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Thread: Calculus Early Transcendentals in sections

  1. #1 Calculus Early Transcendentals in sections 
    Forum Bachelors Degree Demen Tolden's Avatar
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    Sep 2007
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    This post was originally intended to be a post in the thread, Inverse Functions, a thread I started to get help learning about functions and their inverses from Guitarist and Serpicojr, but as I was typing out this post I realized that it will most likely be useful in the future, at least in reference to posts of mine, while I am learning calculus. I decided to create this post as a seperate link to make it easier to find and more accessible.

    The link to the original thread is this:

    This thread is a response to this post from Guitarist:
    What book are you working from? It doesn't seem to me like the logical next step, unless you have already been told about series, sequences, convergence and the like. I may be wrong, but it seems to me you'll need these concepts in hand before you get into limits and derivatives.

    Or maybe you were planning to start there?
    The book I am working from is called: Calculus Early Transcendentals 5/E Volume 1. I believe it is a text book that the sister of a coworker used to learn calculus from. The author is James Stewart.
    The book contains 12 chapters which are named:

    1. Functions and Models
    2. Limits and Derivatives
    3. Differentiation Rules
    4. Applications of Differentiation
    5. Integrals
    6. Applications of Integration
    7. Techniques of Integration
    8. Further Applications of Integration
    9. Differential Equations
    10. Parametric Equations and Polar Coordinates
    11. Infinite Sequences and Series
    12. Vectors and the Geometry of Space
    Chapter 1, Functions and Models, is divided into 6 sections

    1.1 Four Ways to Represent a Function
    1.2 Mathematical Models: A Catolog of Essential Functions
    1.3 New Functinos from Old Functions
    1.4 Graphing Calculators and Computers
    1.5 Exponential funtions
    1.6 Inverse Functions and Logarithms

    Then of course about 70 review questions follow

    Chapter 2, Limits and Derivatives, is divided into 9 sections

    2.1 The Tangent and Velocity Problems
    2.2 The Limit of a Function
    2.3 Cacluating Limits of a function
    2.4 Percise definition of a limit
    2.5 Continuity
    2.6 Limits at Infinity; Horizontal Asymptotes
    2.7 Tangents, Velocities, and other rates of change
    2.8 Derivities
    2.9 Derivative as a function

    (I might as well type in the rest of the book sections.)

    Chapter 3, Differential Rules, is divided into 11 sections

    3.1 Derivitives of polynomials
    3.2 Product and Quotient Rules
    3.3 Rates of change in the Natural and social sciences
    3.4 Derivatives of trigonomentric functions
    3.5 Chain rule
    3.6 Implicit differentiation
    3.7 Higher Derivatives
    3.8 Derivatives of Logarithmic Functions
    3.9 Hyperbolic functions
    3.10 Related rates
    3.11 Linear approximations and differentials

    Chapter 4, Applications of Differentiation, is divided into 10 sections

    4.1 Maximum and Minimum Values
    4.2 Mean Value Theorem
    4.3 How Derivatives Affect the Shape of a Graph
    4.4 Indeterminate forms and L'Hospital's Rule
    4.5 Summary of Curve Sketching
    4.6 Graphing with calculus and calculators
    4.7 Optimization Problems
    4.8 Applications to business and econimics
    4.9 Newton's Method
    4.10 Antiderivatives

    Chapter 5, Integrals, is divided into 6 sections

    5.1 Areas and distances
    5.2 Definte integral
    5.3 Fundamental theorem of calculus
    5.4 Indefinite integrasl and the net change theorem
    5.5 Substitution rule
    5.6 Logarithm defined as an integral

    Chapter 6, Applications of Integration, is divided into 5 sections

    6.1 Areas between curves
    6.2 Volumes
    6.3 Valumes by cylindrical shells
    6.4 Work
    6.5 Average value of a function

    Chapter 7, Techniques of Integration, is divided into 8 sections

    7.1 Integration by parts
    7.2 Trigonometric Integrals
    7.3 Trigonometric substitution
    7.4 Integration of rational functions by partial fractions
    7.5 Strategy for integratino
    7.6 Integration using tables and conputer algebra systems
    7.7 Approximate integration
    7.8 Improper integrals

    Chapter 8, Further Applications of Integration, is divided into 5 sections

    8.1 Arc Length
    8.2 Area of a surface of revolution
    8.3 Applications to physics and engineering
    8.4 Applications to economics and biology
    8.5 Probablitiy

    Chapter 9, Differential Equations, is divided into 7 sections

    9.1 Modeling with differential equations
    9.2 Direction fields and Euler's method
    9.3 Separable equations
    9.4 Exponential growth and decay
    9.5 Logistic Equation
    9.6 Linear Equations
    9.7 Predator-prey systems

    Chapter 10, Parametric Equations and Polar Coordinates, is divided into 6 sections

    10.1 Curves defined by parametric equations
    10.2 Calculus with parametric curves
    10.3 Polar coordinates
    10.4 Areas and lengths in polar coordinates
    10.5 Conic sections
    10.6 Conic sections in polar coordinates

    Chapter 11, Infinite Sequences and Series, is divided into 12 sections

    11.1 Sequnces
    11.2 Series
    11.3 Integral Test and estimates of sums
    11.4 Comparison tests
    11.5 Alternating series
    11.6 Absolute convergence and the ratio and root tests
    11.7 Strategy for testing series
    11.8 Power series
    11.9 Representations of functions as power series
    11.10 Taylor and Maclaurin series
    11.11 Binomial series
    11.12 Applications of Taylor Polynomials

    Chapter 12, Vectors and the Geometry of Space, is divided into 7 sections

    12.1 Three-Dimentional coordinate systems (Now this I should be good at!)
    12.2 Vectors
    12.3 Dot product
    12.4 Cross product
    12.5 Equations of lines and planes
    12.6 Cylinders and quadric surfaces
    12.7 Cylindrical and spherical coordinates

    Then the book has 8 Appendixes

    A. Numbers, Inequalities, and Absolute Values
    B. Coordinate Geometry and Lines
    C. Graphs of Second-Degree Equations
    D. Trigonometry
    E. Sigma Notation
    F. Proofs of Theorems
    G. Complex Numbers
    H. Answers to Odd-Numbered Exercises

    The most important thing I have learned about the internet is that it needs lot more kindness and patience.
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  3. #2  
    Forum Professor serpicojr's Avatar
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    Jul 2007
    I am very familiar with this book--I've taught calculus II out of it a couple of times (chs. 6-11).

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  4. #3  
    Forum Bachelors Degree Demen Tolden's Avatar
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    Sep 2007
    St. Paul, Minnesota, USA
    That's awesome
    The most important thing I have learned about the internet is that it needs lot more kindness and patience.
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  5. #4  
    Forum Bachelors Degree Demen Tolden's Avatar
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    Sep 2007
    St. Paul, Minnesota, USA
    I figured that there may have been a lot of usefull information posted in my calc threads way back, so I wanted to index them from the "main page." I wanted to index these at a later date, maybe when I could finish up the last 5 chapters, but it doesn't seem like that will work out with my new school schedule and perhaps without a tireless serpicojr lurking around.

    Ch 1 - Functions and Models

    Ch 2 - Limits and Derivitives

    Ch 3 - Differential Rules

    Ch 4 - Applications of Differentiation

    Ch 5 - Integrals

    Ch 6 - Applications of Integration

    Ch 7 - Techniques of Integration

    Ch 8 - Further Applications of Integration
    The most important thing I have learned about the internet is that it needs lot more kindness and patience.
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