Applications: Flipped Calculus at Binghamton SUNY [Department of Mathematics and Statistics, Binghamton University]

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<h1 style="margin-top:1; margin-bottom:1;">Flipped Calculus 1 at Binghamton</h1></div>
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<li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources">Home</a></li>
<li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits">Limits</a></li>
<li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives">Derivatives</a></li>
<li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications">Applications</a></li>
<li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/integrals">Integrals</a></li>
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<WRAP centeralign>===== Linearization and Differentials =====</WRAP>
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//Section 2.9 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__\\ 
  * Lines are functions, even tangent lines.\\ 
  * Linearization of a function f(x) approximates the values of f(x).\\ 
  * The change along the y-axis can be approximated with linearization.
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[[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.9_linearization_differentials.pdf|Classroom Slides PDF]]
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[[https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/2.9_linearization_differentials_tex.html|Classroom Slides TEX]]
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<WRAP centeralign>===== Critical Points and the Closed Interval Method =====</WRAP>
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//Section 3.1 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__\\ 
  * Graphical understanding of extrema.\\ 
  * Fermat's Theorem.\\ 
  * Local extrema are critical points, the opposite isn't necessarily true.\\ 
  * Extreme Value Theorem.\\ 
  * The Closed Interval Method.
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[[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.1_critical_points.pdf|Classroom Slides PDF]]
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[[https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/3.1_critical_points_tex|Classroom Slides TEX]]
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<WRAP centeralign>===== The Mean Value Theorem ===== //Section 3.2 in Stewart's Calculus.//</WRAP>
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<WRAP half column centeralign>  [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.2_mean_value_theorem.pdf|Classroom Slides PDF]]  
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[[https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/3.2_mean_value_theorem_tex|Classroom Slides TEX]]
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<WRAP centeralign>===== The Shape of a Graph =====</WRAP>
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//Section 3.3 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__\\ 
  * If the derivative is positive on an interval, the original function is increasing on that interval. If the derivative is negative on an interval, the original function is decreasing on that interval.\\ 
  * Concavity describes the direction a function is bending. A function is concave up on an interval, then the second derivative is positive on that interval and the function bends upwards. A function is concave down on an interval, the second derivative is negative on that interval and the function bends downwards.
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[[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.3_graph_shape.pdf|Classroom Slides PDF]]
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[[https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/3.3_graph_shape_tex|Classroom Slides TEX]]
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<WRAP centeralign>===== Horizontal Asymptotes =====</WRAP>
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//Section 3.4 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__\\ 
  * The end behavior of a function is described with limits.\\ 
  * Horizontal asymptotes of power functions are either zero or do not exist (tend towards infinity).\\ 
  * Determinate and indeterminate forms.\\ 
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[[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.4_horizontal_asymptotes.pdf|Classroom Slides PDF]]
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[[https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/3.4_horizontal_asymptotes_tex|Classroom Slides TEX]]
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<WRAP centeralign>===== Curve Sketching =====</WRAP>
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//Section 3.5 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__ \\ 
  * The basics of curve sketching. 
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<WRAP centeralign>===== Optimization =====</WRAP>
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//Section 3.7 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__ \\ 
  * Optimized solutions to problems are found at critical points. This technique is useful in obtaining information in natural, less mathematical, settings.\\  
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[[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/3.7_optimization.pdf|Classroom Slides PDF]]
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<WRAP centeralign>===== Antiderivatives =====</WRAP>
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//Section 3.9 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__ \\ 
  * Antiderivatives of a function f(x) are functions whose derivative is f(x).\\ 
  * The antiderivatives of a function differ by only a constant.\\ 
  * Antiderivatives of common functions.\\ 
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<div id="footer"><h1>Laura Anderson and Joseph Brennan</h1> </div>
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