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<!DOCTYPE html>
<html lang='en'>
<head>
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<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Math135 Engineering Calc I | Pierce</title>
<meta name="author" content="Mike Pierce">
<meta name="description" content="Course outline/schedule and resources for Mike's Calculus for Engineers I at CMU">
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<header>
<h1>Engineering Calc I</h1>
<ul>
<li> <a href="..">Mike Pierce</a> </li>
<li> Math135 </li>
<li> 2024Fall </li>
<li class="screen"> <a href="https://github.com/mikepierce/Outline-EngineeringCalc1">Fork on GitHub</a> </li>
<li class="print"> Hosted at <a class="url" href="https://org.coloradomesa.edu/~mapierce2/135/">coloradomesa.edu/~mapierce2/135</a> </li>
</ul>
</header>
<main>
<p class="screen">
Within each section are links to notes, video lectures,
technology guides, demonstrations,
practice exercises, problems sets, and past midterm exams.
Chapters enumerated with § refer to
<a href="https://www.stewartcalculus.com"><cite>Calculus 9E</cite> by Stewart</a>.
</p>
<nav class="screen">
<ul class="inline">
<li><a href="summary">Narrative Course Summary</a></li>
<li><a href="workflow">Suggested Course Workflow</a></li>
</ul>
<ul class="inline">
<li><a href="https://www.wolframalpha.com">WolframAlpha</a> </li>
<li><a href="https://www.desmos.com/calculator">Desmos Graphing Calculator</a> </li>
<li><a href="https://copilot.microsoft.com">Microsoft Copilot</a> </li>
</ul>
</nav>
<nav>
<h3 id="one">Week One · August 19</h3>
<details>
<!-- MLK DAY MONDAY Jan20th! -->
<summary>Monday – Review of Algebra</summary>
<ul>
<li>Notes: <a href="https://www.stewartcalculus.com/_update/media/common/reviewofalgebra.pdf"><cite>Review of Algebra</cite>, Stewart</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/Functions.aspx"><cite>Review / Functions</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/InverseFunctions.aspx"><cite>Review / Inverse Functions</cite>, Paul Dawkins</a></li>
</ul>
</details>
<details>
<summary>Tuesday – Review of Analytic Geometry</summary>
<ul>
<li>Notes: <a href="https://www.stewartcalculus.com/_update/media/common/reviewofanalgeom.pdf"><cite>Review of Analytic Geometry</cite>, Stewart</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/CommonGraphs.aspx"><cite>Review / Common Graphs</cite>, Paul Dawkins</a></li>
<li>Lecture: <a href="https://youtu.be/fYyARMqiaag"><cite>Lines, Angle of Inclination, and the Distance Formula</cite>, Professor Leonard</a></li>
<li>Lecture: <a href="https://youtu.be/1EGFSefe5II"><cite>Introduction to Functions</cite>, Professor Leonard</a></li>
<li>Lecture: <a href="https://youtu.be/f-_UsIP5jyA"><cite>Combining and Composing Functions</cite>, Professor Leonard</a></li>
</ul>
</details>
<details>
<summary>Wednesday – Review of Trigonometry</summary>
<ul>
<li>Notes: <a href="https://people.math.sc.edu/girardi/m142/hmwk/Stewart6ET-AppendixD-Trig.pdf"><cite>Review of Trigonometry</cite>, Stewart</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/TrigFcns.aspx"><cite>Review / Trig Functions</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/TrigEquations.aspx"><cite>Review / Solving Trig Equations</cite>, Paul Dawkins</a></li>
<li>Lecture: <a href="https://youtu.be/SzLF-wLZF_I"><cite>Review of Trigonometry</cite>, Professor Leonard</a></li>
</ul>
</details>
<ul>
<li>Thursday – <strong>Preliminary Assessment</strong> </li>
</ul>
<h3 id="two">Week Two · August 26</h3>
