Thursday, May 2, 2013

What is Calculus? Answers to your questions...

What is YOUR biggest question about Calculus right now?

15 of the 69 submissions asked some form of the question: "Is it hard?"

  • How hard will this really be?
  • Will I be able to handle it?
  • Is calculus hard?
  • is calculus going to be as confusing as it sounds?
  • is it very difficult?
  • is it as difficult as it sounds? 
  • Will it kill me?
  • Is it going to be a lot harder than math analysis? 
  • Will I survive?
  • My big question is, how difficult is it really? 
  • Why is it so hard?
  • On a scale of 1-death, how difficult is calculus? 
  • on a scale of one to ten how much harder is it?
  • Is it really complicated?
  • Is this stuff going to get easier? Because it looks extremely confusing and impossible to do right now
    • My response:  Yes, it's hard.  But it's also awesome.  The way things come together and the cool real-life problems you can solve once you understand the basics of calculus is WAY cool!  It gets easier with time and repetition, and understanding will come... trust me :)

Or, like 5 of you asked, "What is the most difficult part?"
  • what will be the most difficult thing about calculus 
  • What is the concept most students struggle with in Calculus?
  • What is the most difficult thing about calculus?
  • is it complicated as it sounds? im kind of nervous about this.... :(
  • Why does it seem so complicated, but so simple.
    • My response: This is different for everybody.  But in general, just wrapping your head around the concepts
  • My biggest question about Calculus right now is, How long does it take to understand the basics of Calculus?
    • My response: There's not one answer to this.  It will come with time.  I always tell my students the story of how I visited my AP Calculus teacher as a freshman in college and sat in the back of class finally understanding something he taught me the year before.  Not saying that I was lost for the whole year, but some parts of the conceptual understanding take time.  And sometimes you need to see the whole picture before some of the small pictures make sense.
  • I'm just overall confused so I can't give just one question about it. i think I just need a class discussion to get a better understanding. 
    • My response: I wish I was there!  Miss you guys!  We can Google Hangout or Skype whenever you want...well as long as I'm free ;)
  • how long will it take to understand derivatives and what would you rate as the level of difficulty?
    • My response: You will just understand it a little this year - there's not enough time to delve into it.  But, next year you'll catch on :)
  • why is calculus so complex?
    • My response:  It's not, once you grasp it.  Seriously though... I took it in high school, 3 semesters in college, and then tutored it for 4-5 years after that.  It was so awesome and cool once I saw the connections between everything!  It just takes time...

Or, "Will it apply to me?"
    • Does calculus apply to bioengineering?
    • Will this help me if i'm pursuing a degree in computer science?
    • How can we use calculus in real life? Will there be a career that relates to calculus?
    • Will I need it for my career?
      • My response: Yes. Calculus applies to everything :).  Well, most things.  Well, most things in the fields of math or science!
    • Is calculus very related to physics? 
    • will we have to apply physics with our understanding of calculus?
      • My response: Yes... in so many ways!!!  If you are taking both courses next year you should really see the connections.
    • does everything we see was impacted by calculas somehow
      • My response: Calculus is everywhere :)  You just won't know it until you learn it
    • what are some real life applications?
      • My response:  AP Calculus will be awesome for you :)
    • What do all these terms actually mean and how do they apply to real world?
      • My response:  Sounds like you are ready to start Units U and V!
      From those of you who I'm assuming are so happy trig is over...
      • Is Calculus as confusing as Trig?
      • Will calculus be as challenging as using fundamental identities to simply expressions?
        • My response:  Certain parts may be, but they are different types of math (although highly interconnected!). Calculus does not have you proving or verifying identities, if that makes you happy.
      • Is Calculus based on geometry more than algebra and trigonometry?  
        • My response: All three...can't really pick one.
      • Will the unit circle or anything related to it be involved with calculus?  
        • My response:  Knowing the UC will help you

      And those of you who have written more in math class this year than in your English class...
        • I know that Calculus requires a lot of writing responses, but are the answers always have to be in the write up response form or is it just for certain topics?
          • My response: You won't be doing as much formal writing in calculus until your AP exam, but being able to explain your thought process either verbally or in writing is still important.  A lot of calculus will still be algebraic processes - but the understanding behind that is where the true beauty lies.

          And many other great questions I'm excited to see you learn about in the next month and all next year!
                  • Are there various types of problems we need to be aware of?
                    • My response:  Yes, but in Units U and V we are just going to focus on a few

