Канал: Kevin Cassel

Finite-Element Method

Finite-Element Method

Spectral Numerical Method

Spectral Numerical Method

Finite-Volume Method

Finite-Volume Method

Numerical Modeling of Turbulent Flows - Reynolds Averaged Navier-Stokes (RANS)

Numerical Modeling of Turbulent Flows - Reynolds Averaged Navier-Stokes (RANS)

Numerical Modeling of Turbulent Flows - Large-Eddy Simulation (LES)

Numerical Modeling of Turbulent Flows - Large-Eddy Simulation (LES)

Numerical Modeling of Turbulent Flows - Introduction and Direct Numerical Simulation (DNS)

Numerical Modeling of Turbulent Flows - Introduction and Direct Numerical Simulation (DNS)

Numerical Solutions of Coupled Partial Differential Equations

Numerical Solutions of Coupled Partial Differential Equations

Conservation Form of the Navier-Stokes Equations

Conservation Form of the Navier-Stokes Equations

Boundary Conditions for Vorticity-Streamfunction Formulation of the Navier-Stokes Equations

Boundary Conditions for Vorticity-Streamfunction Formulation of the Navier-Stokes Equations

Vorticity-Streamfunction Formulation of the Navier-Stokes Equations

Vorticity-Streamfunction Formulation of the Navier-Stokes Equations

Primitive Variables Formulation of the Navier-Stokes Equations

Primitive Variables Formulation of the Navier-Stokes Equations

Parabolic Equations - Factored ADI Method

Parabolic Equations - Factored ADI Method

Parabolic Equations - Fractional-Step Method

Parabolic Equations - Fractional-Step Method

Parabolic Equations - First-Order Methods for Multdimensional Problems

Parabolic Equations - First-Order Methods for Multdimensional Problems

Parabolic Equations - Upwind-Downwind Differencing of Nonlinear Convective Terms

Parabolic Equations - Upwind-Downwind Differencing of Nonlinear Convective Terms

Parabolic Equations - Nonlinear Convective Terms

Parabolic Equations - Nonlinear Convective Terms

Parabolic Equations - Implicit Methods

Parabolic Equations - Implicit Methods

Parabolic Equations - Numerical Stability Analysis Using von Neumann Method

Parabolic Equations - Numerical Stability Analysis Using von Neumann Method

Parabolic Equations - Numerical Stability Analysis Using Matrix Method

Parabolic Equations - Numerical Stability Analysis Using Matrix Method

Parabolic Equations - Explicit Methods

Parabolic Equations - Explicit Methods

Parabolic Equations - Introduction

Parabolic Equations - Introduction

Picard and Newton Linearization of Nonlinear Partial Differential Equations

Picard and Newton Linearization of Nonlinear Partial Differential Equations

Elliptic Equations - Multigrid Methodology 3

Elliptic Equations - Multigrid Methodology 3

Elliptic Equations - Multigrid Methodology 2

Elliptic Equations - Multigrid Methodology 2

Elliptic Equations - Multigrid Methodology 1

Elliptic Equations - Multigrid Methodology 1

Elliptic Equations - Multigrid Motivation

Elliptic Equations - Multigrid Motivation

Elliptic Equations - Alternating-Direction-Implicit (ADI) Method

Elliptic Equations - Alternating-Direction-Implicit (ADI) Method

Elliptic Equations - Boundary Conditions in Iterative Methods

Elliptic Equations - Boundary Conditions in Iterative Methods

Elliptic Equations - Successive Over-Relaxation (SOR)

Elliptic Equations - Successive Over-Relaxation (SOR)

Elliptic Equations - Jacobi and Gauss-Seidel Iterative Methods

Elliptic Equations - Jacobi and Gauss-Seidel Iterative Methods

Elliptic Equations - Direct Methods

Elliptic Equations - Direct Methods

Elliptic Equations - Finite-Difference Methods

Elliptic Equations - Finite-Difference Methods

Hyperbolic, Parabolic, and Elliptic Partial Differential Equations

Hyperbolic, Parabolic, and Elliptic Partial Differential Equations

Classification of Second-Order Partial Differential Equations

Classification of Second-Order Partial Differential Equations

Finite-Difference Methods - Robin Boundary Condition

Finite-Difference Methods - Robin Boundary Condition

Thomas Algorithm for Tridiagonal Systems

Thomas Algorithm for Tridiagonal Systems

Properties of Tridiagonal Matrices

Properties of Tridiagonal Matrices

Finite-Difference Methods - Application to Extended Fin

Finite-Difference Methods - Application to Extended Fin

Finite-Difference Methods - Formal Basis

Finite-Difference Methods - Formal Basis

Finite-Difference Methods - Extended Fin Example

Finite-Difference Methods - Extended Fin Example

Numerical Solution Approaches

Numerical Solution Approaches

Condition Number

Condition Number

Diagonal Dominance and Ill-Conditioned Matrices

Diagonal Dominance and Ill-Conditioned Matrices

Round-Off Errors

Round-Off Errors

Numerical Solution Procedure and Properties

Numerical Solution Procedure and Properties

Is Python the Perfect Programming Language for Scientific Computing

Is Python the Perfect Programming Language for Scientific Computing

Analytical, Computational, and Experimental Approaches in Science and Engineering