<details>
<summary>Mon/Tuesday – Syllabus | Differential Calculus Overview </summary>
<ul>
<li>Display: <a href="display/people.html">Kepler, Newton, Leibniz, and Agnesi</a></li>
<li>Display: <a href="display/dragster.html">How fast was the dragster going?</a></li>
<li>Desmos: <a href="https://www.desmos.com/calculator/3nlj6jqugb">Modelling a Dragster</a></li>
<li>Video: <a href="https://www.3blue1brown.com/lessons/essence-of-calculus"><cite>The essence of calculus</cite>, 3Blue1Brown</a></li>
<li>Video: <a href="https://www.3blue1brown.com/lessons/derivatives"><cite>The paradox of the derivative</cite>, 3Blue1Brown</a></li>
<li>Video: <a href="https://www.3blue1brown.com/lessons/limits"><cite>Limits and the definition of the derivative</cite>, 3Blue1Brown</a></li>
</ul>
</details>
<details>
<summary>Wednesday – Secants, Tangents, and Rates</summary>
<ul>
<li>§1.4 The Tangent and Velocity Problems </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/Tangents_Rates.aspx"><cite>Tangent Lines And Rates of Change</cite>, Paul Dawkins</a></li>
<li>Lecture: <a href="https://youtu.be/PqQ5v94_NGM"><cite>Slope of a Curve, Velocity, and Rates of Change</cite>, Professor Leonard</a></li>
</ul>
</details>
<details>
<summary>Thursday – Problem Solving Session </summary>
<ul class="inline">
<li><a href="problems/secants-tangents-rates.html">Problem Sheet</a></li>
</ul>
</details>
<h3 id="three">Week Three · September 2</h3>
<details>
<summary>Monday – Intro to Limits </summary>
<ul>
<li>§1.5 The Limit of a Function </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/TheLimit.aspx"><cite>The Limit</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/OneSidedLimits.aspx"><cite>One-Sided Limits</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/InfiniteLimits.aspx"><cite>Infinite Limits</cite>, Paul Dawkins</a></li>
<li>Lecture: <a href="https://youtu.be/54_XRjHhZzI"><cite>An Introduction to Limits</cite>, Professor Leonard</a></li>
<li>Desmos: <a href="https://www.desmos.com/calculator/jru4jpde4s">Limits Demonstration</a></li>
<li>Desmos: <a href="https://www.desmos.com/calculator/jvqimdmxci">Limits at Infinite Demonstration</a></li>
<li class="extra">Video: <a href="https://vimeo.com/channels/bkcfilms/101687551"><cite>Limit</cite> (1965), Bruce and Katharine Cornwell</a></li>
</ul>
</details>
<details>
<summary>Tuesday – Evaluating Limits using Limit Laws </summary>
<ul>
<li>§1.6 Calculating Limits using Limit Laws </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/LimitsProperties.aspx"><cite>Limit Properties</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/ComputingLimits.aspx"><cite>Computing Limits</cite>, Paul Dawkins</a></li>
<li>Lecture: <a href="https://youtu.be/VSqOZNULRjQ"><cite>Properties of Limits. Techniques of Limit Computation</cite>, Professor Leonard</a></li>
<li class="extra">Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/LimitProofs.aspx"><cite>Proof of Various Limit Properties</cite>, Paul Dawkins</a></li>
<li class="extra">Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/ProofTrigDeriv.aspx"><cite>Proof of Trig Limits</cite>, Paul Dawkins</a></li>
</ul>
</details>
<details>
<summary>Wednesday – Continuity </summary>
<ul>
<li>§1.8 Continuity </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/Continuity.aspx"><cite>Continuity</cite>, Paul Dawkins</a></li>
<li>Desmos: <a href="https://www.desmos.com/calculator/kq6tat784n">Nasty Example Function</a></li>
<li>Lecture: <a href="https://youtu.be/OEE5-M4aY4k"><cite>Continuity of Functions</cite>, Professor Leonard</a></li>
