This course on Numerical Methods for Engineers teaches Numerical Methods for Engineers fundamentals through 2 interactive modules. If you are , then this course is for you. You can access this course on web and mobile, it’s available in language.
This course on Numerical Methods for Engineers teaches Numerical Methods for Engineers fundamentals through 2 interactive modules. If you are , then this course is for you. You can access this course on web and mobile. This complete course is available in language.
Learn new concepts from professionals in the field.
Acquire a basic understanding of a topic or skill
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Topics you will learn
Scientific Computing
14 videos
Course Overview
Week One Introduction
Binary Numbers | Lecture 1
Double Precision | Lecture 2
MATLAB as a Calculator | Lecture 3
Scripts and Functions | Lecture 4
Vectors | Lecture 5
Line Plots | Lecture 6
Matrices | Lecture 7
Logicals | Lecture 8
Conditionals | Lecture 9
Loops | Lecture 10
Logistic Map (Part A) | Lecture 11
Logistic Map (Part B) | Lecture 12
16 readings
Welcome and Course Information
Certificate or Audit?
How to Write Math in the Discussions Using MathJax
MATLAB Online
Rounding Binary Numbers
Computer Numbers
REALMAX
REALMIN
EPS
Logical Expressions
Logical Vectors
Quadratic Equation
Background for the Logistic Map
Period-2
Reference Solution to *Bifurcation Diagram for the Logistic Map (audit)*
Reference Solution to *Bifurcation Diagram for the Logistic Map*
3 quizzes
Week One Assessment
Diagnostic Quiz
Week One Assessment (audit)
10 app items
Bifurcation Diagram for the Logistic Map
MATLAB as a Calculator
Binet's Formula for the Fibonacci Numbers
Table of Sines and Cosines
Logarithmic Spiral
Lemniscate
Manipulating Matrices
Banded Matrices
Recursion Definition for the Fibonacci Numbers
Bifurcation Diagram for the Logistic Map (audit)
Root Finding
12 videos
Week Two Introduction
Bisection Method | Lecture 13
Newton's Method | Lecture 14
Secant Method | Lecture 15
Order of Convergence| Lecture 16
Convergence of Newton's Method | Lecture 17
Fractals from Newton's Method | Lecture 18
Coding the Newton Fractal | Lecture 19
Root-Finding in MATLAB | Lecture 20
Feigenbaum Delta (Part A) | Lecture 21
Feigenbaum Delta (Part B) | Lecture 22
Feigenbaum Delta (Part C) | Lecture 23
9 readings
Estimate the Square-root of Three Using the Bisection Method
Estimate the Square-root of Three Using Newton's Method
Estimate the Square-Root of Three Using the Secant Method
Rates of Convergence
Order of Convergence of the Secant Method
The Four Fourth Roots of Unity
Compute the Value of m in the Period-Two Cycle
Reference Solution to *Computation of the Feigenbaum Delta (audit)*
Reference Solution to *Computation of the Feigenbaum Delta*
2 quizzes
Week Two Assessment
Week Two Assessment (audit)
4 app items
Computation of the Feigenbaum Delta
Fractals from the Four Fourth Roots of Unity
Elliptical Planetary Orbits
Computation of the Feigenbaum Delta (audit)
1 plugin
Deep Dive into The Newton Fractal
Matrix Algebra
13 videos
Week Three Introduction
Gaussian Elimination without Pivoting | Lecture 24
Gaussian Elimination with Partial Pivoting | Lecture 25
LU Decomposition with Partial Pivoting | Lecture 26
Operation Counts | Lecture 27
Operation Counts for Gaussian Elimination | Lecture 28
Operation Counts for Forward and Backward Substitution | Lecture 29
Eigenvalue Power Method | Lecture 30
Eigenvalue Power Method (Example) |Lecture 31
Matrix Algebra in MATLAB | Lecture 32
Systems of Nonlinear Equations | Lecture 33
Systems of Nonlinear Equations (Example) | Lecture 34
Fractals from the Lorenz Equations | Lecture 35
11 readings
Round-off Errors in Gaussian Elimination
Reduced Round-off Errors in Gaussian Elimination with Partial Pivoting
The (PL)U Decomposition of A
Estimating Computational Time using Operation Counts
Summation Identities
Operation Counts for a Lower Triangular System
Convergence of the Eigenvalue Power Method
Determine the Dominant Eigenvalue
How to Solve Three Nonlinear equations
Reference Solution to *Fractals from the Lorenz Equations (audit)*
Reference Solution to *Fractals from the Lorenz Equations*
2 quizzes
Week Three Assessment
Week Three Assessment (audit)
5 app items
Fractals from the Lorenz Equations
The LU Decomposition of a Matrix
Eigenvalues and Eigenvectors
Fixed-Point Solutions of the Lorenz Equations
Fractals from the Lorenz Equations (audit)
