Topics that must be known for Calc I

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SUMMARY

The essential topics for success in Calculus I and II include sequences, series, trigonometry, polar coordinates, and limits. Key concepts such as the law of cosines, law of sines, and trigonometric identities are crucial for understanding derivatives and solving triangles. While some students report limited use of trigonometry in Calculus I, it becomes significantly more relevant in Calculus II. Resources like Spivak's Calculus and Stuart's Calculus are recommended for foundational learning.

PREREQUISITES
  • Understanding of limits and continuity
  • Familiarity with trigonometric functions and identities
  • Basic knowledge of polar coordinates
  • Proficiency in vector operations and properties
NEXT STEPS
  • Study the law of cosines and law of sines in depth
  • Learn about trigonometric identities and their applications in calculus
  • Explore polar coordinates and their relevance in calculus problems
  • Review vector operations and their applications in calculus contexts
USEFUL FOR

High school students preparing for Calculus I and II, educators teaching precalculus concepts, and anyone seeking to strengthen their understanding of foundational mathematics for advanced calculus studies.

BloodyFrozen
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What are the topics that must be known for Calc I and CalcII from Precalculus? Which are the ones usually tested in the final. I do not know about this because I am planning to skip it. Thanks:smile:

P.S. If you can answer this, could you please help me understand Euler's Identity/ Formula?

https://www.physicsforums.com/showthread.php?t=489432
 
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Sequences, series, trigonometry, polar coordinates, limits

BloodyFrozen said:
P.S. If you can answer this, could you please help me understand Euler's Identity/ Formula?

What are you not understanding about it? Were you looking for a proof or just an explanation of what it is?
 


I just don't understand how this applies to trig.
And are vectors of any use? If, so how deep does precalc go into about it?
 


Trig equations, law of cosines, law of sines, how to solve triangles, exponential equations, trig id's, polar coordinates, vectors, limits, and some other things, but the ones I listed are the main things you must know. I was tested on these when I tested out of pre-cal 1 to calculus 1. So far, I haven't used trig in calculus, but from what I've heard, it's used a lot in calculus 2.
 


Domn said:
Trig equations, law of cosines, law of sines, how to solve triangles, exponential equations, trig id's, polar coordinates, vectors, limits, and some other things, but the ones I listed are the main things you must know. I was tested on these when I tested out of pre-cal 1 to calculus 1. So far, I haven't used trig in calculus, but from what I've heard, it's used a lot in calculus 2.


How much depth do I need to go on in vectors? Anyone know?
 


I want to also skip precalc(after a few more topics ie. series, vectors; almost wrapped my head around them), but the high school won't allow it. I don't know if it's that I'm about to move there or what...

---beside the point---> anyone know if Spivak's 4th Edition(I think) Calculus is good for starters or is it too hard? I know basics of calc (differentiation, limits, integrals). So-so with integrals...

Vectors...*sigh* People say they're but, they look so complicated<-------Back to where we were.
 
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I don't see how polar coordinates are a must-know for calculus; not even vectors are a must know *for calculus*, but you will have to know them well eventually.
"Pre-Calc" doesn't seem like too much to me; just be comfortable with manipulations and properties of numbers.. et c and you can jump right into calculus.

Spivak's Calculus book is very good, even if you find it too hard, working through it is nonetheless very educational
 


Domn said:
Trig equations, law of cosines, law of sines, how to solve triangles, exponential equations, trig id's, polar coordinates, vectors, limits, and some other things, but the ones I listed are the main things you must know. I was tested on these when I tested out of pre-cal 1 to calculus 1. So far, I haven't used trig in calculus, but from what I've heard, it's used a lot in calculus 2.
I'm surprised you haven't used trig in your first calculus course. I take it that you haven't seen any derivative formulas for the trig functions.
 


Ok, I'll get it if I can. Can someone please clarify the topics about vectors in honors precalc?

Anyone know of a way that which they'll test me to see if I can skip precalc?
 
  • #10


Mark44 said:
I'm surprised you haven't used trig in your first calculus course. I take it that you haven't seen any derivative formulas for the trig functions.

We're in week 2. The teacher took 3 days on limits for some reason. I've skipped ahead myself and Trig id's are a must when taking the derivative of functions such as f(x)=sin(x). In my independent studies I only spent three days on vectors. If you find a precal textbook there should be a section just on vectors and polar coordinates.
 
  • #11


BloodyFrozen said:
Ok, I'll get it if I can. Can someone please clarify the topics about vectors in honors precalc?

