Канал: Dr. Bevin Maultsby

The Jacobian Matrix, Real Analysis II

The Jacobian Matrix, Real Analysis II

If f is differentiable, then f is continuous and a little more, Real Analysis II

If f is differentiable, then f is continuous and a little more, Real Analysis II

The Definition of Differentiability (Introduction and Example), Real Analysis II

The Definition of Differentiability (Introduction and Example), Real Analysis II

Review of Linear Transformations T: R^n to R^m

Review of Linear Transformations T: R^n to R^m

Proofs of the Extreme and Intermediate Value Theorems, Real Analysis II

Proofs of the Extreme and Intermediate Value Theorems, Real Analysis II

Continuous functions on compact sets, Real Analysis II

Continuous functions on compact sets, Real Analysis II

Continuous functions on path connected and connected sets, Real Analysis II

Continuous functions on path connected and connected sets, Real Analysis II

A continuous function on a compact set has compact image, Real Analysis II

A continuous function on a compact set has compact image, Real Analysis II

Combinations of Continuous Functions, Real Analysis II

Combinations of Continuous Functions, Real Analysis II

Four characterizations of continuity for a function, Real Analysis II

Four characterizations of continuity for a function, Real Analysis II

Functional Limits and Continuity , Real Analysis II

Functional Limits and Continuity , Real Analysis II

Connected and Path Connected Sets, Real Analysis II

Connected and Path Connected Sets, Real Analysis II

Integrate cos(x)^100 with integration by parts, Calculus

Integrate cos(x)^100 with integration by parts, Calculus

Heine Borel and the completeness of Rn (Consequences of Bolzano Weierstrass), Real Analysis II

Heine Borel and the completeness of Rn (Consequences of Bolzano Weierstrass), Real Analysis II

Example arc length computation with calculus

Example arc length computation with calculus

Nested Compact Set Theorem, Real Analysis I and II

Nested Compact Set Theorem, Real Analysis I and II

Compact iff Sequentially Compact full proof, Real Analysis II

Compact iff Sequentially Compact full proof, Real Analysis II

Compact Sets and Open Covers, Real Analysis II

Compact Sets and Open Covers, Real Analysis II

Sequentially compact sets and totally bounded sets, Real Analysis II

Sequentially compact sets and totally bounded sets, Real Analysis II

Cauchy sequences and complete metric spaces, Real Analysis II

Cauchy sequences and complete metric spaces, Real Analysis II

Sequences and closed sets, Real Analysis II

Sequences and closed sets, Real Analysis II

Sequences in a metric space, Real Analysis II

Sequences in a metric space, Real Analysis II

Integrate e^(-x^2) using a double integral, Multivariable Calculus

Integrate e^(-x^2) using a double integral, Multivariable Calculus

Boundary of a set in a metric space, Real Analysis II

Boundary of a set in a metric space, Real Analysis II

Closure of a set, Real Analysis II

Closure of a set, Real Analysis II

Accumulation Points aka Limit Points, Real Analysis II

Accumulation Points aka Limit Points, Real Analysis II

Closed sets in a metric space, Real Analysis II

Closed sets in a metric space, Real Analysis II

Interior of a set in a metric space, Real Analysis II

Interior of a set in a metric space, Real Analysis II

Unions and intersections of open sets, Real Analysis II

Unions and intersections of open sets, Real Analysis II

Open sets in a metric space (M,d), with examples, Real Analysis II

Open sets in a metric space (M,d), with examples, Real Analysis II

Metric Spaces Introduction, Real Analysis II

Metric Spaces Introduction, Real Analysis II

Norms, lp norms, and the sup norm, Real Analysis II

Norms, lp norms, and the sup norm, Real Analysis II

Integrate ln(x)^1000, Integral Calculus Problem

Integrate ln(x)^1000, Integral Calculus Problem

Inner Product Spaces and Cauchy Schwarz, Real Analysis II

Inner Product Spaces and Cauchy Schwarz, Real Analysis II

Introduction to inner product, norm, and metric on Rn, Real Analysis II

Introduction to inner product, norm, and metric on Rn, Real Analysis II

Flux across a hemisphere, with and without the Divergence Theorem, Multivariable Calculus

Flux across a hemisphere, with and without the Divergence Theorem, Multivariable Calculus

Intersection of two planes: the line and the angle, Multivariable Calculus

Intersection of two planes: the line and the angle, Multivariable Calculus

Line integral along a plane and sphere intersection, with Stokes and without

Line integral along a plane and sphere intersection, with Stokes and without

Integration with residue calculus example with order 2, Complex Analysis

Integration with residue calculus example with order 2, Complex Analysis

Calculating residues at simple poles, Complex Analysis

Calculating residues at simple poles, Complex Analysis

Residue calculus integration example with simple poles, Complex Analysis

Residue calculus integration example with simple poles, Complex Analysis

Why is the tan function called tangent?

