Which chapters of Larson Calculus are covered in BC but NOT in AB?

Test Preparation AP Mathematics & Computer Science
1

<p>I'm taking AB, trying to self-study for the BC exam since my school doesn't offer BC.</p>

<p>Which chapters should I go learn from Larson?</p>

<p>Thank you very much.</p>

2

<p>From the AP Collegeboard site, AP Calculus homepage</p>

<p>Topic Outline</p>

<p>The topic outline for Calculus BC includes all Calculus AB topics. Additional topics are found in paragraphs that are marked with a plus sign (+) or an asterisk (*). The additional topics can be taught anywhere in the course that the instructor wishes. Some topics will naturally fit immediately after their Calculus AB counterparts. Other topics may fit best after the completion of the Calculus AB topic outline. Although the examination is based on the topics listed here, teachers may wish to enrich their courses with additional topics.</p>

<ol>
<li>Functions, Graphs, and Limits</li>
<li>Derivatives</li>
<li>Integrals</li>
<li>*Polynomial Approximations and Series</li>
</ol>

<p>I. Functions, Graphs, and Limits
A. Analysis of Graphs</p>

<p>With the aid of technology, graphs of functions are often easy to produce. The emphasis is on the interplay between the geometric and analytic information and on the use of calculus both to predict and to explain the observed local and global behavior of a function.
B. Limits of Functions (incl. one-sided limits)</p>

<pre><code>* An intuitive understanding of the limiting process.

  • Calculating limits using algebra.
  • Estimating limits from graphs or tables of data.
    </code></pre>

<p>C. Asymptotic and Unbounded Behavior</p>

<pre><code>* Understanding asymptotes in terms of graphical behavior.

  • Describing asymptotic behavior in terms of limits involving infinity.
  • Comparing relative magnitudes of functions and their rates of change. (For example, contrasting exponential growth, polynomial growth, and logarithmic growth.)
    </code></pre>

<p>D. Continuity as a Property of Functions</p>

<pre><code>* An intuitive understanding of continuity. (The function values can be made as close as desired by taking sufficiently close values of the domain.)

  • Understanding continuity in terms of limits.
  • Geometric understanding of graphs of continuous functions (Intermediate Value Theorem and Extreme Value Theorem).
    </code></pre>

<p>E. *Parametric, Polar, and Vector Functions</p>

<p>The analysis of planar curves includes those given in parametric form, polar form, and vector form.
II. Derivatives
A. Concept of the Derivative</p>

<pre><code>* Derivative presented graphically, numerically, and analytically.

  • Derivative interpreted as an instantaneous rate of change.
  • Derivative defined as the limit of the difference quotient.
  • Relationship between differentiability and continuity.
    </code></pre>

<p>B. Derivative at a Point</p>

<pre><code>* Slope of a curve at a point. Examples are emphasized, including points at which there are vertical tangents and points at which there are no tangents.

  • Tangent line to a curve at a point and local linear approximation.
  • Instantaneous rate of change as the limit of average rate of change.
  • Approximate rate of change from graphs and tables of values.
    </code></pre>

<p>C. Derivative as a Function</p>

<pre><code>* Corresponding characteristics of graphs of 'f and f '.

  • Relationship between the increasing and decreasing behavior of f and the sign of f '.
  • The Mean Value Theorem and its geometric consequences.
  • Equations involving derivatives. Verbal descriptions are translated into equations involving derivatives and vice versa.
    </code></pre>

<p>D. Second Derivatives</p>

<pre><code>* Corresponding characteristics of the graphs of f, f ', and f ".

  • Relationship between the concavity of f and the sign of f ".
  • Points of inflection as places where concavity changes.
    </code></pre>

<p>E. Applications of Derivatives</p>

<pre><code>* Analysis of curves, including the notions of monotonicity and concavity.

    • Analysis of planar curves given in parametric form, polar form, and vector form, including velocity and acceleration.
  • Optimization, both absolute (global) and relative (local) extrema.
  • Modeling rates of change, including related rates problems.
  • Use of implicit differentiation to find the derivative of an inverse function.
  • Interpretation of the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration.
  • Geometric interpretation of differential equations via slope fields and the relationship between slope fields and solution curves for differential equations.
    • Numerical solution of differential equations using Euler’s method.
    • L’H
      </code></pre>
3

<p>I have the 7th edition. AB Is chapters 1-6. BC includes chapters 7-8 as well, with a little bit from chapters 9-11. (Integration Techniques; Infinite Series; Polar/Parametric equations)</p>