</ul>
</details>
<details>
<summary>Thursday – Problem Solving Session </summary>
<ul class="inline">
<li><a href="exercises/limits.html">Limit Evaluation Exercises</a></li>
<li><a href="problems/limits-continuity.html">Problem Sheet</a></li>
</ul>
</details>
<h3 id="four" >Week Four · September 9</h3>
<details>
<summary>Mon/Tuesday – The (<var>ε</var>,<var>δ</var>) Definition of a Limit </summary>
<ul>
<li>§1.7 The Precise Definition of a Limit </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/DefnOfLimit.aspx"><cite>The Definition of the Limit</cite>, Paul Dawkins</a></li>
<li>Video: <a href="https://www.3blue1brown.com/lessons/epsilon-delta"><cite><var>(ε,δ)</var> "epsilon delta" definitions of limits</cite>, 3Blue1Brown</a></li>
<li>Desmos: <a href="https://www.desmos.com/calculator/f6t1xbssiz">Epsilon-Delta Limit Demonstration</a></li>
</ul>
</details>
<details>
<summary>Wednes/Thursday – <strong>First Midterm Exam</strong> </summary>
<ul>
<li>Narrative Summary: <a href="summary/#limits-continuity">Limits & Continuity</a></li>
<li>Past Midterm Exams:
<ul class="inline">
<li> <a href="midterms/2022Fall-Midterm1.pdf">2022Fall</a> </li>
<li> <a href="midterms/2023Fall-Midterm1.pdf">2023Fall</a> </li>
<li> <a href="midterms/2024Spring-Midterm1.pdf">2024Spring</a> </li>
<li> <a href="midterms/2024Fall-Midterm1.pdf">2024Fall</a> </li>
</ul>
</li>
</ul>
</details>
<h3 id="five">Week Five · September 16</h3>
<details>
<summary>Monday – The Derivative at a Point</summary>
<ul>
<li>§2.1 Derivatives and Rates of Change </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/DefnOfDerivative.aspx"><cite>The Definition of the Derivative</cite>, Paul Dawkins</a></li>
<li>Lecture: <a href="https://youtu.be/962lLfW-8Jo"><cite>Introduction to the Derivative of a Function</cite>, Professor Leonard</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/DerivativeInterp.aspx"><cite>Interpretation of the Derivative</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/HigherOrderDerivatives.aspx"><cite>Higher Order Derivatives</cite>, Paul Dawkins</a></li>
<li class="extra">Notes: <a href="https://calculusmadeeasy.org/2.html"><cite>Calculus Made Easy No2</cite>, Silvanus P. Thompson </a> <br> (on different degrees of “smallness”)</li>
<li class="extra">Notes: <a href="https://calculusmadeeasy.org/4.html"><cite>Calculus Made Easy No4</cite>, Silvanus P. Thompson </a> <br> (an <em>infinitesimal</em> take on differentiation)</li>
</ul>
</details>
<details>
<summary>Tuesday – The Derivative as a Function </summary>
<ul>
<li>§2.2 The Derivative as a Function </li>
<li>Video: <a href="https://www.3blue1brown.com/lessons/limits"><cite>Limits and the definition of the derivative</cite>, 3Blue1Brown</a></li>
<li>Video: <a href="https://www.3blue1brown.com/lessons/derivatives"><cite>The paradox of the derivative</cite>, 3Blue1Brown</a></li>
<li>Video: <a href="https://www.3blue1brown.com/lessons/higher-order-derivatives"><cite>Higher order derivatives</cite>, 3Blue1Brown</a></li>
<li class="extra">Video: <a href="https://www.3blue1brown.com/lessons/derivatives-and-transforms"><cite>The other way to visualize derivatives</cite>, 3Blue1Brown</a></li>
<li> <a href="https://www.wolframalpha.com/calculators/derivative-calculator/">WolframAlpha Online Derivative Calculator</a> </li>
</ul>
</details>
<details>
<summary>Wednesday – Basic Differentiation Formulas </summary>
<ul>
