Proof

Continuity

Continuity

Continuity and the Composition of 2 Functions

Continuity and the Composition of 2 Functions

The Limit of a Function (Examples)

The Limit of a Function (Examples)

One - Sided Limits

One - Sided Limits

The Limit of a Sum of Functions

The Limit of a Sum of Functions

The Limit of a Quotient of Functions

The Limit of a Quotient of Functions

The Maximum Error of f(x,y)

The Maximum Error of f(x,y)

The Error (delta f) of the function f(x,y)

The Error (delta f) of the function f(x,y)

Error in Power to a Load Resistance

Error in Power to a Load Resistance

The Differential df (or dz) for the function z = f(x,y)

The Differential df (or dz) for the function z = f(x,y)

Classification of Stationary Points

Classification of Stationary Points

The Surface of a Paraboloid

The Surface of a Paraboloid

The Plane

The Plane

Stationary Points

Stationary Points

Stationary Points (Continued)

Stationary Points (Continued)

Proof of Clairault's Theorem for Mixed Partial Derivatives

Proof of Clairault's Theorem for Mixed Partial Derivatives

Limit Definition of First and Mixed Partial Derivatives

Limit Definition of First and Mixed Partial Derivatives

Second Partial Derivatives

Second Partial Derivatives

Partial Derivatives

Partial Derivatives

The Vector Equation of a plane

The Vector Equation of a plane

The Vector Equation of a Line

The Vector Equation of a Line

Direction Cosines

Direction Cosines

Vector Product Examples

Vector Product Examples

The Vector Product - Area of a Triangle and Moment of a Force

The Vector Product - Area of a Triangle and Moment of a Force

The Vector or Cross Product

The Vector or Cross Product

Field due to Point Charges on a Cube

Field due to Point Charges on a Cube

The Scalar or Dot product 2 - Resolving Vectors and the Angle between Vectors

The Scalar or Dot product 2 - Resolving Vectors and the Angle between Vectors

The Distributive Law for Scalar Multiplication - Proof for 2D vectors

The Distributive Law for Scalar Multiplication - Proof for 2D vectors

Vector Examples - Scalar Product, Angle between vectors and Work

Vector Examples - Scalar Product, Angle between vectors and Work

Work done by the Electrostatic Force

Work done by the Electrostatic Force

Vectors and Coulomb's Law

Vectors and Coulomb's Law

Field due to Point Charges on a Cube (continued)

Field due to Point Charges on a Cube (continued)

