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Teaching yourself (Calculus)

  1. Jun 24, 2004 #1
    Hi, Im gonna be a junior next year and I have been put into Algebra2/Trigonametry. I want to learn Calculus before my senior year and in order to that I have to skip Trig and Pre-calc. Since my consoler said if I want to be in Calculus I can but he said its gonna be a huge transition and i agree. :surprise: Since I just past Geometry do you think its possible for me to be in calculus next year?

    Please dont flame...This is a serious question. Thanks in Advance! :smile:
     
  2. jcsd
  3. Jun 24, 2004 #2

    chroot

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    No, I don't believe you'll be ready for calculus next year if you're in Algebra II this year.

    - Warren
     
  4. Jun 24, 2004 #3
    Algebra 2 + trig is equivalent to pre-cal.

    So yeah, you could be in calc by next year. I never took pre-cal either.


    But teaching your self anything past algebra 2 is really hard. I’m pretty much teaching my self cacl2 right now. I have the worst teacher ever, today we reviewed homework for 1 hour and 40 minutes, had a 5 minute break, and then had a 15 minute lecture that covered both le’hospitls (sp?) rule and integration by parts.
     
  5. Jun 24, 2004 #4

    chroot

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    Algebra II/Trig is not, in most programs, the same as pre-cal.

    - Warren
     
  6. Jun 24, 2004 #5
    Wow really? At the school I went to they were the same. Curious, in other school which is more comprehensive and what does the other leave out?
     
  7. Jun 24, 2004 #6
    My schools has these Math Programs:
    -Algebra
    -Geometry
    -Algebra II & Trignometry
    -Pre-Calculus
    -AP Calculus AB or you can take AP Statistics
    -AP Calculus BC

    Maybe other schools are different, i guess. Yeah, some of my friends are going to Algebra II but I really dont want to take that.

    Im skipping Algebra II and Pre-Calculus. Is calculus new? I mean new as in you learn something new and you dont need the skills from the previous mathematics (I hope that didnt confuse anyone).
     
  8. Jun 24, 2004 #7

    chroot

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    You're attempting to go straight from Algebra I to AP Calc AB? You're going to get slaughtered, frankly. Mathematics builds upon itself very strongly -- you need to have mastered all of algebra and trigonometry before even attempting calculus, because you will need those skills at every step.

    - Warren
     
  9. Jun 24, 2004 #8
    Im attempting to go from Geometry to Calculus AB. I agree to what you said...
     
  10. Jun 24, 2004 #9

    chroot

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    Geometry, however, will not help you much in calculus class. I really advise that you follow the normal progression -- you are in no way prepared for calculus yet.

    - Warren
     
  11. Jun 24, 2004 #10
    How much are you willing to work over the summer?

    I agree with chroot that you can't go into Calculus without, at the very least, Algebra II. I personally skipped Pre-calc, but I had to put a pretty sizable amount of work into doing it, and I don't know of anybody else who's done it where I went to school.

    You'd probably have to work your tail off over the summer to get to where you'd need to be for Calculus, and you'd still very likely not be properly prepared.

    cookiemonster
     
  12. Jun 24, 2004 #11

    jcsd

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    What is pre-calculus anyway? i.e. what topics are covered?
     
  13. Jun 24, 2004 #12

    Doc Al

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    I agree with Warren 100%. In my experience, what nails most students is not the new ideas of the calculus (many find that part easy) but the lack of experience with the trig and exponential functions that you'll be doing the calculus on.

    If you really want to get a jump on things, teach yourself calculus. In the process, you'll end up learning all the other math along the way. That's what I did, back in the day. (I actually used a book called "Teach Yourself Calculus"--did every problem in the book and thus sailed through the course when I finally took it. This was in keeping with my philosophy of "never take a course until you already know the subject". A philosophy I eventually had to abandon. :grumpy: )

    There are many decent calculus books out there suitable for self-study. But ya gotta want it.
     
  14. Jun 24, 2004 #13

    chroot

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    Yup. Even if the ideas and concepts of calculus -- limits and derivatives and integrals and so on -- are clear as a bell to you (and they can be made clear through self-study with an appropriate book), the mechanics of actually solving problems will require you to thoroughly understand the underlying mathematics: advanced algebra and trig.

    - Warren
     
  15. Jun 24, 2004 #14
    Hmmmm...I guess I can take Algebra II over the fall at a community college and finnish it there while taking calc but its gonna be hard. Oh well.
     
  16. Jun 24, 2004 #15
    Wow...I envy you. Books is a good way to start. Well, I have nothing to do over the summer so books/computer tutorials can help. Maybe ill try that. Is there any book recommendations?
     
  17. Jun 25, 2004 #16
    I taught myself derivative calculus pretty thoroughly, and I managed shaky understanding of integral calculus and the basics of differential equations. "How to Ace Calculus: The Streetwise Guide" is a good book to introduce yourself to the concepts of a first calculus course. I chose to go back over the material with an actual college textbook once it was not foreign to me anymore. I would still love to take classes on integral calculus and beyond.

    When I took it, it was mostly a class on using the TI-86. Towards the end of the class, we were introduced to such earth-shaking concepts as "the difference quotient". The teacher hinted at limits and derivatives while carefully avoiding those actual terms for them. I think it's more of a second chance to catch up on algebra for those who didn't get a good grasp on it in the preceding classes.

    Trigonometry was also classified as pre-calculus, but I don't see why, since the subject stands on its own quite well and does not bridge the gap between algebra and introductory calculus.
     