Analytical, Computational, and Experimental Approaches in Science and Engineering

Separation of Variables for Partial Differential Equations - Wave Equation

Separation of Variables for Partial Differential Equations - Wave Equation

Separation of Variables for Partial Differential Equations - Unsteady Diffusion Equation

Separation of Variables for Partial Differential Equations - Unsteady Diffusion Equation

Separation of Variables for Partial Differential Equations - Laplace Equation

Separation of Variables for Partial Differential Equations - Laplace Equation

Sturm-Liouville Operators - Special Situations

Sturm-Liouville Operators - Special Situations

Eigenfunctions of Sturm-Liouville Operators

Eigenfunctions of Sturm-Liouville Operators

Self-Adjoint (Sturm-Liouville) Differential Operators

Self-Adjoint (Sturm-Liouville) Differential Operators

Adjoint of a Differential Operator

Adjoint of a Differential Operator

Fundamental Lemma of the Calculus of Variations

Fundamental Lemma of the Calculus of Variations

Integration by Parts

Integration by Parts

Dynamics of Deformable Bodies - Wave Equation

Dynamics of Deformable Bodies - Wave Equation

Dynamics Problems with Constraints

Dynamics Problems with Constraints

Hamilton's Prinicple vs. Newton's Second Law

Hamilton's Prinicple vs. Newton's Second Law

Derivation of Hamilton's Principle

Derivation of Hamilton's Principle

Euler-Lagrange Equations for Hamilton's Principle

Euler-Lagrange Equations for Hamilton's Principle

Hamilton's Principle for Continuous Systems

Hamilton's Principle for Continuous Systems

Hamilton's Principle for Discrete Systems - Examples

Hamilton's Principle for Discrete Systems - Examples

Hamilton's Principle for Discrete Systems

Hamilton's Principle for Discrete Systems

Algebraic and Differential Constraints in Variational Methods

Algebraic and Differential Constraints in Variational Methods

Shape of a Hanging Cable - Catenary

Shape of a Hanging Cable - Catenary

Integral Constraints in Variational Methods

Integral Constraints in Variational Methods

Functionals of Two Dependent Variables

Functionals of Two Dependent Variables

Inverse Variational Problem

Inverse Variational Problem

Functionals of Two Independent Variables - Minimal Surfaces

Functionals of Two Independent Variables - Minimal Surfaces

Functionals of Two Independent Variables - Example

Functionals of Two Independent Variables - Example

Functionals of Two Independent Variables - Euler Equation

Functionals of Two Independent Variables - Euler Equation

Functionals with Higher-Order Derivatives

Functionals with Higher-Order Derivatives

Dual Functionals

Dual Functionals

Natural Boundary Conditions

Natural Boundary Conditions

Shortest Distance Between Two Points

Shortest Distance Between Two Points

Calculus of Variations Example

Calculus of Variations Example

Calculus of Variations and Variational Notation

Calculus of Variations and Variational Notation

Calculus of Variations and the Euler Equation

Calculus of Variations and the Euler Equation

Calculus of Variations and the Functional Derivative

Calculus of Variations and the Functional Derivative

Shape of a Liquid Drop

Shape of a Liquid Drop

Optimization of River Crossing Trajectory - Zermelo's Problem

Optimization of River Crossing Trajectory - Zermelo's Problem

Fermat's Principle of Optics

Fermat's Principle of Optics

Variational Methods - A Bit of History and Introduction

Variational Methods - A Bit of History and Introduction

Potential Flow - Conformal Mapping

Potential Flow - Conformal Mapping

Potential Flow - Superposition of Basic Flows

Potential Flow - Superposition of Basic Flows

Potential Flow - Basic Flows

Potential Flow - Basic Flows

Potential Fluid Flow Formulation

Potential Fluid Flow Formulation

Poisson Integral Formula in a Circular Disk

Poisson Integral Formula in a Circular Disk

Poisson Integral Formula in the Upper Half Plane

Poisson Integral Formula in the Upper Half Plane

What Does Laplace's Equation Map To?

What Does Laplace's Equation Map To?

What Makes a Mapping Conformal?

What Makes a Mapping Conformal?

Conformal Mapping Example

Conformal Mapping Example

Elementary Mappings

Elementary Mappings

What Makes a Mapping One-to-One?