Field due to Point Charges - Example

Field due to Point Charges - Example

The Force Vectors on an Aeroplane in Steady Flight

The Force Vectors on an Aeroplane in Steady Flight

Vectors - Radar Gun Example

Vectors - Radar Gun Example

Vectors - Basic Concepts 1

Vectors - Basic Concepts 1

The Scalar or Dot product 1

The Scalar or Dot product 1

Three Dimensional Coordinate Frames

Three Dimensional Coordinate Frames

Two dimensional Coordinate Frames

Two dimensional Coordinate Frames

Vectors - Basic Concepts 2

Vectors - Basic Concepts 2

Bilinear Transformations

Bilinear Transformations

The Inversion Mapping of a Line

The Inversion Mapping of a Line

Proof of the Conformal Mapping Theorem

Proof of the Conformal Mapping Theorem

Conformal Mappings 2

Conformal Mappings 2

Analytic and Harmonic Functions - Examples

Analytic and Harmonic Functions - Examples

Conformal Mappings 1

Conformal Mappings 1

Analytic Functions and Harmonic Functions

Analytic Functions and Harmonic Functions

The Cauchy Riemann Equations 2

The Cauchy Riemann Equations 2

The Cauchy Riemann Equations 1

The Cauchy Riemann Equations 1

Differentiating Functions of a Complex Variable

Differentiating Functions of a Complex Variable

Limits and Continuity

Limits and Continuity

Functions of a Complex Variable

Functions of a Complex Variable

Water Wheel Efficiency

Water Wheel Efficiency

Vector Differentiation - Uniform Circular Motion

Vector Differentiation - Uniform Circular Motion

$The Principle of Least Time - Refraction$

The Principle of Least Time - Refraction

The curvature of a function

The curvature of a function

The curvature of a function - Examples

The curvature of a function - Examples

Tangents and Normals to Curves

Tangents and Normals to Curves

Newton Raphson Method Examples

Newton Raphson Method Examples

Newton - Raphson Method Derivation

Newton - Raphson Method Derivation

Maxima and Minima 2

Maxima and Minima 2

Maxima and Minima 1

Maxima and Minima 1

Maxima and Minima - Area Example

Maxima and Minima - Area Example

Fluid Power Transmission

Fluid Power Transmission

Equivalent Resistance in an Electrical Circuit

Equivalent Resistance in an Electrical Circuit

Differentiation of Vector Functions

Differentiation of Vector Functions

Crank used to drive a Piston 2

Crank used to drive a Piston 2

Crank used to drive a Piston

Crank used to drive a Piston

Complex Impedance

Complex Impedance

Buckling Load Example

Buckling Load Example

Centre of mass of a collection of point masses

Centre of mass of a collection of point masses

Integration of Vectors - Trajectory Solution

Integration of Vectors - Trajectory Solution

The Capstan Friction Equation

The Capstan Friction Equation

Areas of Surfaces of Revolution

Areas of Surfaces of Revolution

Length of a Curve

Length of a Curve

Volumes of Revolution

Volumes of Revolution

The Integral as the Limit of a Sum - Area under a Curve

The Integral as the Limit of a Sum - Area under a Curve

Mean and Root Mean Square Value of a Function

Mean and Root Mean Square Value of a Function

The Perpendicular Axis Theorem

The Perpendicular Axis Theorem

The Parallel Axis Theorem

The Parallel Axis Theorem

The Moment of Inertia of a thin Uniform Rod

The Moment of Inertia of a thin Uniform Rod

The Moment of Inertia of a Circular lamina about the Centre

The Moment of Inertia of a Circular lamina about the Centre

The Moment of Inertia of a Uniform Square Lamina

The Moment of Inertia of a Uniform Square Lamina

Suspended Cable Example

Suspended Cable Example

The Centre of Mass of a Uniform Semi-Circular Lamina

The Centre of Mass of a Uniform Semi-Circular Lamina

The Centre of Mass of a Uniform Triangular Lamina 2

The Centre of Mass of a Uniform Triangular Lamina 2

The Centre of Mass of a Uniform Triangular Lamina 1

The Centre of Mass of a Uniform Triangular Lamina 1

Convolution - Examples including Inverse Laplace Transforms

Convolution - Examples including Inverse Laplace Transforms

Transfer Functions

Transfer Functions

Convolution 2

Convolution 2

Convolution 1

Convolution 1

LCR Circuit

LCR Circuit

Coupled Oscillators

Coupled Oscillators

RL circuit

RL circuit

Systems of differential Equations

Systems of differential Equations

Damped Spring with Unit Impulse

Damped Spring with Unit Impulse

Second Order Differential Equations

Second Order Differential Equations

Laplace Transforms and Differential Equations

Laplace Transforms and Differential Equations

Laplace Transform of the Delta Function

Laplace Transform of the Delta Function

Free Mechanical Oscillations - Heavy Damping

Free Mechanical Oscillations - Heavy Damping

Free Mechanical Oscillations - Light and Critical Damping

Free Mechanical Oscillations - Light and Critical Damping

Free Mechanical Oscillations

Free Mechanical Oscillations

LR circuit - Integrating Factor Method

LR circuit - Integrating Factor Method

Dissolving Spherical Pill Example

Dissolving Spherical Pill Example

Second Order Linear Differential Equations 4 - Non-Homogeneous Equations

Second Order Linear Differential Equations 4 - Non-Homogeneous Equations

Second Order Linear Differential Equations 3 - Equal Roots

Second Order Linear Differential Equations 3 - Equal Roots

Second Order Linear Differential Equations 2 - Complex Roots

Second Order Linear Differential Equations 2 - Complex Roots

RC circuit with a single frequency input

RC circuit with a single frequency input

Second Order Linear Differential Equations 1

Second Order Linear Differential Equations 1

Integrating Factor Method - Proof and Examples

Integrating Factor Method - Proof and Examples

Integrating Factor Method Example - LR circuit

Integrating Factor Method Example - LR circuit

Exact Differential Equations

Exact Differential Equations

Separable Differential Equations

Separable Differential Equations

Differential Equations - Basic Concepts

Differential Equations - Basic Concepts

Differential Equation Example - Newton's Law of Cooling

Differential Equation Example - Newton's Law of Cooling

Laplace Transforms - The Second Shift Theorem

Laplace Transforms - The Second Shift Theorem

Laplace Transforms of Derivatives

Laplace Transforms of Derivatives

Proof of the Sifting Property and Example of the Delta Function

Proof of the Sifting Property and Example of the Delta Function

The Delta Function

The Delta Function

Inverse Laplace Transforms Examples 1

Inverse Laplace Transforms Examples 1

Inverse Laplace Transform Examples 2

Inverse Laplace Transform Examples 2

Laplace Transforms - The First Shift Theorem

Laplace Transforms - The First Shift Theorem

Laplace Transforms - Example using The First Shift Theorem

Laplace Transforms - Example using The First Shift Theorem

Causal Functions including the unit step function U(t)

Causal Functions including the unit step function U(t)

Laplace Transforms of U(t), e^(-at) and Sinh(at)

Laplace Transforms of U(t), e^(-at) and Sinh(at)

Laplace Transform of U(t-a) and Examples

Laplace Transform of U(t-a) and Examples

Laplace Transform of t^n where n is a natural number

Laplace Transform of t^n where n is a natural number

Laplace Transforms and Unit Step Functions

Laplace Transforms and Unit Step Functions

The graphs of sin(t-2).u(t-2) and (u(t-1) - u(t-2)) e^t

The graphs of sin(t-2).u(t-2) and (u(t-1) - u(t-2)) e^t

Inverse Laplace Transforms

Inverse Laplace Transforms

Logic - Proving statements using the logical equivalences table

Logic - Proving statements using the logical equivalences table

Sets - Examples, Cartesian Product and Cardinality

Sets - Examples, Cartesian Product and Cardinality

Sets - Proofs of Set Statements by the subset method and by using the laws of set theory

Sets - Proofs of Set Statements by the subset method and by using the laws of set theory

Sets - Proofs of the laws of sets

Sets - Proofs of the laws of sets

Logic - Proofs of Logical Equivalences

Logic - Proofs of Logical Equivalences

Logic and truth table examples 3

Logic and truth table examples 3

Logic and truth table examples 2

Logic and truth table examples 2

Logic and truth table examples 1

Logic and truth table examples 1

Differential Equations - Flow Problem (Solving the Differential Equation)

Differential Equations - Flow Problem (Solving the Differential Equation)

Differential Equations - Flow Problem (Setting up the differential Equation)

Differential Equations - Flow Problem (Setting up the differential Equation)