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I didn't learn things in Calc 1 that is needed in Calc 2

  1. Jan 9, 2006 #1
    I have a pretty big problem. I just got out of my first Calc 2 class and we are using James Stewarts Calculus 5th edition. The problem is that we are starting on ch. 12 in the calc 2 class, but we only went up to chapter 7 in my calc 1 class. I talked to my prof. and he said I should self teach myself very fast the 4 chapters(!) that we failed to learn in Calc 1. Here is the way the chapters are set up all the way to the end of calc 2:
    1 - Functions and Models
    2 - Limits and Rate of Change
    3 - Derivatives
    4 - Applications of Differentiation
    5 - Integrals
    6 - Applications of Integration
    7 - Inverse Functions
    8 - Techniques of Integration
    9 - Further Applications of Integration
    10 - Differential Equations
    11 - Parametric Equations and Polar Coordinates
    12 - Infinite Sequences and Series
    13 - Vectors and the Geometry of Space
    14 - Vector Functions
     
    Last edited: Jan 9, 2006
  2. jcsd
  3. Jan 9, 2006 #2
    The calc 2 class covers ch 12-14. So I have not done ch 8-11.
    Here is what those chapters consist of:

    ---------CHAPTER 8 - Techniques of Integration
    8.1 - Integration by Parts
    8.2 - Trigonometric Integrals
    8.3 - Trigonometric Subsitution
    8.4 - Integration of Rational Functions by Partial Fractions
    8.5 - Strategy for Integration
    8.6 - Integration Using Tables and Computer Algebra Systems
    8.7 - Approximation Integration
    8.8 - Improper Integrals

    ---------CHAPTER 9 - Further Applications of Integration
    9.1 - Arc Length
    9.2 - Area of a Surface of Revolution
    9.3 - Applications to Physics and Engineering
    9.4 - Applications to Economics and Biology
    9.5 - Probability

    ---------CHAPTER 10 - Differential Equations
    10.1 - Modeling with Differential Equations
    10.2 - Direction Fields and Euler's Method
    10.3 - Separable Equations
    10.4 - Exponential Growth and Decay
    10.5 - The Logistic Equation
    10.6 - Linear Equations
    10.7 - Predator-Prey Systems

    ---------CHAPTER 11 - Parametric Equations and Polar Coordinates
    11.1 - Curves Defined by Parametric Equations
    11.2 - Calculus with Parametric Curves
    11.3 - Polar Coordinates
    11.4 - Areas and Lengths in Polar Coordinates
    11.5 - Conic Sections
    11.6 - Conic Sections in Polar Coordinates
     
    Last edited: Jan 9, 2006
  4. Jan 9, 2006 #3
    So my question is which of these sections should I self study? I plan on self studdying the sections I need within the next 7 days, so I want to only study the sections that are most important. My professor said the most important ones are the one dealing with Integration, but I still can't study every section from those chapters. What sections would you recomend for me to studdy. I preffer to study no more than 10 sections.
     
  5. Jan 9, 2006 #4

    LeonhardEuler

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    Gold Member

    I would say that most of those sections are important in themselves, but the ones most important to vector calculus would be 9.1, 9.2, 11.1, 11.2, 11.3, and 11.4. These will be important to undertanding the concepts of vector calculus, but I could see something from 8.1-8.5 popping up as part of a question on a test. You should catch up on the rest eventually, but I think these are the most important.
     
  6. Jan 9, 2006 #5
    You could probably skip all of chapter 10, and sections 9.3, 9.4, 9.5, and do the rest if that is not too much.

    edit...

    If you are starting with Sequences/Series ch12, then you could cover sections 8.1-8.5 and also 9.1, 9.2 (as Leonhard said) right now. Then later on, maybe a week or so before you finish Sequences/Series you could do Chapter 11. Unless I am mistaken, you won't need anything from chapter 11 for chapter 12.
     
    Last edited: Jan 9, 2006
  7. Jan 9, 2006 #6
    Ok, Euler, you say I should do sections:
    9.1
    9.2
    11.1
    11.2
    11.3
    11.4

    And Mattmns, you say I should do everything on my list except Ch. 10 and section 9.3 - 9.5?
     
  8. Jan 9, 2006 #7
    Sorry Mattmns, but I don't think there is any way I can do all the stuff you mentioned.
    But Euler, you say that the sections from ch 8 are not too important for understanding of more advanced topics?
     
  9. Jan 9, 2006 #8
    Are you sure that the stuff in ch 8 isn't to most important? He did say that the integration stuff is most important. Do you really think that doing all that stuff from ch 11 is important? I was under the impression that the polar coordinate stuff was the least important.
     
  10. Jan 9, 2006 #9
    Thanks for helping me guys. I plan on start studying these sections in about one hour from now, so I really apreciate the fast responses to my questions.
     
  11. Jan 9, 2006 #10
    What do you guys think about this:
    8.1 - Integration by Parts
    8.4 - Integration of Rational Functions by Partial Fractions
    9.1 - Arc Length
    9.2 - Area of a Surface of Revolution
    11.1 - Curves Defined by Parametric Equations
    11.2 - Calculus with Parametric Curves
    11.3 - Polar Coordinates
    11.4 - Areas and Lengths in Polar Coordinates
     
  12. Jan 9, 2006 #11
    Whoa, whoa, whoa, whoa, whoa.

    Chapter 8 is what you're supposed to be covering in your Calc 2 class. There is no possible way you can teach yourself that material "quickly."

    If you did not cover that material in Calc 1, and you're not going to do it in Calc 2, when are you supposed to learn integration?

    I used the same textbook you did in my Calc class. We started at chapter 8.

    However, if you really need to do crash course, just FOCUS on chapter 8. The other stuff you will barely use, and if you do, you can learn it as you go along.

    Integration is incredibly, insanely, big time important.

    Honestly, I think you should drop your current class and find one that will focus on chapter 8. I spent over a month in my Calculus 2 class learning the techniques of integration.
     
  13. Jan 9, 2006 #12
    Or am I making too big of a deal out of this? Should I just skip all of those chapters I did not learn and just go straight into ch 12-14? Do I really need any of the stuff from ch 8-11?
     
  14. Jan 9, 2006 #13
    Also, you will take a class on Differential Equations. Don't worry about covering them now.
     
  15. Jan 9, 2006 #14
    Maxwell, how long are you going to be online?
     
  16. Jan 9, 2006 #15
    NO! You NEED, NEED, NEED the stuff in chapter 8. It is INCREDIBLY important. You will be using integrals, or have to understand their function for your ENTIRE time as an engineering student.

    Every single class you take you will be integrating or seeing integrals.
     
  17. Jan 9, 2006 #16
    I'll be online all day.
     
  18. Jan 9, 2006 #17
    Thats what I thought. So you think I should just focus on Ch. 8?
     
  19. Jan 9, 2006 #18
    Cool. I might need to ask you advice throughout the next couple of hours, is that going to be ok? I am freaking out.
     
  20. Jan 9, 2006 #19
    I don't mean I am going to talk to you for four hours straight, I just mean I might need to ask you a a question every 20 minutes of so. While I try to figure out what I should do.
     
  21. Jan 9, 2006 #20
    Yeah, I'll be here if you need anything.

    And don't freak out. It's just the guys earlier in the thread gave you suggestions about which topics you need for the vector calc material. And they are right -- for the vector calc material.

    However, as an electrical engineering student, having never taken a class where you were given an in-depth treatment on the techniques of integration will REALLY hurt you.

    I'd definitely recommend you find a class that goes over chapter 8 for most of the curriculum.
     
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