<li> §2.3 Differentiation Formulas </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/DiffFormulas.aspx"><cite>Differentiation Formulas</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/ProductQuotientRule.aspx"><cite>Product and Quotient Rules</cite>, Paul Dawkins</a></li>
<li>Lecture: <a href="https://youtu.be/EY6FHX6asU0"><cite>Techniques of Differentiation (Finding Derivatives of Functions Easily)</cite>, Professor Leonard</a></li>
<li>Lecture: <a href="https://youtu.be/AvCQQ3X4Nuc"><cite>The Product and Quotient Rules for Derivatives of Functions</cite>, Professor Leonard</a></li>
<li>Video: <a href="https://www.3blue1brown.com/lessons/derivatives-power-rule"><cite>Power Rule through geometry</cite>, 3Blue1Brown</a></li>
<li class="extra">Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/DerivativeProofs.aspx"><cite>Proof of Various Derivative Properties</cite>, Paul Dawkins</a></li>
<li class="extra">Notes: <a href="https://calculusmadeeasy.org/5.html"><cite>Calculus Made Easy No5</cite>, Silvanus P. Thompson </a> <br> (an <em>infinitesimal</em> narrative)</li>
<li class="extra">Notes: <a href="https://calculusmadeeasy.org/6.html"><cite>Calculus Made Easy No6</cite>, Silvanus P. Thompson </a> <br> (an <em>infinitesimal</em> narrative)</li>
</ul>
</details>
<details>
<summary>Thursday – Problem Solving Session </summary>
<ul class="inline">
<li><a href="problems/differentiation.html">Problem Sheet</a></li>
</ul>
</details>
<h3 id="six">Week Six · September 23</h3>
<details>
<summary>Monday – Derivatives of Trigonometric Functions </summary>
<ul>
<li>§2.4 Derivatives of Trigonometric Functions </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/DiffTrigFcns.aspx"><cite>Derivatives of Trig Functions</cite>, Paul Dawkins</a></li>
<li>Video: <a href="https://www.3blue1brown.com/lessons/derivatives-trig-functions"><cite>Trig Derivatives through geometry</cite>, 3Blue1Brown</a></li>
<li>Lecture: <a href="https://youtu.be/RJJSiNz5oto"><cite>Finding Derivatives of Trigonometric Functions</cite>, Professor Leonard</a></li>
<li class="extra">Notes: <a href="https://calculusmadeeasy.org/15.html"><cite>Calculus Made Easy No15</cite>, Silvanus P. Thompson </a> <br> (an <em>infinitesimal</em> narrative)</li>
</ul>
</details>
<details>
<summary>Tuesday – The Chain Rule </summary>
<ul>
<li>§2.5 The Chain Rule </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/ChainRule.aspx"><cite>Chain Rule</cite>, Paul Dawkins</a></li>
<li>Lecture: <a href="https://youtu.be/8dr1dZjfhmc"><cite>Discussion of the Chain Rule for Derivatives of Functions</cite>, Professor Leonard</a></li>
<li>Video: <a href="https://www.3blue1brown.com/lessons/chain-rule-and-product-rule"><cite>Visualizing the chain rule and product rule</cite>, 3Blue1Brown</a></li>
<li class="extra">Notes: <a href="https://calculusmadeeasy.org/9.html"><cite>Calculus Made Easy No9</cite>, Silvanus P. Thompson </a> <br> (an <em>infinitesimal</em> narrative)</li>
</ul>
</details>
<details>
<summary>Wednesday – Implicit Differentiation</summary>
<ul>
<li>§2.6 Implicit Differentiation</li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/classes/calci/implicitdiff.aspx"><cite>Implicit Differentiation</cite>, Paul Dawkins</a> </li>
<li>Lecture: <a href="https://youtu.be/RUS4mKo9tBk"><cite>Implicit Differentiation</cite>, Professor Leonard</a></li>
<li>Video: <a href="https://www.3blue1brown.com/lessons/implicit-differentiation"><cite>Implicit differentiation, what’s going on here?</cite> 3Blue1Brown</a></li>
</ul>
</details>
<details>
<summary>Thursday – Problem Solving Session </summary>
<ul class="inline">