Anyone know of a way that which they'll test me to see if I can skip precalc?

Ask your math teacher. Don't just expect to be able to though. I'm taking college classes through the running start program and it seems like professors are more lenient in allowing people to test out of classes than high school teachers. I don't see why you want to test out of pre-cal if you don't have a knowledge of the material though. Maybe it would be better if you finished pre-cal.
 
  • #12


Domn said:
Ask your math teacher. Don't just expect to be able to though. I'm taking college classes through the running start program and it seems like professors are more lenient in allowing people to test out of classes than high school teachers. I don't see why you want to test out of pre-cal if you don't have a knowledge of the material though. Maybe it would be better if you finished pre-cal.

I know the topics in this, but I don't know how much in depth as the books that are sold online for precalc have nothing about vectors, etc. And my math teacher doesn't really know either =/
 
  • #13


BloodyFrozen said:
---beside the point---> anyone know if Spivak's 4th Edition(I think) Calculus is good for starters or is it too hard? I know basics of calc (differentiation, limits, integrals). So-so with integrals...

Depends on you. Are you well-motivated and are you a little bit gifted for math?? In that case, yes, Spivak is one of the best references for you...
 
  • #14


BloodyFrozen said:
I know the topics in this, but I don't know how much in depth as the books that are sold online for precalc have nothing about vectors, etc. And my math teacher doesn't really know either =/

Google pre-cal vectors and there should be a summary on it somewhere. Oh and I suggest stuarts for a calculus book. It's what I'm currently using. There's also a free calculus book that my professor is making us use and i'll provide the link after I get home later tonight. Its free and it's a pretty good textbook. I also have a free pre-cal book that will explain vectors but I will provide the link later.
 
  • #15


Domn said:
Google pre-cal vectors and there should be a summary on it somewhere. Oh and I suggest stuarts for a calculus book. It's what I'm currently using. There's also a free calculus book that my professor is making us use and i'll provide the link after I get home later tonight. Its free and it's a pretty good textbook. I also have a free pre-cal book that will explain vectors but I will provide the link later.

Alright thanks, no rush, get to it whenever you have time.
 
  • #16


micromass said:
Depends on you. Are you well-motivated and are you a little bit gifted for math?? In that case, yes, Spivak is one of the best references for you...

How hard is it to understand, I mean does it use common/semiformal language or like very mathematical notation?
 
  • #17
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  • #18


Alright thanks and to everyone who has helped so far; I'll post back if I have any questions.
 
  • #19


Domn said:
http://www.stitz-zeager.com/Free_College_Algebra_Book_Download.html

Precalculus is the one you want to download.

http://www.whitman.edu/mathematics/california_calculus/calculus.pdf

Here is the Calculus textbook my class is using, it's from a different website but it's the same material.

I tried to open both of them, but they won't run.. will they again later. Any ideas to open it?
 
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  • #20


Anyone that could help?
 
  • #21


Update or install adobe acrobat to open the PDF files. They work just fine for me.
 
  • #22


BloodyFrozen said:
How hard is it to understand, I mean does it use common/semiformal language or like very mathematical notation?

it's not hard to understand at all. It's a very "modern" book, and it exposites the mathematics in a very conversational style. If you want to see an old-school ( but good, according to most people ) rigorous calculus book, check out Courants "integral and differential calculus" book
 
  • #23


QuarkCharmer said:
Update or install adobe acrobat to open the PDF files. They work just fine for me.

What he said, if you have adobe reader updated they should open fine.
 
  • #24


Domn said:
What he said, if you have adobe reader updated they should open fine.

Alright thanks, I'll check it out later.o:)
 
  • #25


wisvuze said:
it's not hard to understand at all. It's a very "modern" book, and it exposites the mathematics in a very conversational style. If you want to see an old-school ( but good, according to most people ) rigorous calculus book, check out Courants "integral and differential calculus" book

Is it suitable for first year Calculus students in high school?, and is it very indepth?:biggrin:
 
  • #26


Considering the title, it should work well for you. Integrals and Diferention (sorry for my spelling) are the two main parts of calculus. Are you preparing for the AB AP calculus test or the BC?
 
  • #27


Domn said:
Considering the title, it should work well for you. Integrals and Diferention (sorry for my spelling) are the two main parts of calculus. Are you preparing for the AB AP calculus test or the BC?

Actually, I would like to learn both. Especially what's taught in both class, if not more.
 
  • #28


Additional Question: Does Spivak use lots of notation in his textbooks?

And which edition should I get?
 

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