I've never had a problem in life, after university, that required calculus.

Nor have I. Used trig a lot. Tons of algebra (esp in programming). Never needed calculus though... and I was quite good at it in HS. I asked GPT what uses calculus might have in "day-to-day" life, and I'm still not sold...

Details

While many people may think calculus isn't applicable to everyday life, it actually has several practical uses that can be quite significant. Here are some examples:

1. Home Maintenance and Improvement:
   - Optimizing materials: When planning home projects, such as building a deck or remodeling a room, calculus can help optimize the amount of materials needed, reducing waste and costs.
   - Heating and cooling: Understanding how heat dissipates in different materials can help in designing more efficient insulation or choosing the right heating and cooling systems.

2. Financial Planning:
   - Investment growth: Calculus is used to model and predict the growth of investments over time, taking into account changing interest rates and compound interest.
   - Loan payments: Calculus helps in understanding the amortization of loans and the impact of different interest rates on monthly payments and overall cost.

3. Travel and Navigation:
   - Optimizing routes: Calculus can be used to find the shortest or fastest route for travel, taking into account varying speeds and distances.
   - Fuel efficiency: Calculus helps in modeling the fuel consumption of vehicles over different terrains and speeds, aiding in more efficient travel planning.

4. Health and Medicine:
   - Dosage calculations: Doctors and pharmacists use calculus to determine the correct dosage of medications based on rates of absorption and elimination from the body.
   - Medical imaging: Techniques like MRI and CT scans rely on calculus for constructing detailed images from raw data.

5. Economics and Business:
   - Supply and demand models: Calculus is used to analyze and predict how changes in market conditions affect supply and demand, helping businesses make informed decisions.
   - Cost minimization and profit maximization: Businesses use calculus to find the optimal production levels that minimize costs or maximize profits.

6. Technology and Engineering:
   - Design and analysis: Engineers use calculus in designing various systems and structures, ensuring they can withstand forces and operate efficiently.
   - Computer graphics: Calculus is essential in rendering realistic graphics in video games and movies, involving algorithms that calculate light, shadow, and movement.

7. Everyday Problem Solving:
   - Cooking and baking: Understanding rates of heat transfer can help in perfecting cooking times and temperatures.
   - Gardening and landscaping: Calculus can aid in determining the optimal placement of plants and irrigation systems for efficient water use and plant growth.

While these examples may not be directly encountered by everyone daily, they highlight how calculus is deeply embedded in various aspects of modern life and professional fields.

Yeah, I'm not gonna use calculus to plan my home projects. I've got functions like PMT that do financial planning for me. I've got Google Maps for travel and navigation. I still don't see any EVERY DAY uses for calculus.

Details

I understand your point. While calculus might not be explicitly used in many everyday tasks, its principles underpin a lot of the tools and technologies we rely on daily. However, there are more subtle ways in which a basic understanding of calculus can be beneficial:

1. Understanding Trends and Rates of Change:
   - Fitness Tracking: Apps and devices that monitor your exercise use calculus principles to calculate changes in speed, distance, and calories burned over time. Understanding the basic concept of derivatives can help you interpret this data more effectively.
   - Health Monitoring: Monitoring changes in your vital signs, such as heart rate or blood sugar levels, and understanding how they trend over time can help you make informed decisions about your health.

2. Personal Finance:
   - Interest Rates: While functions like PMT help with specific calculations, understanding how changing interest rates affect your mortgage or savings can provide deeper insights into your financial planning.
   - Budgeting: Calculus concepts help in understanding how incremental changes in spending or saving habits can impact long-term financial goals.

3. Cooking and Baking:
   - Recipe Scaling: When you scale a recipe up or down, understanding how ingredients change proportionally can involve basic calculus concepts.
   - Heat Transfer: While you might not do the math yourself, knowing that smaller pieces of food cook faster than larger ones (due to surface area to volume ratios) is a practical application of calculus.

4. Environmental Awareness:
   - Energy Consumption: Understanding how your household energy consumption changes with different activities can help you make more energy-efficient choices.
   - Resource Management: If you're interested in sustainability, calculus can help you understand how small changes in your daily habits can lead to significant long-term environmental impacts.

5. Decision Making:
   - Optimizing Time: Making decisions on how to allocate your time efficiently, whether it's balancing work, hobbies, and family, can be approached with a calculus mindset, considering how small changes can lead to the best overall outcomes.