<li><a href="exercises/differentiation.html">Differentiation Exercises</a></li>
<li><a href="problems/trig-chain-rule.html">Problem Sheet</a></li>
</ul>
</details>
<h3 id="seven">Week Seven · September 30</h3>
<details>
<summary>Monday – Related Rates of Change</summary>
<ul>
<li>§2.7 Rates of Change</li>
<li>§2.8 Related Rates</li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/RateOfChange.aspx"><cite>Rates of Change</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/RelatedRates.aspx"><cite>Related Rates</cite>, Paul Dawkins</a></li>
<li>Lecture: <a href="https://youtu.be/43Qt6wc44To"><cite>Related Rates</cite>, Professor Leonard</a></li>
<li>Display: <a href="display/related-rates.html">In-Class Examples</a></li>
<li class="extra">Paper: <a href="https://iopscience.iop.org/article/10.1088/0143-0807/37/6/065008">Beyond velocity and acceleration: jerk, snap and higher derivatives</a></li>
<li class="extra">Notes: <a href="https://calculusmadeeasy.org/3.html"><cite>Calculus Made Easy No3</cite>, Silvanus P. Thompson </a> <br> (an <em>infinitesimal</em> narrative)</li>
</ul>
</details>
<details>
<summary>Tuesday – Optimization </summary>
<ul>
<li>§3.7 Optimization Problems </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/Optimization.aspx"><cite>Optimization</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/MoreOptimization.aspx"><cite>More Optimization</cite>, Paul Dawkins</a></li>
<li>Lecture: <a href="https://youtu.be/SWZcq_biZLw"><cite>Optimization; Max/Min Application Problems</cite>, Professor Leonard</a></li>
<li>Display: <a href="display/optimization.html">In-Class Examples</a></li>
</ul>
</details>
<details>
<summary>Wednes/Thursday – Problem Solving Session </summary>
<ul class="inline">
<li><a href="problems/related-rates.html">Related Rates Problems</a></li>
<li><a href="problems/optimization.html">Optimization Problems</a></li>
</ul>
</details>
<h3 id="eight">Week Eight · October 7</h3>
<details>
<summary>Monday – Extrema and Points of Inflection</summary>
<ul>
<li>§3.1 Maximum and Minimum Values</li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/CriticalPoints.aspx"><cite>Critical Points</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/MinMaxValues.aspx"><cite>Minimum and Maximum Values</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/AbsExtrema.aspx"><cite>Finding Absolute Extrema</cite>, Paul Dawkins</a></li>
<li>Lecture: <a href="https://youtu.be/Mx39JbbzEAo"><cite>Increasing/Decreasing and Concavity of Functions</cite>, Professor Leonard</a></li>
</ul>
</details>
<details>
<summary>Tuesday – Some Theorems</summary>
<ul>
<li>§3.2 The Mean Value Theorem</li>
<li>§3.3 What Derivatives Tell Us about the Shape of a Graph </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/MeanValueTheorem.aspx"><cite>The Mean Value Theorem</cite>, Paul Dawkins</a></li>
<li>Lecture: <a href="https://youtu.be/qW89xdGfSzw"><cite>A BRIEF Discussion of Rolle's Theorem and Mean-Value Theorem.</cite>, Professor Leonard</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/ShapeofGraphPtI.aspx"><cite>The Shape of a Graph, Part I</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/ShapeofGraphPtII.aspx"><cite>The Shape of a Graph, Part II</cite>, Paul Dawkins</a></li>
<li>Lecture: <a href="https://youtu.be/nQ6tOORDQ3I"><cite>The First Derivative Test for Increasing and Decreasing</cite>, Professor Leonard</a></li>
<li>Lecture: <a href="https://youtu.be/29GbRaQxtzY"><cite>The Second Derivative Test for Concavity of Functions</cite>, Professor Leonard</a></li>