Quadrature and Interpolation
13 videos
Week Four Introduction
Midpoint Rule | Lecture 36
Trapezoidal Rule | Lecture 37
Simpson's Rule | Lecture 38
Composite Quadrature Rules | Lecture 39
Gaussian Quadrature | Lecture 40
Adaptive Quadrature | Lecture 41
Quadrature in MATLAB | Lecture 42
Interpolation | Lecture 43
Cubic Spline Interpolation (Part A) | Lecture 44
Cubic Spline Interpolation (Part B) | Lecture 45
Interpolation in MATLAB | Lecture 46
Bessel Functions and their Zeros | Lecture 47
12 readings
The Midpoint Rule is the Area of a Rectangle
Midpoint Rule for a Quadratic Function
Derive the Trapezoidal Rule
Derive Simpson's Rule
Simpson's 3/8 Rule
Three-point Legendre-Gauss Quadrature
Computing the Error in an Adaptive Quadrature
Linear and Quadratic Interpolation
Cubic Spline Interpolation with Endpoint Slopes Known
Cubic Spline Interpolation with the Not-a-Knot Condition
Reference Solution to *Bessel Function Zeros (audit)*
Reference Solution to *Bessel Function Zeros*
2 quizzes
Week Four Assessment
Week Four Assessment (audit)
4 app items
Bessel Function Zeros
Cornu Spiral
Interpolate Two Data Files
Bessel Function Zeros (audit)
Ordinary Differential Equations
13 videos
Week Five Introduction
Euler Method | Lecture 48
Modified Euler Method | Lecture 49
Runge-Kutta Methods | Lecture 50
Second-Order Runge-Kutta Methods | Lecture 51
Higher-Order Runge-Kutta Methods | Lecture 52
Higher-Order ODEs and Systems | Lecture 53
Adaptive Runge-Kutta Method | Lecture 54
Integrating ODEs in MATLAB (Part A) | Lecture 55
Integrating ODEs in MATLAB (Part B) | Lecture 56
Shooting Method for Boundary Value Problems | Lecture 57
The Two-Body Problem (Part A) | Lecture 58
The Two-Body Problem (Part B) | Lecture 59
10 readings
When the Euler Method is Exact
When the Modified Euler Method is Exact
Ralston's Method
Runge-Kutta Methods and Quadrature Formulas
Fourth-Order Runge-Kutta Method and Simpson's Rule
Systems of ODEs
Example of Adaptive Integration
Circular orbits
Reference Solution to *Two-Body Problem (audit)*
Reference Solution to *Two-Body Problem*
2 quizzes
Week Five Assessment
Week Five Assessment (audit)
4 app items
Two-Body Problem
The Lorenz Equations
Swing a Pendulum to the Top
Two-Body Problem (audit)
Partial Differential Equations
17 videos
Week Six Introduction
Boundary and Initial Value Problems | Lecture 60
Central Difference Approximation | Lecture 61
Discrete Laplace Equation | Lecture 62
Natural Ordering | Lecture 63
Matrix Formulation | Lecture 64
MATLAB Solution of the Laplace Equation (Direct Method) | Lecture 65
Jacobi, Gauss-Seidel and SOR Methods | Lecture 66
Red-Black Ordering | Lecture 67
MATLAB Solution of the Laplace Equation (Iterative Method) | Lecture 68
Explicit Methods for Solving the Diffusion Equation | Lecture 69
Von Neumann Stability Analysis of the FTCS Scheme | Lecture 70
Implicit Methods for Solving the Diffusion Equation | Lecture 71
Crank-Nicolson Method for the Diffusion Equation | Lecture 72
MATLAB Solution of the Diffusion Equation | Lecture 73
Two-Dimensional Diffusion Equation | Lecture 74
Concluding Remarks
16 readings
Higher-order Central Difference Approximation
Mean Value Property of the Laplace Equation
Coordinates of the four corners
The Discrete Laplace Equation on a Four-by-Four Grid
Number of Interior and Boundary Points
Iterative Solution of a System of Linear Equations
Using a Second-Order Time-Stepping Method
FTCS Scheme for the Advection Equation
Von Neumann Stability Analysis of the FTCS Scheme for the Advection Equation
Implicit Discrete Advection Equation
Lax Scheme for the Advection Equation
Difference Approximations for the Derivative at Boundary Points
Reference Solution to *Two-Dimensional Diffusion Equation (audit)*
Reference Solution to *Two-Dimensional Diffusion Equation*
Please Rate this Course
Acknowledgements
3 quizzes
Week Six Assessment
Classify Partial Differential Equations
Week Six Assessment (audit)
5 app items
Two-Dimensional Diffusion Equation
Direct Solution of the Laplace Equation
Iterative Solution of the Laplace Equation
The Diffusion Equation with No-Flux Boundary Conditions
Two-Dimensional Diffusion Equation (audit)
Course Offerings
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Pre Requsites
Curious Mind to learn new concepts
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After this Course
Course is for
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