While you might not sit down and solve calculus problems daily, the critical thinking and problem-solving skills developed through understanding calculus can enhance your ability to interpret data, make informed decisions, and understand the world around you. These subtle benefits can improve your everyday life, even if the math isn't directly apparent.

So, sure, there's calculus USED in a lot of tools we use every day... but the average person still doesn't need to use it. Our tools use it. Just like my car allows me to travel 100 miles in 2 hours (or less. LOL).

So, when I double a recipe or decide to install LED bulbs, I guess I use calculus?  Wow, I never knew.  We probably need to study up on our metallurgy so we can be better drivers.  I knew a 40-year electrical engineer who openly stated that calculating the square root of three (used for calculating three phase power) was the most advanced math he needed for work.  I also have used lots of math including trig but never found myself a need for calculus.  I guess I could calculate the volume of a doughnut but I'd rather eat it.

At one of my first programming jobs, I was tasked by the VP of Sales to calculate the best price to sell gasoline at the hundreds of gas stations owned by the company. I asked, "So, you want to maximize sales?" He replied "Yes", I told him, "Somewhere around 50 cents, you'll sell all the gas you can refine" (they owned refineries too). "No programming needed", obviously he was not understanding. He looked at me oddly. Gas was selling in California, at the time, for around $2.25.

Being a young smart-ass, I then said, "But if you want to maximize PROFITS", that's going to be one heck of an equation."

Calculus courses, even with no "everyday" applications, train how our minds think and reason better than the "everyday" person.  That is a valuable benefit in itself.  None of what we do on this site is what I would call "everyday" applications either -- they require great thinking and reasoning.  And calculus does play a big part in many professions; yours just happens to be not one of them.  That doesn't say anything about calculus; it only says something about you, gentlemen.  I'm puzzled by this line of logic, guys.  We are supposed to love the hard stuff, regardless of what we use it or not.  And if you haven't touched calculus since college, I suggest you brush up on it a little bit.  That was how you sharpened your mind in the first place.

I was not passing judgement on calculus, per se.  I was poking fun at GPT's response and observing that I, personally, have found little application for calculus in my daily life.  I could brush up on my calculus but then it would just be another hobby that I don't have time for.  I am, however, having fun learning Access and have found many applications for it in my personal and professional life.

Would you consider *living* your life an "application in your life" too?  Our daily lives are driven by nothing but high tech that wouldn't be possible without advanced math.  We are college-trained professionals and we are supposed to think better than the average person in matters such as this.  We are not supposed to have that kind of compromising thought at all.  We are supposed to preach to the uninitiated how important and foundational math is in pretty much everything we do.  Math is the universal language of the natural world after all.

As a mathematician, I am biased. Having said that, I agree with Kevin that high math affects positively the way you think and the way you solve problems. Richard gives us a clue on why he is so good at what he does. He said he was very good at calculus in high school.

Oh yeah, I absolutely loved calculus in high school, and I still love learning and relearning Math and Science issues today. In fact, one of the things I used to hate that my friends would say back in high school is "I'm never going to use this in real life," but that's not the point. As KY pointed out, the point of learning algebra and trigonometry and calculus, and things in science like calculating moles, is that they teach your brain how to think.

The material that you're learning isn't as important as learning the methods and the tools for coming to the right answer. It wires your brain scientifically and teaches you analytical thinking. That's one of the great things about computer programming, and why I suggest that new computer learners and beginner programmers don't rely on GPT. You want to train your brain in that algorithmic thinking that basic computer programming teaches you with loops and if-then statements and stuff like that. People that just copy and paste from GPT that aren't already experienced programmers are doing themselves an injustice.

And don't get me wrong, I'll use GPT once in a while myself, but it's usually just to have it quickly throw together a procedure that I know how to build. I just don't want to go through the hassle of writing it because I've done it a thousand times.

But I am now on a mission to find a calculus example to put in a Microsoft Access database. LOL.

One good one that I can think of is the rocket fuel problem where you have to calculate the perfect amount of fuel that you'll need to launch a rocket into space. At the beginning, most of the weight that you're lifting is fuel, but you need that fuel to get the rocket off the ground and into orbit. But the higher you go, the more fuel you burn, the less fuel you need because you don't have to push as much, and the effects of gravity are lower. That's definitely a calculus problem. But I want to find one that pertains to average people. What would be a good calculus example?

