Need an idea for calculus presentation

• confused calc
In summary, during the presentation, the speaker discussed the relationship between distance, speed, and acceleration and gave examples of how these concepts can be applied in everyday life such as free fall, car driving, and plane travel. They also mentioned the four general problems that calculus was originally used for: tangents to curves, problems of motion, arc lengths, and areas and volumes under curves. The speaker then demonstrated how calculus can be used to predict the trajectory of a football in space, sparking interest in half of the audience while the other half felt overwhelmed. Finally, they explained how calculus was developed to solve the problem of calculating acceleration at a specific instant, a concept that was previously impossible to define.
confused calc
keep in mind that the people that i am presenting to have no clue what calculus is and i want to show them how they use it in everyday life.

Distance, speed, acceleration relationship could give examples. Free fall, car driving, plane travel are examples.

what about the 4 general problems that calculus was originally used for? that would be tangents to curves, problems of motion (especially planetary motion), arc lengths, areas & volumes under curves or bounded by curves, and maxima/minima problems.

went with a demonstration using a football and how to use calculus to predict where the ball is going to go. in the end i think half the class was actually interested in calculus and the other half was a little overwhelmed.

Here's an example that I've used in introductory lectures: Imagine that you are in spaceship high above the plane of the solar system and you take a "snap shot" that includes both the sun and the planet Jupiter. Knowing the scale, you could use that snap shot to determine the distance from the sun to Jupiter at that instant. And, then, using Newton's gravity formula, you could calculate the force the sun exerts on Jupiter and so Jupiter's acceleration at that instant.

But what does "acceleration at a specific instant" mean? Acceleration is defined as "change in speed over change in time" and speed itself is defined as "change in distance over change in time". Both of those require a "change in time" and so make no sense "at a specific instant". That was the problem that Newton faced in developing his formula for gravitational force and he created Calculus to solve it!

1. What is the importance of calculus in the field of science?

Calculus is a powerful mathematical tool that allows us to study and understand the behavior of complex systems. It is used in various fields of science such as physics, engineering, economics, and biology to model and solve real-world problems.

2. Can you suggest a topic for a calculus presentation?

Some interesting topics for a calculus presentation could be the applications of calculus in different fields, the history of calculus, or a comparison between different methods of integration.

3. How can calculus be used to solve real-world problems?

Calculus provides us with a framework for solving optimization problems, finding rates of change, and analyzing the behavior of complex systems. It is used in a wide range of applications such as predicting stock market trends, designing bridges and buildings, and understanding the spread of diseases.

4. What are some resources for learning more about calculus?

There are many online resources available for learning calculus, such as Khan Academy, MIT OpenCourseWare, and Coursera. You can also refer to textbooks or attend a calculus course at a local college or university.

5. Can you explain the difference between differential and integral calculus?

Differential calculus deals with the study of rates of change and slopes of curves, while integral calculus focuses on finding the area under a curve and solving accumulation problems. These are two complementary branches of calculus that are used together to solve a variety of problems.

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