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Merge Learning: Matrices to Numerical Methods using Excel
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14 students

Merge Learning: Matrices to Numerical Methods using Excel

Solve linear algebraic equations with Numerical methods using Excel
Created byDr. V. R. Lakshmi Gorty
Last updated 10/2021
English
English [Auto],

What you'll learn

  • Redefine Numerical Methods using Matrices in an interdisciplinary mode
  • Solve problems related to Numerical Methods using knowledge of Matrices
  • Analyze the concept of Numerical methods through Matrices
  • Apply acquired knowledge to problems using Excel

Course content

5 sections • 33 lectures • 4h 57m total length

  • Introduction to the course1:27

    Explore matrices and numerical methods with Excel to build reusable method sheets, solve problems by replacing numbers, and apply linear algebra concepts to real life problems using Excel.

  • Determinants2:16

    Let's start with determinants. A determinant is a square array of numbers entered within a pair of horizontal lines or vertical lines. The solution is obtained by sum of products in a certain manner. On simplifying the determinants, the value is a single number that is a scalar quantity. Determinants are useful calculating areas in real-life problems.


    Let's start with 2x2 determinants mathematical representation. Here you can see a, b, c, d and the value of the determinants is given by ad minus bc. Further adding to the representation we also say that a is located in 11 position, b is located in 12 position, c is located in to one position, and d is located in 22 position

    Now here is 3x3 determinant, where the position of a1 is at 11, b1 is at 12 and the position 13 is given by c1. In the second row 21 position is given by a2, 22 position is given by b2 and 23 position is given by c2. Similarly in the third row, as you can see the 31 position is given by a3, 32 position is given by b3 and and 33 position is given by c3. And the value of the determinant is given as:

  • Determinants using Excel10:10

    Learn to represent determinants in Excel with cell references, work through 2 by 2 and 3 by 3 examples, and apply the M.D. Tom function to compute the determinant efficiently.

  • Minors3:01

    Explore the mathematical representation of minors by deleting the chosen row and column to form determinants, illustrated for 2x2 and 3x3 cases, with plans to compute minors in Excel.

  • Minors using Excel10:41

    Compute minors and cofactors by deleting the appropriate row and column in determinants, using three-by-three examples and Excel's built-in formulas for quick results.

  • Cofactors5:18

    Compute cofactors for 2x2 and 3x3 determinants using the definition C_ij = (-1)^{i+j} M_ij and corresponding minors, assemble the cofactor matrix, and preview representing cofactors in Excel.

  • Co-factors using Excel3:49

    Learn to compute cofactors in Excel by applying the minor values and the sign pattern (-1)^(i+j) to determinants, with 3x3 examples.

  • Calculate Determinants and Minors using Excel
  • Cramer's Rule 2x2, 3x35:40

    Learn Cramer's rule for solving two-variable and three-variable linear systems using determinants, column replacements, and the conditions for unique solutions, with an Excel-based approach planned.

  • Cramer's Rule using Excel10:40

    Learn to solve Cramer's rule in Excel by replacing columns with constants to compute x, y, and z using D, Dx, Dy, and Dz. Build an automatic, multi-equation solver.

  • Cramer's Rule on 3x3 using Excel

Requirements

  • Basic knowledge of matrices and excel

Description

The course aims to explore areas,  which are otherwise excluded in traditional classroom learning. Matrices are a modern tool in science and technology. Determinant helps to find the consistency of the given matrix. Numerical methods approximate true solutions and are repeatedly applied to better approximate until an accurate solution is obtained. The bridge between Matrices and Numerical methods is narrowed for the students to grasp multi-facet knowledge. The blending of these subjects taught in online mode would bring the learner ease to connect with applications in real-life. The learner is no more restricted to the narrow platform of knowledge. Interdisciplinary approaches are inculcated naturally through this course.  The course imbibes the learner to apply in various fields of the study and allows them to think in a broader aspect to bridge the gap between two subjects. The course is designed in two parts. One part of the topic would be about mathematical notations and formulations and second part is designed for solving using excel.

The course consists of:

  1. Introduction to Matrices (includes properties like addition, subtraction, multiplication, adjoint, etc.)

  2. Basic knowledge of determinant, Cramer's rule (2x2,3x3)

  3. Two ways to find the inverse, and in Excel

  4. normal form and echelon form

  5. normal form and echelon form using Excel.

  6. Introduction to Numerical methods extended from Matrices

  7. Numerical methods of Gauss methods

  8. Gauss-elimination with Excel

  9. Gauss-Jordan with Excel

  10. Gauss-Jacobi and with Excel

  11. Gauss-Seidel collaborating with Excel.

Who this course is for:

  • Undergraduate students can extend classroom learning to practice connecting two different subjects of mathematics using Excel

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