<li class="extra">Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/DerivativeAppsProofs.aspx"><cite>Proof of Derivative Application Facts</cite>, Paul Dawkins</a></li>
</ul>
</details>
<details>
<summary>Wednesday – Asymptotics</summary>
<ul>
<li>§3.4 Limits at Infinity; Horizontal Asymptotes </li>
<li>§3.5 Summary of Curve Sketching</li>
<li>§3.6 Graphing with Calculus <em>and</em> Technology</li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/LimitsAtInfinityI.aspx"><cite>Limits At Infinity, Part I</cite>, Paul Dawkins</a></li>
<li>Lecture: <a href="https://youtu.be/-PYebK8DKPc"><cite>Limits of Functions at Infinity</cite>, Professor Leonard</a></li>
<li>Lecture: <a href="https://youtu.be/8u6woY05aL0"><cite>How to Sketch Graphs of Functions</cite>, Professor Leonard</a></li>
<li>Desmos: <a href="https://www.desmos.com/calculator/u4wdnuc6hk">Asymptotics Demo</a></li>
</ul>
</details>
<details>
<summary>Thursday – Problem Solving Session </summary>
<ul class="inline">
<li><a href="problems/graphing.html">Problem Sheet</a></li>
</ul>
</details>
<h3 id="nine">Week Nine · October 14</h3>
<details>
<summary>Monday – Newton’s Method </summary>
<ul>
<li>§2.9 Linear Approximations and Differentials</li>
<li>§3.8 Newton’s Method </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/LinearApproximations.aspx"><cite>Linear Approximations</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/Differentials.aspx"><cite>Differentials</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/NewtonsMethod.aspx"><cite>Newton's Method</cite>, Paul Dawkins</a></li>
<li>Video: <a href="https://vimeo.com/channels/bkcfilms/101830435"><cite>Newton's Method</cite> (1966), Bruce and Katharine Cornwell</a></li>
<li>Desmos: <a href="https://www.desmos.com/calculator/bghkbysedr">Newton’s Method Demo</a></li>
</ul>
</details>
<details>
<summary>Tuesday – Problem Solving Session </summary>
<ul class="inline">
<li><a href="problems/newton.html">Problem Sheet</a></li>
</ul>
</details>
<details>
<summary>Wednes/Thursday – <strong>Second Midterm Exam</strong> </summary>
<ul>
<li>Narrative Summary: <a href="summary/#differentiation">Differentiation</a></li>
<li>Past Midterm Exams:
<ul class="inline">
<li> <a href="midterms/2022Fall-Midterm2.pdf">2022Fall</a> </li>
<li> <a href="midterms/2023Fall-Midterm2.pdf">2023Fall</a> </li>
<li> <a href="midterms/2024Spring-Midterm2.pdf">2024Spring</a> </li>
<li> <a href="midterms/2024Fall-Midterm2.pdf">2024Fall</a> </li>
</ul>
</li>
</ul>
</details>
<h3 id="ten">Week Ten · October 21</h3>
<details>
<summary>Monday – Integral Calculus Overview</summary>
<ul>
<li>Display: <a href="display/maserati.html">Motivating Question</a></li>
<li>Desmos: <a href="https://www.desmos.com/calculator/j9fogbi3i0">The Accumulated Distance as Area</a></li>
<li>Video: <a href="https://www.3blue1brown.com/lessons/integration"><cite>Integration and the fundamental theorem of calculus</cite>, 3Blue1Brown</a></li>
<li>Video: <a href="https://www.3blue1brown.com/lessons/area-and-slope"><cite>What does area have to do with slope?</cite> 3Blue1Brown</a></li>
</ul>
</details>
<details>
<summary>Tuesday – Summation Notation and Riemann Sums</summary>
<ul>
<li>§4.1 The Area and Distance Problems </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/AreaProblem.aspx"><cite>Area Problem</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/SummationNotation.aspx"><cite>Summation Notation</cite>, Paul Dawkins</a></li>
<li>Lecture: <a href="https://youtu.be/F0uuW-I6icY"><cite>Area Under a Curve, Limit Approach, Riemann Sums</cite>, Professor Leonard</a></li>