What Makes a Mapping One-to-One?

Introduction to Conformal Mapping

Introduction to Conformal Mapping

Harmonic Functions

Harmonic Functions

Cauchy-Riemann Equations - Examples

Cauchy-Riemann Equations - Examples

Analytic Functions and Cauchy-Riemann Equations

Analytic Functions and Cauchy-Riemann Equations

Complex Arithmetic and Functions

Complex Arithmetic and Functions

Introduction to Complex Variables

Introduction to Complex Variables

Beam-Column Buckling - Stability of Continuous Systems

Beam-Column Buckling - Stability of Continuous Systems

Eigenfunction Solutions of Ordinary Differential Equations - Part 4

Eigenfunction Solutions of Ordinary Differential Equations - Part 4

Eigenfunction Solutions of Ordinary Differential Equations - Part 3

Eigenfunction Solutions of Ordinary Differential Equations - Part 3

Eigenfunction Solutions of Ordinary Differential Equations - Part 2

Eigenfunction Solutions of Ordinary Differential Equations - Part 2

Eigenfunction Solutions of Ordinary Differential Equations - Part 1

Eigenfunction Solutions of Ordinary Differential Equations - Part 1

Eigenfunctions of Differential Operators - Definitions

Eigenfunctions of Differential Operators - Definitions

Function Spaces and Bases

Function Spaces and Bases

Orthogonalization of Functions

Orthogonalization of Functions

Differential Eigenproblems - Introduction

Differential Eigenproblems - Introduction

QR Decomposition

QR Decomposition

Polar Decomposition

Polar Decomposition

Singular-Value Decomposition - Image Compression

Singular-Value Decomposition - Image Compression

Singular-Value Decompostion - Vector Form

Singular-Value Decompostion - Vector Form

Singular-Value Decomposition - Method

Singular-Value Decomposition - Method

Singular-Value Decomposition - Framework

Singular-Value Decomposition - Framework

Matrix Decompositions

Matrix Decompositions

Systems of Ordinary Differential Equations - Illustrative Example from Dynamics - Part 2

Systems of Ordinary Differential Equations - Illustrative Example from Dynamics - Part 2

Systems of Ordinary Differential Equations - Illustrative Example from Dynamics - Part 1

Systems of Ordinary Differential Equations - Illustrative Example from Dynamics - Part 1

