Metodo de la bisección en excel

Introduction to Key Values and Concepts

Defining Variables

• The session begins with an apology for not sending prior information, noting that the discussion will be recorded.

• Key variables are introduced: K (counter), A (lower limit), M (midpoint), and B (upper limit).

• User input is emphasized for the lower limit, which should be between 1 and 2; these cells are marked in green as they do not contain formulas.

Calculating Midpoint

• The midpoint calculation is discussed, defined as B - A/2 .

• The function evaluation at point A is explained, using a non-linear equation involving sine.

Formula Application in Excel

Copying Formulas

• Instructions on how to copy formulas across cells in Excel are provided, emphasizing dragging the corner of the cell.

• An example formula is given: x - sin(x) - 0.5 .

Error Calculation

• The error calculation method is introduced, defined as half of the initial interval B - A/2 .

• It’s noted that the first error value remains constant at one.

Understanding Excel Functions

Decimal Notation Differences

• Differences between desktop and web versions of Excel regarding decimal notation are highlighted; commas vs. periods.

Conditional Logic in Formulas

• Importance of understanding conditional logic within formulas is stressed for effective calculations.

Evaluating Function Signs

Sign Analysis for Solutions

• Discussion on evaluating signs of functions at points A and M to determine if a solution exists between them.

Adjusting Intervals Based on Results

• If both function values have the same sign, it indicates no root exists between them; adjustments to intervals are necessary based on results.

Finalizing Formulas and Errors

Absolute Error Calculation

• The final formula for calculating error differences involves absolute values to avoid negative results.

Copying Down Formulas Efficiently

• Instructions on copying down entire rows of formulas once they’re established correctly in yellow-highlighted cells.

New Problem Introduction

Motor Control Scenario

• Introduction of a new problem involving a motor controlled by resistance with specific amperage requirements.

Formula Setup

• Participants are instructed to set up a quadratic function related to this scenario: f(x)= ax^2 - 6x + 5 - 2 .