</ul>
</details>
<details>
<summary>Wednesday – Antiderivatives </summary>
<ul>
<li>§3.9 Antiderivatives </li>
<li>Lecture: <a href="https://youtu.be/b2ZFpE_yrLg"><cite>An Introduction to the Indefinite Integral</cite>, Professor Leonard</a></li>
</ul>
</details>
<details>
<summary>Thursday – Problem Solving Session </summary>
<ul class="inline">
<li><a href="problems/antiderivatives.html">Problem Sheet</a></li>
</ul>
</details>
<h3 id="eleven">Week Eleven · October 28</h3>
<details>
<summary>Monday – Definite Integrals </summary>
<ul>
<li>§4.2 The Definite Integral </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/DefnofDefiniteIntegral.aspx"><cite>Definition of the Definite Integral</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/DefnofDefiniteIntegral.aspx"><cite>Computing Definite Integrals</cite>, Paul Dawkins</a></li>
<li>Lecture: <a href="https://youtu.be/K0ORDCt5Ig0"><cite>The Evaluation of Definite Integrals</cite>, Professor Leonard</a></li>
<li class="extra">Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/ProofIntProp.aspx"><cite>Proof of Various Integral Properties</cite>, Paul Dawkins</a></li>
<li>Video: <a href="https://vimeo.com/channels/bkcfilms/101832466"><cite>The Definite Integral as a Limit</cite> (1966), Bruce and Katharine Cornwell</a></li>
<li>MathSE: <a href="https://math.stackexchange.com/q/15294/167197">Why is the area under a curve the integral?</a> </li>
<li class="extra">MathSE: <a href="https://math.stackexchange.com/q/1637409/167197">What does the integral of position with respect to time mean? </a> </li>
<li>Paper: <a href="https://doi.org/10.2337/diacare.17.2.152"><cite>A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves</cite></a>, Mary M Tai, MS, EDD </li>
<li><a href="https://www.wolframalpha.com/calculators/integral-calculator/">WolframAlpha Online Integral Calculator</a> </li>
<li class="extra">Notes: <a href="https://calculusmadeeasy.org/17.html"><cite>Calculus Made Easy No17</cite>, Silvanus P. Thompson </a> <br> (an <em>infinitesimal</em> narrative)</li>
<li class="extra">Notes: <a href="https://calculusmadeeasy.org/18.html"><cite>Calculus Made Easy No18</cite>, Silvanus P. Thompson </a> <br> (an <em>infinitesimal</em> narrative)</li>
<li class="extra">Notes: <a href="https://calculusmadeeasy.org/19.html"><cite>Calculus Made Easy No19</cite>, Silvanus P. Thompson </a> <br> (an <em>infinitesimal</em> narrative)</li>
</ul>
</details>
<details>
<summary>Tuesday – The Fundamental Theorem of Calculus </summary>
<ul>
<li>§4.3 The Fundamental Theorem of Calculus </li>
<li>Lecture: <a href="https://youtu.be/xjtEfS0vY2o"><cite>The Fundamental Theorem of Calculus</cite>, Professor Leonard</a></li>
<li>Video: <a href="https://www.3blue1brown.com/lessons/integration">Integration and the fundamental theorem of calculus, 3Blue1Brown</a></li>
<li>Video: <a href="https://www.3blue1brown.com/lessons/area-and-slope">What does area have to do with slope? 3Blue1Brown</a></li>
<li>MathSE: <a href="https://math.stackexchange.com/q/333441/167197">The Meaning of the Fundamental Theorem of Calculus</a> </li>
</ul>
</details>
<details>
<summary>Wednesday – Indefinite Integrals</summary>
<ul>
<li>§4.4 Indefinite Integrals and the Net Change Theorem </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/IndefiniteIntegrals.aspx"><cite>Indefinite Integrals</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/ComputingIndefiniteIntegrals.aspx"><cite>Computing Indefinite Integrals</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/ConstantOfIntegration.aspx"><cite>Constant of Integration</cite>, Paul Dawkins</a></li>