Systems of Ordinary Differential Equations - Higher-Order Equations

Systems of Ordinary Differential Equations - Higher-Order Equations

Systems of Ordinary Differential Equations - Nonhomogeneous Example

Systems of Ordinary Differential Equations - Nonhomogeneous Example

Jordan Canonical Form

Jordan Canonical Form

Systems of Ordinary Differential Equations - General Approach

Systems of Ordinary Differential Equations - General Approach

Systems of Ordinary Differential Equations - Homogeneous Example

Systems of Ordinary Differential Equations - Homogeneous Example

Diagonalization

Diagonalization

Normal and Orthogonal Matrices

Normal and Orthogonal Matrices

Real Symmetric Matrices - Diagonalization

Real Symmetric Matrices - Diagonalization

Real Symmetric Matrices - Quadratic Forms

Real Symmetric Matrices - Quadratic Forms

Real Symmetric Matrices - Linear Systems of Equations

Real Symmetric Matrices - Linear Systems of Equations

Real Symmetric Matrices - Properties of Eigenvectors

Real Symmetric Matrices - Properties of Eigenvectors

Eigenvalues and Eigenvectors - Part 3

Eigenvalues and Eigenvectors - Part 3

Eigenvalues and Eigenvectors - Part 2

Eigenvalues and Eigenvectors - Part 2

Eigenvalues and Eigenvectors - Part 1

Eigenvalues and Eigenvectors - Part 1

Applications of Eigenproblems

Applications of Eigenproblems

MMAE 350 - 6 May 2021 Lecture

MMAE 350 - 6 May 2021 Lecture

MMAE 350 - 4 May 2021 Lecture

MMAE 350 - 4 May 2021 Lecture

MMAE 350 - 29 April 2021 Lecture

MMAE 350 - 29 April 2021 Lecture

MMAE 350 - 27 April 2021 Lecture

MMAE 350 - 27 April 2021 Lecture

MMAE 350: 22 April 2021 Lecture

MMAE 350: 22 April 2021 Lecture

MMAE 350 - 20 April 2021 Leccture

MMAE 350 - 20 April 2021 Leccture

MMAE 350 - 13 April 2021 Lecture

MMAE 350 - 13 April 2021 Lecture

MMAE 350: 6 April 2021 Lecture

MMAE 350: 6 April 2021 Lecture

MMAE 350: 1 April 2021 Lecture

MMAE 350: 1 April 2021 Lecture

MMAE 350: 30 March 2021 Lecture

MMAE 350: 30 March 2021 Lecture

MMAE 350 - 25 March 2021 Lecture

MMAE 350 - 25 March 2021 Lecture

MMAE 350 - 23 March 2021 Lecture

MMAE 350 - 23 March 2021 Lecture

MMAE 350 - 18 March 2021 Lecture

MMAE 350 - 18 March 2021 Lecture

MMAE 350 - 16 March 2021 Lecture

MMAE 350 - 16 March 2021 Lecture

MMAE 350 - 9 March 2021 Lecture

MMAE 350 - 9 March 2021 Lecture

MMAE 350 - 4 March 2021 Lecture

MMAE 350 - 4 March 2021 Lecture

MMAE 350 - 2 March 2021 Lecture

MMAE 350 - 2 March 2021 Lecture

MMAE 350 - 25 February 2021 Lecture

MMAE 350 - 25 February 2021 Lecture

MMAE 350 - 23 February 2021 Lecture

MMAE 350 - 23 February 2021 Lecture

MMAE 350 - 16 February 2021 Lecture

MMAE 350 - 16 February 2021 Lecture

MMAE 350 - 18 February 2021 Lecture

MMAE 350 - 18 February 2021 Lecture

MMAE 350 - 11 February 2021 Lecture

MMAE 350 - 11 February 2021 Lecture

MMAE 350 - 4 February 2021 Lecture

MMAE 350 - 4 February 2021 Lecture

MMAE 350 - 2 February 2021 Lecture

MMAE 350 - 2 February 2021 Lecture

MMAE 350 - 28 January 2021 Lecture

MMAE 350 - 28 January 2021 Lecture

MMAE 350 - 26 January 2021 Lecture

MMAE 350 - 26 January 2021 Lecture

MMAE 350 - 21 January 2021 Lecture

MMAE 350 - 21 January 2021 Lecture

MMAE 350 - 19 January 2021 Lecture

MMAE 350 - 19 January 2021 Lecture

APS-DFD 2020 Presentation Video

APS-DFD 2020 Presentation Video

Remote Exam Instructions

Remote Exam Instructions

MMAE 350 - Sections 9.4.3 and 9.4.4

MMAE 350 - Sections 9.4.3 and 9.4.4

MMAE 350 - Sections 9.4.1 and 9.4.2

MMAE 350 - Sections 9.4.1 and 9.4.2

MMAE 350 - Section 9.3

MMAE 350 - Section 9.3

MMAE 350 - Section 9.2.4(c)

MMAE 350 - Section 9.2.4(c)

MMAE 350 - Section 9.2.4(b)

MMAE 350 - Section 9.2.4(b)

MMAE 350 - Section 9.2.4(a)

MMAE 350 - Section 9.2.4(a)

MMAE 350 Sections 9.2.2 and 9.2.3

MMAE 350 Sections 9.2.2 and 9.2.3

MMAE 350 - Section 9.2.1(b)

MMAE 350 - Section 9.2.1(b)

MMAE 350 - Section 9.2.1(a)

MMAE 350 - Section 9.2.1(a)

MMAE 350 - Section 9.1

MMAE 350 - Section 9.1

MMAE 350 - Section 8.3.2

MMAE 350 - Section 8.3.2

MMAE 350 - Section 8.3.1

MMAE 350 - Section 8.3.1

MMAE 350 - Section 8.2

MMAE 350 - Section 8.2

MMAE 350 - Sections 8.1.2 and 8.1.3

MMAE 350 - Sections 8.1.2 and 8.1.3

MMAE 350 - Section 8.1.1

MMAE 350 - Section 8.1.1

MMAE 350 - Section 7.3

MMAE 350 - Section 7.3

MMAE 350 - Section 7.2

MMAE 350 - Section 7.2

MMAE 350 - Section 7.1.4(b)

MMAE 350 - Section 7.1.4(b)

MMAE 350 - Section 7.1.4(a)

MMAE 350 - Section 7.1.4(a)

MMAE 350 - Section 7.1.3

MMAE 350 - Section 7.1.3

MMAE 350 - Sections 7.1.1 and 7.1.2

MMAE 350 - Sections 7.1.1 and 7.1.2

Mac+iPad Screen Recording

Mac+iPad Screen Recording

MMAE 350 - Section 6.3.3(b)

MMAE 350 - Section 6.3.3(b)

MMAE 350 - Section 6.3.3(a)

MMAE 350 - Section 6.3.3(a)

MMAE 350 - Section 6.3.2

MMAE 350 - Section 6.3.2

MMAE 350 - Section 6.3.1

MMAE 350 - Section 6.3.1

MMAE 350 - Review of Nonlinear Programming

MMAE 350 - Review of Nonlinear Programming

iPad Screen Recording

iPad Screen Recording