Calculus...difficult for a newbie?

[911 Turbo]

Imma break down calculus for you.

Newton was a smart guy. He realized that you can use the old rise/run formula from algebra to find the slope of a function. He was tricky because he realized that using really small run values will allow you to find the slope at every point in the function. The rise/run formula, using really small run values at lots of different points in the function, becomes the new derivative formula. This derivative function will give you the slope at any point for a given starting function.

Similarly, Newton realized that you can construct a bunch of little squares under a curve to find the area under that curve. If you make the squares really small and over a range of values, you get an integral function.

Derivatives are useful for figuring out the behavior of an object, such as the classic projectile problems in physics--you can find out whether it's speeding up or slowing down. Integrals are useful because you can figure out how far the ball went over time.

You spend most of calculus 1 figuring out how Newton arrived at the simple method of differentiating functions and why differentiating works. The latter part of calc 1 is usually practicing and applying differentiation; you may start on integrating, which is the opposite of differentiating. Calc 2 focuses half on integrals and half on proving weird stuff related to series approximations, which don't make any sense until you apply them in engineering classes way down the road (I hated calc 2, ftr). Calc 3 uses more than one variable, diff EQ uses more than one derivative.

See? Calculus and calc-based physics are not that hard. Most math teachers just use difficult, obfuscating terminology to make it hard to digest. The good math teachers are the ones who explain things in simple words and more conceptually/applicably than just theoretically.

Were you a math or physics major? Saw your username and post and was just wondering.

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[FlowRate]

Were you a math or physics major? Saw your username and post and was just wondering.

Chemical engineering.

I wish my math teachers had connected the dots more in lecture. It wasn't until I was applying the mathematics of my calculus classes in much more advanced chem/engineering classes (pchem and thermo come to mind) that I actually understood why these things were useful.

 

[BMEN]

Chemical engineering.

I wish my math teachers had connected the dots more in lecture. It wasn't until I was applying the mathematics of my calculus classes in much more advanced chem/engineering classes (pchem and thermo come to mind) that I actually understood why these things were useful.

Same. The best teachers i had for calc and physics where in high school. Then when i got to engineering classes the profs there taught math better. I learned Diffy Q better from my biomechnaics prof rather than my Diffy Q prof that semester . Same with linear algebra

 

[deleted393595]

Chemical engineering.

I wish my math teachers had connected the dots more in lecture. It wasn't until I was applying the mathematics of my calculus classes in much more advanced chem/engineering classes (pchem and thermo come to mind) that I actually understood why these things were useful.

Just out of curiosity, how do you use series approximations in engineering? Because the Taylor polynomial stuff I learned in class still seems so pointless.

 

[BMEN]

Just out of curiosity, how do you use series approximations in engineering? Because the Taylor polynomial stuff I learned in class still seems so pointless.

Its useful in derivation and calculation in which there are changes of delta something. A taylor series will help you evaluate it. good for approximations when no real answer exist. I used it a lot in my fluids courses.

 

[FlowRate]

Just out of curiosity, how do you use series approximations in engineering? Because the Taylor polynomial stuff I learned in class still seems so pointless.

IIRC we used taylor series approximations in things like process control, but they seemed to pop up once in almost every class I had, as if only to remind us that they exist.

 

[FlowRate]

Same. The best teachers i had for calc and physics where in high school. Then when i got to engineering classes the profs there taught math better. I learned Diffy Q better from my biomechnaics prof rather than my Diffy Q prof that semester . Same with linear algebra

My PChem teacher taught Diff EQ super well. I swear those derivations are what taught me all the tricks.

I guess homework does teach ya' somethin...

 

[BMEN]

My PChem teacher taught Diff EQ super well. I swear those derivations are what taught me all the tricks.

I guess homework does teach ya' somethin...

Yea
My upper level fluid mechanics course had a lot of partial diffy Q's and I swear I learned all my math in that course

 

[deleted393595]

IIRC we used taylor series approximations in things like process control, but they seemed to pop up once in almost every class I had, as if only to remind us that they exist.

I see. But are they used often in real life? Or is it just one of those hoops you have to jump through?

 

[BMEN]

I see. But are they used often in real life? Or is it just one of those hoops you have to jump through?

Ill take a shot at this,

I've used them in engineering work before. Mainly in coding and data analysis with AFM. You dont need to do the whole series,but some terms do help

 

[FlowRate]

I see. But are they used often in real life? Or is it just one of those hoops you have to jump through?

Ill take a shot at this,

I've used them in engineering work before. Mainly in coding and data analysis with AFM. You dont need to do the whole series,but some terms do help

Yeah exactly. Taylor series are good approximations of functions that are otherwise extremely difficult to determine. Related to some of the Laplace transforms we did in controls IIRC.