Why is the tan function called tangent?

Compute T, N, and B for a parameterized curve, Multivariable Calculus

Compute T, N, and B for a parameterized curve, Multivariable Calculus

Prove the double angle identities using Euler's formula

Prove the double angle identities using Euler's formula

Projectile motion: optimal angle, landing time and location in Multivariable Calculus

Projectile motion: optimal angle, landing time and location in Multivariable Calculus

Laplace Transforms 12: Dirac Delta Examples

Laplace Transforms 12: Dirac Delta Examples

Laplace Transforms 11: The Dirac Delta (Unit Impulse)

Laplace Transforms 11: The Dirac Delta (Unit Impulse)

Work done pulling a rope to the top of a building

Work done pulling a rope to the top of a building

SIR Model for Epidemiology, Ordinary Differential Equations

SIR Model for Epidemiology, Ordinary Differential Equations

Euler's Method for a system of differential equations

Euler's Method for a system of differential equations

Buffon's needle problem to estimate pi, explained

Buffon's needle problem to estimate pi, explained

Linearization in Mathematica, Multivariable Calculus

Linearization in Mathematica, Multivariable Calculus

Example finding the osculating circle, Multivariable Calculus

Example finding the osculating circle, Multivariable Calculus

Implicit Differentiation in Mathematica

Implicit Differentiation in Mathematica

Osculating plane and circle, Multivariable Calculus

Osculating plane and circle, Multivariable Calculus

Newton's Method to find roots

Newton's Method to find roots

Laplace Transforms 7: Example with resonance y'' + 4y = cos(2t)

Laplace Transforms 7: Example with resonance y'' + 4y = cos(2t)

Least Squares Method Part 2: residuals, setting up your model, examples

Least Squares Method Part 2: residuals, setting up your model, examples

Least Squares Method Part 1: background and derivation, with examples

Least Squares Method Part 1: background and derivation, with examples

Laplace Transforms 9: Introduction to the Heaviside (unit step) function

Laplace Transforms 9: Introduction to the Heaviside (unit step) function

Laplace Transforms 10: Examples with the Heaviside Function

Laplace Transforms 10: Examples with the Heaviside Function

Laplace Transforms 8: The complex frequency domain for s

Laplace Transforms 8: The complex frequency domain for s

Linking WebAssign to Moodle with the Cengage external tool

Linking WebAssign to Moodle with the Cengage external tool

Surface Integrals: Why 'r' Isn't Needed When Parametrizing with Polar Coordinates

Surface Integrals: Why 'r' Isn't Needed When Parametrizing with Polar Coordinates

Which is bigger? e^pi vs pi^e, a quick solution

Which is bigger? e^pi vs pi^e, a quick solution

Tangent Plane and Normal Line using a gradient, Multivariable Calculus

Tangent Plane and Normal Line using a gradient, Multivariable Calculus

Multivariable Calculus: Find the point on the sphere closest to a plane

Multivariable Calculus: Find the point on the sphere closest to a plane

Multivariable Calculus: Parameterize the curve of intersection

Multivariable Calculus: Parameterize the curve of intersection

Multivariable Calculus: Distance from a point to a plane

Multivariable Calculus: Distance from a point to a plane

Laplace Transforms 6: F(s-a), translation in s

Laplace Transforms 6: F(s-a), translation in s

Laplace Transforms 5: Example 2y'' + 3y' + y = e^(4t)

Laplace Transforms 5: Example 2y'' + 3y' + y = e^(4t)

One flux example two ways: using Stokes' and the Divergence Theorem

One flux example two ways: using Stokes' and the Divergence Theorem

How to Easily Remember Cosine and Sine Values for Unit Circle Angles

How to Easily Remember Cosine and Sine Values for Unit Circle Angles

Laplace Transforms 4: cosine and sine with Euler's formula

Laplace Transforms 4: cosine and sine with Euler's formula

Laplace Transforms 3: The Laplace transform of t^n

Laplace Transforms 3: The Laplace transform of t^n

Laplace Transforms 2: The Laplace transform of exponential functions e^(at)

Laplace Transforms 2: The Laplace transform of exponential functions e^(at)

