2.1-2.2 Math

Introduction

  • Overview of today’s class structure and initial clarifications.

  • Reminder to check the syllabus and to complete WebAssign registration.

Syllabus and Announcements

  • Weekly announcements will be updated at the end of each class.

  • Link to last class recording is available for those who missed it.

  • Responses to questions about supplemental problems provided in the course.

    • These problems are for practice only and will not be graded.

    • Not all problems will be reviewed in class; focus on WebAssign homework.

Today's Agenda

  • Focus on sections 2.1 and 2.2, with a break scheduled after the first hour.

  • Discussion on process for submitting quizzes and tests via D2L.

  • Recommendations for alternatives if a printer is not available.

Calculus Session

  • Recap of the previous discussion on the slope of tangent lines and finding slopes near a fixed point.

  • Emphasis on approximating slopes by using secant lines between points that are close to the fixed point.

  • Calculating specific slopes between designated points, using example calculations.

Example Calculations

  • Slope calculations between points such as (1, 1.5) reviewed in class.

  • Noticing trends in values as approximations to the tangent slope.

Using the TI-84 Calculator

  • Instructions on how to use the TI-84 for calculating slopes quickly.

  • Guidelines for setting up functions and using the graphing calculator efficiently to compute slopes.

Concept of Limits

  • Introduction to limits as a mathematical concept pivotal for calculus.

  • Limit definitions will be explored in section 2.2.

    • Understanding that approaching a value (like 0) does not equate to reaching it.

    • Emphasis on the behavior of functions as they approach specific points.

  • The limit of a function can be evaluated through various methods including tables, graphs, or calculators.

Evaluating Limits

  • Example of evaluating the limit of sin(x)/x as x approaches 0, detailing calculations including identifying indeterminate forms.

  • Understanding the importance of approximation and how to approach functions around defined points.

Conclusion and Homework

  • Reminder to complete practice quiz, which is an opportunity to test understanding of today’s topics.

  • Upcoming homework assignments and their expectations discussed.

  • Closing notes on making sure technology works (PDF submissions, etc.) and maintaining clarity in written work.

Future Topics

  • Next classes will cover formal definitions and processes for calculating derivatives to handle slope problems efficiently.