                      1. Finding the Slopes of Curves - YES, lots and lots in Unit U!
                      2. Calculating the Area of Bizarre Shapes - YES, you will get introduced to this in Unit V Concept 5
                      3. Justifying Old Formulas - A LITTLE, but not a big focus this year
                      4. Calculate Complicated X-Intercepts - NOT TILL CALCULUS!
                      5. Visualizing Graphs - A LITTLE, but the big ideas NOT TILL CALCULUS!
                      6. Finding the Average Value of a Function -NOT TILL CALCULUS!
                      7. Calculating Optimal Values" - A LITTLE, but the big ideas NOT TILL CALCULUS!
                  • How is that you can zoom in to a curve to find the slope? 
                    • My response:  If you zoom in so much, eventually it looks straight.  Try it with your graphing calculator - if you graph any sort of curved polynomial and zoom in on just one point over and over again, eventually all you see in the screen is a straight line.  Same idea
                  • My biggest question is on how we will use the derivatives and integrals.
                    • My response:  You will draw the symbols over and over again until you can do it sleeping.  And then it will be summer break.  Just kidding :).  I hope this question is answered in about a month after you finish U and V.
                  • I want to learn about limits and what exactly they are. 
                    • My response: Oh yay!!!  Just wait for class on next Friday then!  Starting in Unit U Concept 2-8, limits are your new BFF (sorry Unit Circle...)
                  • does it deal with infinite numbers?
                    • My response: Um, yes.  Did you read the material? ;)  Just kidding (can you sense any of my sarcasm in this blog post?).  Calculus deals with INFINITY all over the place!
                  • how to use the formulas and apply them to the problems.
                  • What do all these symbols mean ..?
                    • My response: You'll learn...patience my dear child, patience...
                  • Does Calculus use similar formulas to that of algebra or geometry?
                    • My response:  Everything you've learned will come together... so I hope you've learned it well!
                  • How fun will this be?
                    • My response: Amazingly fun.  Best time of your life.  Except I won't be there to share it with you :(
                  • Will we be introduced to things we have never seen before?
                    • My response: Yes. And it will be scary.  Really scary.  Just kidding - it will be awesome and new and exciting because I think some of the math we go over so many times it's not fresh anymore... and now there will be NEW and exciting stuff!
                  • Does calculus have many formulas to memorize?
                    • My response: Yes.  Once you learn what derivatives and integrals are, you will learn the shortcuts and have to memorize a lot of them.
                  • how does this apply to the whole world and where i will be using it 
                    • My response: Calculus is everywhere. :)
                  • How does differential calculus, which deals with the derivative, correlate with integral calculus?
                  • My biggest question... what are derivatives and integrals used for. I've heard so much about them, yet learned so little."
                    • My response:  Derivatives and Integrals are "opposites" of each other.  In fact, before learning the term "integral", you will refer to it as the "anti-derivative".  The real life applications are quite different - while derivatives can be used to find instantaneous velocity and acceleration of objects, integrals are used to find areas and volumes of weird shapes.
                  • Will we be working with chain rule this year? (:
                    • My response:  Not this year... but next year!
                  • Will there be shortcuts that will make our lives easier when solving Calculus problems, and if so, will these be taught to us?
                    • My response:  Yes.  Shortcuts exist.  You will not be taught them this year, but you may discover them.  If you discover them, Mrs. Contreras has been told to NOT tell you if you are right or not ;).  Next year you will learn the shortcuts... but you must understand the LONG WAY first (sounds like my whole class, doesn't it?)
                  • This year, in math analysis, it seems as though we only dealt with ideal situations rather than irregular. How different is next year going to be???
                  • Is Calculus a lot like what we learned this year just a lot more complex?
                  • So it's like math analysis but more complex?
                    • My response:  Good point!  That's because Algebra is "more regular, less real" because it's easier to comprehend.  All of your skills will still be used, but now you will be applying it to different types of situations that are not so ideal... and seeing that all the skills your teachers have made you learn finally are worth it!
                  • how much content will we cover in calculus?
                    • My response:  A lot. But it's all awesome.
                  • If we have to split the complex figures about to find the values for them, couldn't we still use formulas we learned from before to solve them by putting them into shapes we know?
                    • My response:  Hmmm you might want to use that knowledge on Unit V Concept 5.  Good starting point!
                  • What's a derivative
                    • My response:  Unit V Concepts 1-4 will be your best friend!
                  • Can you teach me how to calculus? 
                    • My response:  I'll do my best on my videos...
                  • what is the basis of calculus? Meaning, where did the derivative and the integral come from? how/where did they originate?
                    • My response:  Sounds like a great question for Google :)
                  • How complicated are derivatives and what level of trigonometry is involved?
                    • My response:  Derivatives - understanding them is hard at first.  Solving them is basic algebra.  Trigonometry - certain parts of calculus will have you use trigonometric formulas instead of algebraic formulas, but it won't be as big of a focus as it was this year.  Remember, this class was NOT "pre-calculus" for a reason.  It was "Math Analysis" because it's a combination of "Pre-Calc" and "Trigonometry".  So, we had quite a long time on trig because that's what the course entails...

                  And to those of you wondering if I actually had a plan with what I was teaching you this year :)
                      • is it just an extention on pre calc?
                        • My response: It IS extensions on Pre-Calc... but it's not JUST extensions on Pre-Calc... it will go further than we were able to ever go.
                      • Will some of the concepts that we learned this year be in Calculus also?
                        • My response: Yes... all the algebra skills we've used you will use again... but the most easily transferrable concept is the DIFFERENCE QUOTIENT WOO HOO!!
                      • Where do you start in order to begin understanding the concepts of calculus? 
                        • My response: Right where I'm having you start :).  We will first learn about limits and how everything in calculus deals with infinity in some form, and then tie that into derivatives.  Lastly, we will see how the area problem is set up... but we won't go into the calculus of it yet.
                      • Will all the material of calculus tie/ relate with each other to make the learning process more understandable? 
                        • My response: I think it does.  I hope you at least see the connections between the concepts I am having you learn in U and V.
                      • Is everything we already know building blocks? Or will it be thrown out the window as calc deals with new ways of finding answers.
                        • My response:  It's all building blocks.  I wouldn't teach you something without a may take a while to see all the connections, but they are there.

                      PLEASE POST FOLLOW-UP 
                      COMMENTS AND QUESTIONS BELOW :)

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