Laplace Transforms 1: definition and properties

Laplace Transforms 1: definition and properties

Example using Green's Theorem to compute a circulation integral

Example using Green's Theorem to compute a circulation integral

Second order differential equation for spring-mass systems

Second order differential equation for spring-mass systems

How to set up a scalar line integral, Multivariable Calculus

How to set up a scalar line integral, Multivariable Calculus

Average value with polar coordinates example, Multivariable Calculus

Average value with polar coordinates example, Multivariable Calculus

Euler's Formula for the complex exponential

Euler's Formula for the complex exponential

Trig Sub: Integration with Trigonometric Substitution 1, Single Variable Calculus

Trig Sub: Integration with Trigonometric Substitution 1, Single Variable Calculus

Method of Undetermined Coefficients 4, extra examples

Method of Undetermined Coefficients 4, extra examples

Method of Undetermined Coefficients 1, with example of exponential forcing

Method of Undetermined Coefficients 1, with example of exponential forcing

Method of Undetermined Coefficients 3, examples with trigonometric forcing

Method of Undetermined Coefficients 3, examples with trigonometric forcing

Method of Undetermined Coefficients 2, examples with polynomial forcing

Method of Undetermined Coefficients 2, examples with polynomial forcing

Tank Mixing Problems

Tank Mixing Problems

Euler's method for first-order ordinary differential equations

Euler's method for first-order ordinary differential equations

Integrating sec^3(x)

Integrating sec^3(x)

Complex roots: Linear second order differential equations

Complex roots: Linear second order differential equations

Pure imaginary roots: Linear second order differential equations

Pure imaginary roots: Linear second order differential equations

One repeated root: Linear second order differential equations

One repeated root: Linear second order differential equations

Introduction to Linear Second Order Differential Equations

Introduction to Linear Second Order Differential Equations

Real and distinct roots: Linear second order differential equations

Real and distinct roots: Linear second order differential equations

Separable differential equations example: Newton's law of cooling

Separable differential equations example: Newton's law of cooling

Using separable differential equations to find orthogonal trajectories

Using separable differential equations to find orthogonal trajectories

Separable Differential Equations with four examples

Separable Differential Equations with four examples

Slope fields for first-order ordinary differential equations

Slope fields for first-order ordinary differential equations

Introduction to Ordinary Differential Equations

Introduction to Ordinary Differential Equations

Work pumping fluid from a tank (with many examples), Single Variable Calculus

Work pumping fluid from a tank (with many examples), Single Variable Calculus

Hooke's Law and work done moving a spring, Single Variable Calculus

Hooke's Law and work done moving a spring, Single Variable Calculus

Force and Work (lifting problems), Single Variable Calculus

Force and Work (lifting problems), Single Variable Calculus

Average value of a function, Single Variable Calculus

Average value of a function, Single Variable Calculus

Single Variable Calculus: Arc length

Single Variable Calculus: Arc length

Taylor series for sin(x) and cos(x), Single Variable Calculus

Taylor series for sin(x) and cos(x), Single Variable Calculus

Taylor series for e^x, Single Variable Calculus

Taylor series for e^x, Single Variable Calculus

Taylor series for ln(1+x), Single Variable Calculus

Taylor series for ln(1+x), Single Variable Calculus

Taylor Series Coefficients, Single Variable Calculus

Taylor Series Coefficients, Single Variable Calculus

Power Series for arctan(x), Single Variable Calculus

Power Series for arctan(x), Single Variable Calculus

Integrating Power Series, Single Variable Calculus

Integrating Power Series, Single Variable Calculus

Representing functions as power series, Single Variable Calculus

Representing functions as power series, Single Variable Calculus

Differentiating Power Series, Single Variable Calculus

Differentiating Power Series, Single Variable Calculus

Finding the radius R of convergence for a power series, Single Variable Calculus

Finding the radius R of convergence for a power series, Single Variable Calculus

Power Series Interval of Convergence, Single Variable Calculus

Power Series Interval of Convergence, Single Variable Calculus

Introduction to Power Series, Single Variable Calculus

Introduction to Power Series, Single Variable Calculus

Absolute Convergence and the Ratio Test for series with lots of examples, Single Variable Calculus

Absolute Convergence and the Ratio Test for series with lots of examples, Single Variable Calculus