GPT suggested this one:

Problem: Minimizing Fuel Costs on a Road Trip

Scenario: You're planning a road trip and want to minimize how much you spend on fuel. You know that your car's fuel efficiency varies with your driving speed. If you drive too fast or too slow, your car uses more fuel per mile. Your goal is to figure out the best speed to drive that will save you the most money on gas.

Steps:
1. Understand the Relationship: You need to know how your car's fuel efficiency changes with speed. Generally, there's an optimal speed range where your car uses fuel most efficiently.

2. Calculate Costs: Consider how much fuel you'll need for the entire trip and how the cost changes depending on the speed you choose. The faster or slower you drive, the more or less fuel you'll consume.

3. Find the Best Speed: By analyzing the relationship between speed and fuel consumption, you can determine the speed at which you'll spend the least amount of money on gas for the whole trip.

4. Apply the Decision: Once you know the optimal speed, you can drive at that speed to minimize your fuel costs, making your trip more economical.

Application:
This approach can help you save money by optimizing fuel consumption, which is a practical consideration for anyone who drives regularly. It's a way to make smarter decisions about how you use your resources, like fuel, in everyday life.

Here's how you could write a simple VBA function to find the speed that minimizes fuel costs based on the provided fuel efficiency equation. The function will use a loop to check different speeds and find the one with the lowest cost.

VBA Code Example

Code


Function MinimizeFuelCost() As Double
    Dim v As Double ' Speed in miles per hour
    Dim E As Double ' Fuel efficiency in miles per gallon
    Dim cost As Double ' Fuel cost for the trip
    Dim minCost As Double ' Minimum fuel cost found
    Dim optimalSpeed As Double ' Speed that gives the minimum fuel cost

    Dim tripDistance As Double
    Dim fuelPrice As Double

    tripDistance = 300 ' Trip distance in miles
    fuelPrice = 4 ' Fuel price in dollars per gallon

    minCost = 1E+10 ' Initialize with a very high value

    ' Loop through possible speeds from 1 to 100 mph
    For v = 1 To 100
        ' Calculate fuel efficiency based on the speed
        E = -0.02 * v^2 + 2.4 * v
        
        ' Avoid division by zero in case efficiency is zero or negative
        If E > 0 Then
            ' Calculate the total fuel cost for the trip at this speed
            cost = (tripDistance / E) * fuelPrice

            ' Check if this cost is the lowest found
            If cost < minCost Then
                minCost = cost
                optimalSpeed = v
            End If
        End If
    Next v

    ' Return the optimal speed
    MinimizeFuelCost = optimalSpeed
End Function


How It Works:
1. Loop Through Speeds: The function checks speeds from 1 to 100 mph.
2. Calculate Efficiency: For each speed, it calculates the fuel efficiency using the given formula.
3. Avoid Invalid Calculations: It ensures the fuel efficiency is positive to avoid errors.
4. Compute Fuel Cost: The function calculates the fuel cost for the trip at each speed.
5. Track Minimum Cost: It keeps track of the lowest fuel cost and the corresponding speed.
6. Return Optimal Speed: After the loop finishes, the function returns the speed that results in the lowest fuel cost.

Usage:
You can call this function from a VBA-enabled application, like Microsoft Excel, to find the optimal driving speed for your trip. This example demonstrates how to apply calculus concepts (optimization) in a practical VBA solution.

No level of math skill will solve this problem. The best have tried for over 100 years.
I give it to programmer candidates. The best need about thirty minutes to solve it. Of that, about ten minutes is programming and testing.
>>>
Five explorers go into the jungle and pick coconuts all day. They put all the coconuts in one big pile and go to bed. The first explorer wakes up and divides the coconuts into five equal piles, and gives the remaining coconut to a monkey. He hides his pile in the jungle and pushes the remaining four piles into one pile, he goes back to bed. The other four explorers do the same throughout the rest of the night. In the morning, all wake up, see a smaller pile than the day before, say nothing, divide up the pile five ways with nothing for the monkey. What is the minimum number of coconuts the explorers picked the day before?

that's a good one

I failed the test the first time I tried it, late one night. After an hour of getting hopelessly bogged down in the algebraic equation, I diverted to a five-line BASIC program to get the answer.

One poor candidate didn't know my system, so I let him go home and write it out. He came back in two days with five pages of C+ code and a note from his sponsoring professor. I showed him my five lines of code and he swore up and down that there was no way it could be that simple. One woman came in, did the five lines a bit different, cutting the calculation time to a fraction of mine. I hired her on the spot.

Nice