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calculus:resources:calculus_videos:chapter2 [2014/09/13 09:54] jbrennan |
calculus:resources:calculus_videos:chapter2 [2015/11/21 16:35] (current) kaz |
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+ | ~~META:title=Chapter 2~~ | ||
+ | ~~NOTOC~~ | ||
+ | <html> | ||
+ | <style> | ||
+ | #header { | ||
+ | background-color:#006f3f; | ||
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+ | </style> | ||
+ | <div id="header"> | ||
+ | <h1 style="margin-top:1; margin-bottom:1;">Calculus Chapter 2</h1></div> | ||
+ | <div id="menu"> | ||
+ | <ul> | ||
+ | <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_videos">Home</a></li> | ||
+ | <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_videos/chapter1">Chapter 1</a></li> | ||
+ | <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_videos/chapter3">Chapter 3</a></li> | ||
+ | <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_videos/chapter4">Chapter 4</a></li> | ||
+ | <li><a href="http://www2.math.binghamton.edu/p/calculus/resources/calculus_videos/chapter5">Chapter 5</a></li> | ||
+ | </ul> | ||
+ | </div> | ||
+ | </html> | ||
+ | \\ | ||
+ | <WRAP box 750px> | ||
+ | <WRAP centeralign>===== The Derivative as a Function =====\\ //Section 2.2 in Stewart's Calculus.//</WRAP> | ||
+ | <WRAP group> | ||
+ | <WRAP centeralign> [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.2_derivative_function.pdf|Classroom Slides PDF]] | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | \\ | ||
+ | <WRAP box 750px> | ||
+ | <WRAP centeralign>===== Differentiation Formulas =====</WRAP> | ||
+ | <WRAP group> | ||
+ | <WRAP half column> | ||
+ | {{youtube>qFHSXnXSaS4}} | ||
+ | </WRAP> | ||
+ | <WRAP half column> | ||
+ | <WRAP> | ||
+ | //Section 2.3 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__ \\ | ||
+ | * Derivative formulas for powers and roots.\\ | ||
+ | * Derivative formulas for sums/differences/products/quotients. | ||
+ | </WRAP> | ||
+ | <WRAP clear></WRAP> | ||
+ | <WRAP centeralign> | ||
+ | [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.3_differentiation_formulas.pdf|Classroom Slides PDF]] | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | \\ | ||
+ | |||
+ | <WRAP box 750px> | ||
+ | <WRAP centeralign>===== Trigonometric Derivatives =====</WRAP> | ||
+ | <WRAP group> | ||
+ | <WRAP half column> | ||
+ | {{youtube>tafh4ANt-gs}} | ||
+ | </WRAP> | ||
+ | <WRAP half column> | ||
+ | <WRAP> | ||
+ | //Section 2.4 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__ \\ | ||
+ | * Familiarity with the limit of sin(x)/x as x approaches zero. | ||
+ | </WRAP> | ||
+ | <WRAP clear></WRAP> | ||
+ | <WRAP centeralign> | ||
+ | [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.4_trig_derivatives.pdf|Classroom Slides PDF]] | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | \\ | ||
+ | |||
+ | <WRAP box 750px> | ||
+ | <WRAP centeralign>===== The Chain Rule =====</WRAP> | ||
+ | <WRAP group> | ||
+ | <WRAP half column> | ||
+ | {{youtube>bNwaBeNamr0}} | ||
+ | </WRAP> | ||
+ | <WRAP half column> | ||
+ | <WRAP> | ||
+ | //Section 2.5 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__ \\ | ||
+ | * Composition and rates of change.\\ | ||
+ | * Chain Rule Formula. | ||
+ | </WRAP> | ||
+ | <WRAP clear></WRAP> | ||
+ | <WRAP centeralign> | ||
+ | [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.5_chain_rule.pdf|Classroom Slides PDF]] | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | \\ | ||
+ | |||
+ | <WRAP box 750px> | ||
+ | <WRAP centeralign>===== Implicit Differentiation =====</WRAP> | ||
+ | <WRAP group> | ||
+ | <WRAP half column> | ||
+ | {{youtube>LUtciqbWhyw}} | ||
+ | </WRAP> | ||
+ | <WRAP half column> | ||
+ | {{youtube>hUEDDP7CvPs}} | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | \\ | ||
+ | |||
+ | <WRAP group> | ||
+ | <WRAP half column> | ||
+ | //Section 2.6 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__\\ | ||
+ | * An equation implicitly defines many functions.\\ | ||
+ | * Implicitly versus explicitly defined functions.\\ | ||
+ | * Basics of Implicit Differentiation. | ||
+ | </WRAP> | ||
+ | <WRAP group> | ||
+ | <WRAP half column centeralign> | ||
+ | [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.6_implicit_differentiation.pdf|Classroom Slides PDF]] | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | \\ | ||
+ | |||
+ | <WRAP box 750px> | ||
+ | <WRAP centeralign>===== Rates of Change in the Sciences =====</WRAP> | ||
+ | <WRAP group> | ||
+ | <WRAP half column> | ||
+ | {{youtube>ZImKZBJlkRE}} | ||
+ | </WRAP> | ||
+ | <WRAP half column> | ||
+ | <WRAP> | ||
+ | //Section 2.7 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__ \\ | ||
+ | * Instantaneous Rates of Change are everywhere! | ||
+ | </WRAP> | ||
+ | <WRAP clear></WRAP> | ||
+ | <WRAP centeralign> | ||
+ | [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.7_sciences.pdf|Classroom Slides PDF]] | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | \\ | ||
+ | |||
+ | <WRAP box 750px> | ||
+ | <WRAP centeralign>===== Related Rates =====</WRAP> | ||
+ | <WRAP group> | ||
+ | <WRAP half column> | ||
+ | {{youtube>W6sPil54GQ8}} | ||
+ | </WRAP> | ||
+ | <WRAP half column> | ||
+ | {{youtube>Q0wgb9pYMoo}} | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | \\ | ||
+ | |||
+ | <WRAP group> | ||
+ | <WRAP> | ||
+ | //Section 2.8 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__\\ | ||
+ | * Rates of change can be found by implicitly differentiating an equation. This technique is useful in obtaining information in natural, less mathematical, settings.\\ | ||
+ | </WRAP> | ||
+ | <WRAP group> | ||
+ | <WRAP half column centeralign> | ||
+ | [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.8_related_rates.pdf|Classroom Slides PDF]] | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | \\ | ||
+ | |||
+ | <WRAP box 750px> | ||
+ | <WRAP centeralign>===== Linearization and Differentials =====</WRAP> | ||
+ | <WRAP group> | ||
+ | <WRAP half column> | ||
+ | {{youtube>1rtvN3dcxbU}} | ||
+ | </WRAP> | ||
+ | <WRAP half column> | ||
+ | {{youtube>2bf00We0FNg}} | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | \\ | ||
+ | |||
+ | <WRAP group> | ||
+ | <WRAP> | ||
+ | //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. | ||
+ | </WRAP> | ||
+ | <WRAP group> | ||
+ | <WRAP half column centeralign> | ||
+ | [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.9_linearization_differentials.pdf|Classroom Slides PDF]] | ||
+ | </WRAP> | ||
+ | <WRAP half column centeralign> | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | </WRAP> | ||
+ | \\ | ||
+ | |||
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