Alternating Series Test (AST) for Infinite Series, Single Variable Calculus

Alternating Series Test (AST) for Infinite Series, Single Variable Calculus

Limit Comparison Test (LCT) for Series, Single Variable Calculus

Limit Comparison Test (LCT) for Series, Single Variable Calculus

The (Ordinary) Comparison Test for Series (OCT), Single Variable Calculus

The (Ordinary) Comparison Test for Series (OCT), Single Variable Calculus

Integral Test for infinite series and p-series, Single Variable Calculus

Integral Test for infinite series and p-series, Single Variable Calculus

Geometric Series, Single Variable Calculus

Geometric Series, Single Variable Calculus

Test for Divergence for Infinite Series, Single Variable Calculus

Test for Divergence for Infinite Series, Single Variable Calculus

Introduction to infinite series, Single Variable Calculus

Introduction to infinite series, Single Variable Calculus

Proof of the Directional Derivative Formula, Real Analysis

Proof of the Directional Derivative Formula, Real Analysis

Monotone Convergence Theorem

Monotone Convergence Theorem

Theorems about the limits of sequences, Single Variable Calculus

Theorems about the limits of sequences, Single Variable Calculus

Convergent Sequences, Single Variable Calculus

Convergent Sequences, Single Variable Calculus

Introduction to Sequences, Single Variable Calculus

Introduction to Sequences, Single Variable Calculus

The imaginary number i and complex numbers

The imaginary number i and complex numbers

Improper Integrals 3 (vertical asymptotes), Single Variable Calculus

Improper Integrals 3 (vertical asymptotes), Single Variable Calculus

Improper Integrals 2 (from -infinity to infinity), Single Variable Calculus

Improper Integrals 2 (from -infinity to infinity), Single Variable Calculus

Improper Integrals, Single Variable Calculus

Improper Integrals, Single Variable Calculus

Integration with Partial Fractions 1, Single Variable Calculus

Integration with Partial Fractions 1, Single Variable Calculus

Integration with Partial Fractions 2, Single Variable Calculus

Integration with Partial Fractions 2, Single Variable Calculus

Simpson's Rule, Single Variable Calculus

Simpson's Rule, Single Variable Calculus

Simpson's Rule MATLAB Supplement, Single Variable Calculus

Simpson's Rule MATLAB Supplement, Single Variable Calculus

Example finding the osculating plane and TNB, Multivariable Calculus

Example finding the osculating plane and TNB, Multivariable Calculus

Trapezoidal Rule MATLAB Supplement, Single Variable Calculus

Trapezoidal Rule MATLAB Supplement, Single Variable Calculus

Trapezoidal Rule, Single Variable Calculus

Trapezoidal Rule, Single Variable Calculus

Inverse Trigonometric Functions Review

Inverse Trigonometric Functions Review

Trig Sub: Integration with Trigonometric Substitution 2, Single Variable Calculus

Trig Sub: Integration with Trigonometric Substitution 2, Single Variable Calculus

Trigonometric Integrals 1 (sines and cosines), Single Variable Calculus

Trigonometric Integrals 1 (sines and cosines), Single Variable Calculus

How to integrate tan^2(x) and sec(x)

How to integrate tan^2(x) and sec(x)