  18. Jun 25, 2004 #17

    Math Is Hard

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    I think pre-calculus was one of the hardest classes I ever took. It was actually even harder than Calc 1 and 2. I think this was because it was such an abrupt transition, and also because I never took any trigonometry prior to the class.
     
  19. Jun 25, 2004 #18

    jcsd

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    What sort of ages take pre-calculus? When I was at school in England , our classes were not divided up in such a way we just took maths, though I did also do discrete maths but I gave that up to play football (IIRC). the first time I encountered calculus was at the age of 15 or 16 in the higher-tier GCSE.

    I'm still having trouble vioualizng pre-calc; as I imagined you obviously cover concepts such as slope, but I really can't think of it as something that warrants an entire class to itself.
     
  20. Jun 27, 2004 #19
    I guess the oldest person I've tutored in pre-calculus was in their seventies or so, and the youngest was about 15. In high school, I'd guess most students take pre-calculus when they're about 16 or 17 years old.

    Here's a table of contents from a precalculus textbook. Chapters one through five would be studied in a precalculus class, and chapters six through ten would be probably be studied in a Trigonometry class, which is classified as precalculus. Chapters eleven through thirteen would probably be skipped over entirely, although all of this would vary from school to school and teacher to teacher:

    1. BASICS.
    The Real Number System. Special Topics: Decimal Representation of Real Numbers. Solving Equations Algebraically. Special Topics: Absolute Value Equations. Special Topics: Variation. The Coordinate Plane. Lines. Discovery Project: Modeling the Real World with Lines.
    2. GRAPHS AND TECHNOLOGY.
    Graphs. Solving Equations Graphically and Numerically. Applications of Equations. Optimization Applications. Linear Models. Discovery Project: Supply and Demand.
    3. FUNCTIONS AND GRAPHS.
    Functions. Function Notation. Graphs of Functions. Special Topics: Graph Reading. Graphs and Transformations. Special Topics: Symmetry. Operations on Functions. Rates of Change. Inverse Functions. Discovery Project: Feedback: Good and Bad.
    4. POLYNOMIAL AND RATIONAL FUNCTIONS.
    Quadratic Functions. Polynomial Functions. Special Topics: Synthetic Division. Real Roots of Polynomials. Graphs of Polynomial Functions. Special Topics: Polynomial Models. Rational Functions. Special Topics: Other Rational Functions. Polynomial and Rational Inequalities. Special Topics: Absolute Value Inequalities. Complex Numbers. Theory of Equations. Discovery Project: Architectural Arches.
    5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
    Radicals and Rational Exponents. Special Topics: Radical Equations. Exponential Functions. Special Topics: Compound Interest and the Number e. Common and Natural Logarithmic Functions. Properties of Logarithms. Special Topics: Logarithmic Functions to Other Bases. Algebraic Solutions of Exponential and Logarithmic Equations. Exponential, Logarithmic, and Other Models. Discovery Project: Exponential and Logistic Modeling of Diseases.
    6. TRIGONOMETRIC FUNCTIONS.
    Angles and Their Measurement. The Sine, Cosine, and Tangent Functions. Alternate: The Sine, Cosine, and Tangent Functions. Algebra and Identities. Basic Graphs. Periodic Graphs and Simple Harmonic Motion. Special Topics: Other Trigonometric Graphs. Other Trigonometric Functions. Discovery Project: Pistons and Flywheels.
    7. TRIGONOMETRIC IDENTITIES AND EQUATIONS.
    Basic Identities and Proofs. Addition and Subtraction Identities. Special Topics: Lines and Angles. Other Identities. Inverse Trigonometric Functions. Trigonometric Equations. Discovery Project: The Sun and the Moon.
    8. TRIANGLE TRIGONOMETRY.
    Trigonometric Functions of Angles. Alternate: Trigonometric Functions of Angles. Applications of Right Triangle Trigonometry. The Law of Cosines. The Law of Sines. Special Topics: The Area of a Triangle. Discovery Project: Life on a Sphere.
    9. APPLICATIONS OF TRIGONOMETRY
    The Complex Plane and Polar Form for Complex Numbers. DeMoivre' s Theorem and nth Roots of Complex Numbers. Vectors in the Plane. The Dot Product. Discovery Project: Surveying.
    10. ANALYTIC GEOMETRY.
    Circles and Ellipses. Hyperbolas. Parabolas. Rotations and Second-Degree Equations. Special Topics: Rotation of Axes. Plane Curves and Parametric Equations. Polar Coordinates. Polar Equations of Conics. Discovery Project: Designing Machines to Make Designs.
    11. SYSTEMS OF EQUATIONS.
    Systems of Linear Equations in Two Variables. Special Topics: Systems of Nonlinear Equations. Large Systems of Linear Equations. Matrix Methods for Square Systems. Discovery Project: Input-Output Analysis.
    12. DISCRETE ALGEBRA.
    Sequences and Sums. Arithmetic Sequences. Geometric Sequences. Special Topics: Infinite Series. The Binomial Theorem. Mathematical Induction. Discovery Project: Taking Your Chances.
    13. LIMITS AND CONTINUITY.
    Limits of Functions. Properties of Limits. Special Topics: The Formal Definition of Limit. Continuity. Limits Involving Infinity. Discovery Project: Black Holes.
     
  21. Jun 27, 2004 #20

    Math Is Hard

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    Yep, that almost exactly what we covered in my Pre-calc - chapters one through 10 - with a huge emphasis on being able to find domains and ranges for functions. The only real difference was that we primarily studied unit-circle based trigonometry rather than the right-triangle-based version in my class.
     
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