Applicable to the real life of a janitor? No. To a doctor? Maybe if you're doing some research biotech stuff. To an engineer? Oh yes, according to BMEN (and many other engineers)

 

[Neurosis]

taking calc 1 in the fall

 

[Eric01]

You use taylor series when you're solving nonlinear differential equations (which can't be solved easily) by changing them into linear differential equations (which can be solved in an easier way)

A simple case of this would be the simple pendulum and changing the sine term for a linear term in small angle approximation. However pretty much every field of science deals with nonlinear differential equations and so without things like taylor series approximations, we would most likely not be as advanced a civilization as we are today.

 

[FlowRate]

You use taylor series when you're solving nonlinear differential equations (which can't be solved easily) by changing them into linear differential equations (which can be solved in an easier way)

A simple case of this would be the simple pendulum and changing the sine term for a linear term in small angle approximation. However pretty much every field of science deals with nonlinear differential equations and so without things like taylor series approximations, we would most likely not be as advanced a civilization as we are today.

Mechanical engineer?

 

[deleted393595]

Ill take a shot at this,

I've used them in engineering work before. Mainly in coding and data analysis with AFM. You dont need to do the whole series,but some terms do help

Yeah exactly. Taylor series are good approximations of functions that are otherwise extremely difficult to determine. Related to some of the Laplace transforms we did in controls IIRC.

Applicable to the real life of a janitor? No. To a doctor? Maybe if you're doing some research biotech stuff. To an engineer? Oh yes, according to BMEN (and many other engineers)

You use taylor series when you're solving nonlinear differential equations (which can't be solved easily) by changing them into linear differential equations (which can be solved in an easier way)

A simple case of this would be the simple pendulum and changing the sine term for a linear term in small angle approximation. However pretty much every field of science deals with nonlinear differential equations and so without things like taylor series approximations, we would most likely not be as advanced a civilization as we are today.

Wow. I didn't know that Taylor series and approximations were used that much in engineering. Thanks a lot for the explanations guys! Reading all of that kinda made me want to go into engineering instead of biology

taking calc 1 in the fall

Calc 1's easy. Just derivatives and basic integrals.

 

[BMEN]

You use taylor series when you're solving nonlinear differential equations (which can't be solved easily) by changing them into linear differential equations (which can be solved in an easier way)

A simple case of this would be the simple pendulum and changing the sine term for a linear term in small angle approximation. However pretty much every field of science deals with nonlinear differential equations and so without things like taylor series approximations, we would most likely not be as advanced a civilization as we are today.

bingo. bingo

 

[ChristianTroy1]

Single-variable calculus can be mastered with practice. A+'s all 3 quarters simply by doing tons and tons of practice problems. It's Multi-variable calculus that seperates the boys from the men.

 

[Goblue89]

Single-variable calculus can be mastered with practice. A+'s all 3 quarters simply by doing tons and tons of practice problems. It's Multi-variable calculus that seperates the boys from the men.

This is so true. Im a boy btw

 

[FlowRate]

Single-variable calculus can be mastered with practice. A+'s all 3 quarters simply by doing tons and tons of practice problems. It's Multi-variable calculus that seperates the boys from the men.

I always thought calc 3 (multivariable) was the easiest one. You already have pretty much all the tools (integrals and derivatives), the added rules for multivariable are easy, go to down. That was, notably, at my school, your mileage may certainly vary.

 

[Drogo]

Math right now by far is my biggest weak point, especially since I've been out of school for quite a few years now.

Would doing the college algebra and trig courses help me out a lot better than say jumping into precalculus? (which of course is trig/coll algebra condensed down)

In general I'm good at the sciences, but when it comes to math I feel as if I have a few mental blocks to overcome.

I eventually have to work up to Calc II and I want to have a real good understanding of all the trig and algebra used.

Thanks in advance for any feedback!

 

[Wafflyw]

Any tips on doing well in Calculus 2, besides doing a lot of problems? I've heard that the course is difficult and the most hated of the three.

 

[BMEN]

Any tips on doing well in Calculus 2, besides doing a lot of problems? I've heard that the course is difficult and the most hated of the three.

just practice practice practice. When you learn a new integration technique do tons of problems.

 

[cham90]

Any tips on doing well in Calculus 2, besides doing a lot of problems? I've heard that the course is difficult and the most hated of the three.

Practice for sure. I would use Paul's math notes for different explanations and example problems. The trick is to stay on top of things; if you wait until preparing for an exam you may feel overwhelmed by all of the techniques that your professor wants you to know.

http://tutorial.math.lamar.edu/Classes/CalcII/CalcII.aspx

 

[Wafflyw]

just practice practice practice. When you learn a new integration technique do tons of problems.

Practice for sure. I would use Paul's math notes for different explanations and example problems. The trick is to stay on top of things; if you wait until preparing for an exam you may feel overwhelmed by all of the techniques that your professor wants you to know.

http://tutorial.math.lamar.edu/Classes/CalcII/CalcII.aspx

Thanks for your advice.

Yeah, I've heard of Paul's math notes. They're really helpful!

 

[HeavyMetalMiss]

my school actually requires you to take College Algebra & Trigonometry as a pre-req to Precalculus, and Precalculus as a pre-req to Calc I. so maybe that is your best bet if time allows. the more practice, the better