Topic outline
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Hi everyone.
Do you know that our everyday life has problems involving mathematics?
For example, finding daily traveling hours, finding electricity consumed in a week or year, finding the entry fees of adults and children visiting places, and many more.
What are some mathematics problems?
Some of the mathematics problems are problems involving systems of linear and nonlinear equations, polynomial, differentiation, integration, and initial value problems.
You have studied all these topics before. For instance, to find the solution involving a two-dimensional linear system, you can use an inverse matrix or elementary row operations. This approach is also known as the analytical approach or finding the exact solution.
But how about problems, where the exact solution is hard to find.
For example, if you need to solve 5 dimensions or more systems of linear equations or systems of nonlinear equations?
You need to find another method to solve hard problems.
In this course, you are going to learn some numerical methods to find the solution.
Numerical methods are an approach to solving mathematical or physical equations using the help of mathematics software.
I am Dr. Annie Gorgey and I am looking forward to having you all in my course.
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Hi Students,
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Hi everyone,
These videos give you a complete introduction to Numerical Methods covering numerical errors, the Taylor series, and Scilab programming.
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😉In this topic, you will learn how
⋆ To estimate the solution of small systems of linear equations by hand and by Scilab using Jacobi’s and Gauss-Seidel methods.
⋆ To study the convergence of Jacobi’s and Gauss-Seidel's methods.
⋆ To evaluate the minimum number of iterations required by Jacobi’s and Gauss-Seidel's methods.
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We have learned iterative approaches, the next is to solve linear systems by using direct approaches.
There are several direct approaches that you might have studied on your own such as elementary row operations (ERO), inverse matrix and etc.
In this topic, you are going to learn other direct approaches such as Gauss Elimination and LU factorization with maximum column pivoting. -
In this video, you will be introduced to some of the methods for solving nonlinear scalar equations.
Watch all the videos given to get the full ideas on how these methods works.-
What are scalar nonlinear equations?
Watch the given video to find out.
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The bisection method is an approximation method to find the roots of the given equation by repeatedly dividing the interval. This method will divide the interval until the resulting interval is found, which is extremely small.
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The secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f.
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The secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f.
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View Make a choice
Consider the following function f(x)=x^2+1 in [0,3].
The numerical results are given by three different methods as below:
From the given Tables above, choose the best method in solving the given function f(x).
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Use Scilab instead of Octave or Matlab.
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In Topic 4, you learned several methods to solve scalar nonlinear equations.
Do you remember some of the scalar nonlinear equations?
Let's test yourself! Which one of the following equations is a nonlinear equation?
a) 2x+6=0
b) 4x+sin(x)=0
c) 3x^2+6=0
Now, Topic 5 is about finding the roots or solutions to nonlinear systems of equations.
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Quiz 3
This Quiz will test your knowledge on Topic 4 and Topic 5.
Before taking this quiz make sure you have completed watching all the videos given in Topic 4 and Topic 5.
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Topic 6 explains the solution to polynomials such as interpolating polynomials by using some numerical methods. The numerical methods are Lagrange polynomial, Vandermonde, and Newton Divided Difference.
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Topic 7 is all about solving differentiation by using some numerical approaches such as central and forward difference formulas.
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This topic is about solving integration problems by using numerical approaches such as trapezoidal, Simpsons, and midpoint rules.
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Topic 9 gives solutions to initial value problems.
UPSIMOOC