What is Calculus Used For? | Jeff Heys | TEDxBozeman
TLDRThe speaker, an engineer and former student from Montana State University, discusses the practical applications of calculus and mathematical models in everyday life. They share personal experiences, such as calculating smoke dispersion in restaurants and developing models for understanding glaucoma, to illustrate how these tools can predict future outcomes, avoid costly experiments, and provide alternatives to unethical research. The talk concludes with a challenge to the audience, especially younger individuals, to learn math and calculus to contribute to the development of new mathematical models for complex, currently impossible experiments.
Takeaways
- 🤔 The speaker initially struggled to understand the practical applications of calculus until a unique assignment in graduate school clarified its utility.
- 🚭 The Boulder smoking ordinance in the mid-90s served as a real-world example of how mathematical models can be applied to solve complex problems related to public health and safety.
- 🌫️ Mathematical models can predict future outcomes, such as weather patterns or stock market trends, by solving complex calculus equations like those used in weather forecasting and financial options pricing.
- 🚀 Models are used to avoid costly and time-consuming experiments, exemplified by Boeing's shift from wind tunnel testing to computer-based design and simulation of aircraft.
- 🧪 The development of mathematical models is crucial for understanding complex systems and phenomena that are difficult or unethical to study directly, such as certain health conditions and behaviors.
- 👀 In ophthalmology, mathematical models have provided insights into the development of glaucoma by simulating the forces experienced by the eye's fluids, avoiding invasive procedures.
- 💊 Inhalable drug delivery can be optimized through mathematical models that predict particle deposition in the lungs, offering a safer alternative to radioactive tracer studies.
- 💓 Echocardiograms combined with mathematical models have the potential to provide a more comprehensive assessment of heart health and efficiency, guiding better treatment strategies.
- 🌡️ Hyperthermia treatment for cancer requires improved mathematical models to understand and optimize the process, as direct experimentation is challenging.
- 📚 The speaker encourages learning calculus and mathematical modeling as they are essential tools for solving problems and advancing knowledge in various fields, especially where direct experimentation is impossible or unethical.
Q & A
What was the speaker's initial question about calculus?
-The speaker initially asked what the practical applications of calculus were, as they did not see the relevance of the subject during their engineering studies and high school math courses.
How did the speaker's perspective on calculus change?
-The speaker's perspective changed after developing a mathematical model in graduate school to calculate the amount of smoke released from a restaurant's smoking area every time the door was opened. This experience made them realize the practical utility of calculus and mathematical models in real-world scenarios.
What are the three categories of mathematical models the speaker mentioned?
-The three categories of mathematical models mentioned are: models that predict the future, models that help avoid expensive experiments, and models that serve as alternatives to unethical experiments.
How does the speaker describe the first category of mathematical models?
-The first category includes models that predict the future, such as weather forecasting models based on current pressure and temperature data, and the Black-Scholes equation used for predicting stock prices and option pricing.
What is an example of the second category of mathematical models?
-An example of the second category is the use of computer simulations by Boeing to design aircraft, which allows them to test only the most efficient designs in wind tunnels, saving significant costs.
What is an example of the third category of mathematical models?
-An example of the third category is a mathematical model developed to understand the development of glaucoma, which provides insights without the need for invasive experiments on the human eye.
How do mathematical models help in inhalable drug development?
-Mathematical models can predict where different sizes and densities of particles will be deposited in an individual's unique airways, allowing for personalized treatment plans and more effective drug delivery.
What is the potential application of combining mathematical models with echocardiogram data?
-By combining mathematical models with echocardiogram data, it may be possible to add a health or efficiency gauge to the ultrasound display, helping echocardiologists better understand heart function and design more effective treatments.
What is the current research project the speaker mentioned?
-The speaker mentioned working on a project using hyperthermia, or higher temperatures, to kill cancer cells. They are developing better mathematical models of this process because the actual experiments are too difficult.
What challenge does the speaker issue to the audience?
-The speaker challenges the audience, especially younger individuals, to consider learning math and calculus due to the vast number of applications and the need for further development of mathematical models in various fields.
Why is the speaker passionate about mathematical models?
-The speaker is passionate about mathematical models because they provide practical solutions, save costs, and offer insights into complex systems without the need for unethical or expensive experiments.
Outlines
🤔 The Purpose of Calculus and its Practical Applications
The speaker, an engineering student from Montana State University, reflects on the practical uses of calculus and mathematical models. Initially unsure of the applications of calculus, the speaker found clarity during graduate school in Boulder, Colorado, where a unique smoking ordinance led to a project modeling the dispersion of smoke from designated areas in restaurants. This experience highlighted the utility of mathematical models in predicting and understanding real-world phenomena. The speaker categorizes mathematical models into three types: those that predict the future, those that replace expensive experiments, and those that circumvent unethical experiments. The speaker emphasizes the importance and broad applicability of mathematical modeling across various fields.
🧠 Glaucoma Research and Inhalable Drug Modeling
This paragraph discusses the speaker's work on mathematical models in the medical field, specifically focusing on glaucoma and inhalable drugs. The speaker explains how a malfunction in the fluid circulation of the eye can lead to glaucoma, a condition not fully understood by scientists. Instead of invasively measuring the forces within the eye, a mathematical model was developed to predict the impact of various forces, leading to insights about different forms of glaucoma. The speaker also talks about the development of inhalable drugs and the need to understand how particles of different sizes and densities will be distributed in the lungs, which is crucial for targeted drug delivery. To address this, a mathematical model is being developed to predict particle deposition in unique airway geometries. Additionally, the speaker mentions ongoing work to enhance echocardiogram readings by integrating mathematical models to assess heart health and efficiency, thereby improving treatment design.
Mindmap
Keywords
💡Engineering
💡Calculus
💡Mathematical Model
💡Predicting the Future
💡Avoiding Experiments
💡Ethical Considerations
💡Inhalable Drugs
💡Echocardiogram
💡Hyperthermia
💡Learning Math and Calculus
Highlights
The speaker was an engineering student at Montana State University and had to take many calculus and math courses.
The speaker often asked what the practical applications of calculus were but did not get a satisfactory answer until graduate school.
In Boulder, Colorado, there was an interesting smoking ordinance that required smoking areas in restaurants to be completely sealed off.
The speaker's class was tasked with developing a mathematical model to calculate the amount of smoke released from smoking rooms when the door was opened.
This assignment was transformative for the speaker, as they realized the practical applications of calculus and mathematical models.
Mathematical models can be categorized into three types: predicting the future, avoiding expensive experiments, and replacing unethical experiments.
Predictive models are familiar to many, such as weather forecasting and stock price prediction using complex calculus equations.
Boeing uses mathematical models to design aircraft, saving millions of dollars by only testing the most efficient designs in wind tunnels.
Mathematical models can predict the outcome of experiments that would be too expensive or unethical to perform in reality.
The development of a mathematical model helped understand the development of different forms of glaucoma.
Inhalable drug particle size and density can be optimized for individual airway geometries using mathematical models, instead of risky radioactive particle tests.
Combining ultrasound data with mathematical models may lead to a health or efficiency gauge for echocardiograms, aiding in treatment design.
The speaker is currently working on a model for hyperthermia treatment of cancer, as the experimental process is too difficult.
The speaker challenges listeners, especially younger individuals, to learn math and calculus to contribute to the development of new mathematical models.
There are many processes in the world that still require the development of mathematical models due to the impossibility of conducting real experiments.
Transcripts
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