Trigonometric Integrals 2 (secants and tangents), Single Variable Calculus

Trigonometric Integrals 2 (secants and tangents), Single Variable Calculus

Center of Mass, Single Variable Calculus

Center of Mass, Single Variable Calculus

Hydrostatic pressure and force, Single Variable Calculus

Hydrostatic pressure and force, Single Variable Calculus

Single Variable Calculus: Integration by parts examples

Single Variable Calculus: Integration by parts examples

Six examples of u substitution, Single Variable Calculus

Six examples of u substitution, Single Variable Calculus

The limit of sin(x)/x as x goes to 0

The limit of sin(x)/x as x goes to 0

Differential equation for the logistic model

Differential equation for the logistic model

Differential equation for exponential growth dP/dt = kP

Differential equation for exponential growth dP/dt = kP

Example of a flux integral, Multivariable Calculus

Example of a flux integral, Multivariable Calculus

Example computing surface area with a surface integral, Multivariable Calculus

Example computing surface area with a surface integral, Multivariable Calculus

Examples of scalar and vector line integrals, Multivariable Calculus

Examples of scalar and vector line integrals, Multivariable Calculus

Computing a volume with double and triple integrals, Multivariable Calculus

Computing a volume with double and triple integrals, Multivariable Calculus

Double integral in polar example, Multivariable Calculus

Double integral in polar example, Multivariable Calculus

Green's Theorem Example, Multivariable Calculus

Green's Theorem Example, Multivariable Calculus

Spherical Integration Example, Multivariable Calculus

Spherical Integration Example, Multivariable Calculus

Areas between circles with double integrals, Multivariable Calculus

Areas between circles with double integrals, Multivariable Calculus

Stability: Sinks, Sources, and Nodes in Differential Equations

Stability: Sinks, Sources, and Nodes in Differential Equations

Modeling Predator-Prey Dynamics with Lotka-Volterra Equations, Part 2

Modeling Predator-Prey Dynamics with Lotka-Volterra Equations, Part 2

The (Discrete) Logistic Map for population modeling

The (Discrete) Logistic Map for population modeling

The Power of Log-Log Plots

The Power of Log-Log Plots

Bifurcations and bifurcation diagrams

Bifurcations and bifurcation diagrams

Difference Equations in Mathematics

Difference Equations in Mathematics

The Rule of 72 for doubling time for compounded interest

The Rule of 72 for doubling time for compounded interest

Modeling closed populations with a differential equation

Modeling closed populations with a differential equation

Intro to Math Modeling: The Logistic Model

Intro to Math Modeling: The Logistic Model

Supply and Demand Mathematics: Cobweb Diagrams and Difference Equations

Supply and Demand Mathematics: Cobweb Diagrams and Difference Equations

Equilibrium Solutions and Phase Lines in Differential Equations

Equilibrium Solutions and Phase Lines in Differential Equations

Mathematical modeling using proportionality

Mathematical modeling using proportionality

Intro to Math Modeling: More about exponential growth

Intro to Math Modeling: More about exponential growth

Mathematical modeling with dimensional analysis

Mathematical modeling with dimensional analysis

Modeling Predator-Prey Dynamics with Lotka-Volterra Equations, Part 1

Modeling Predator-Prey Dynamics with Lotka-Volterra Equations, Part 1

Markov Chains and Transition Matrices

Markov Chains and Transition Matrices

Transition matrices: computing probability and making long-term predictions

Transition matrices: computing probability and making long-term predictions

Multivariable Calculus: Quick right-hand rule demo

Multivariable Calculus: Quick right-hand rule demo

Tangent Planes in Multivariable Calculus

Tangent Planes in Multivariable Calculus

Conservation of Energy, Multivariable Calculus

Conservation of Energy, Multivariable Calculus

Conservative Vector Fields, Multivariable Calculus

Conservative Vector Fields, Multivariable Calculus

Gradients and Tangent Planes, Multivariable Calculus

Gradients and Tangent Planes, Multivariable Calculus

Multivariable Calculus Unit 1 Lecture 02: Five examples in R3

Multivariable Calculus Unit 1 Lecture 02: Five examples in R3

The decomposition of acceleration in Multivariable Calculus

The decomposition of acceleration in Multivariable Calculus

Examples with T, N, B, κ and the osculating circle, Multivariable Calculus

Examples with T, N, B, κ and the osculating circle, Multivariable Calculus

Applications of triple integrals, Multivariable Calculus Unit 4 Lecture 6

Applications of triple integrals, Multivariable Calculus Unit 4 Lecture 6

Multivariable Calculus: Work

Multivariable Calculus: Work

Examples of integrating with polar coordinates, Multivariable Calculus

Examples of integrating with polar coordinates, Multivariable Calculus

Introduction to line integrals, Multivariable Calculus

Introduction to line integrals, Multivariable Calculus

Multivariable Calculus Unit 3 Lecture 10: General definition of differentiability

Multivariable Calculus Unit 3 Lecture 10: General definition of differentiability

Multivariable Calculus: Calculus on vector-valued functions (Curves)

Multivariable Calculus: Calculus on vector-valued functions (Curves)

Curl and divergence of a vector field, Multivariable Calculus

Curl and divergence of a vector field, Multivariable Calculus

Spherical coordinates integration examples

Spherical coordinates integration examples

Multivariable Calculus: Newton's second law and projectile motion

Multivariable Calculus: Newton's second law and projectile motion

Scalar line integrals, Multivariable Calculus

Scalar line integrals, Multivariable Calculus

Optimization over bounded regions, Multivariable Calculus

Optimization over bounded regions, Multivariable Calculus

Scalar line integrals practice and properties, Multivariable Calculus

Scalar line integrals practice and properties, Multivariable Calculus

Multivariable Optimization

Multivariable Optimization

Multivariable Calculus: Curvature κ(t) for a parametrized curve

Multivariable Calculus: Curvature κ(t) for a parametrized curve

Vector Equation of a Plane and General Form, Multivariable Calculus

Vector Equation of a Plane and General Form, Multivariable Calculus