</ul>
</details>
<details>
<summary>Thursday – Problem Solving Session </summary>
<ul class="inline">
<li><a href="exercises/integration.html">Integration Exercises</a></li>
<li><a href="problems/integration.html">Problem Sheet</a></li>
</ul>
</details>
<h3 id="twelve">Week Twelve · November 4</h3>
<details>
<summary>Mon/Tuesday – Integration by Substitution </summary>
<ul>
<li>§4.5 The Substitution Rule </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/SubstitutionRuleIndefinite.aspx"><cite>Substitution Rule for Indefinite Integrals</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/SubstitutionRuleIndefinitePtII.aspx"><cite>More Substitution Rule</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/SubstitutionRuleDefinite.aspx"><cite>Substitution Rule for Definite Integrals</cite>, Paul Dawkins</a></li>
<li>Lecture: <a href="https://youtu.be/aiBD9aI69C8"><cite>Integration by Substitution</cite>, Professor Leonard</a></li>
</ul>
</details>
<details>
<summary>Wednesday – Areas Between Curves </summary>
<ul>
<li>§5.1 Areas Between Curves </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/AreaBetweenCurves.aspx"><cite>Areas Between Curves</cite>, Paul Dawkins</a></li>
<li>Lecture: <a href="https://youtu.be/c7wur9Lixb0"><cite>Finding Area Between Two Curves</cite>, Professor Leonard</a></li>
<li class="extra">Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/Area_Volume_Formulas.aspx"><cite>Area and Volume Formulas</cite>, Paul Dawkins</a></li>
</ul>
</details>
<details>
<summary>Thursday – Problem Solving Session </summary>
<ul class="inline">
<li><a href="problems/substitution-areas.html">Problem Sheet</a></li>
<li class="extra"><a href="problems/chebyshev.html">Chebyshev Polynomials</a></li>
<li class="extra"><a href="problems/bernoulli.html">Bernoulli Polynomials</a></li>
</ul>
</details>
<h3 id="thirteen">Week Thirteen · November 11</h3>
<details>
<summary>Mon/Tuesday – Volumes of “Symmetric” Solids</summary>
<ul>
<li>§5.2 Volumes </li>
<li>§5.3 Volumes by Cylindrical Shells </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/VolumeWithRings.aspx"><cite>Volumes with Rings</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/VolumeWithCylinder.aspx"><cite>Volumes with Cylinders</cite>, Paul Dawkins</a></li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/MoreVolume.aspx"><cite>More Volume Problems</cite>, Paul Dawkins</a></li>
<li>Lecture: <a href="https://youtu.be/GJOJl47l2_4"><cite>Volume of Solids By Disks and Washers Method</cite>, Professor Leonard</a></li>
<li>Lecture: <a href="https://youtu.be/BDmlottZVd4"><cite>Volume of Solids By Cylindrical Shells Method</cite>, Professor Leonard</a></li>
<li>Video: <a href="https://vimeo.com/channels/bkcfilms/101863686"><cite>Volume of a Solid of Revolution</cite> (1964), Bruce and Katharine Cornwell</a></li>
<li>Video: <a href="https://vimeo.com/channels/bkcfilms/101866618"><cite>Volume by Shells</cite> (1966), Bruce and Katharine Cornwell</a></li>
</ul>
</details>
<details>
<summary>Wednesday – Work </summary>
<ul>
<li>§5.4 Work </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/Work.aspx"><cite>Work</cite>, Paul Dawkins</a></li>
<li>Display: <a href="display/work.html">Calculating Work</a></li>
</ul>
</details>
<details>
<summary>Thursday – Problem Solving Session </summary>
<ul class="inline">
<li> <a href="problems/volumes-work.html">Problem Sheet</a></li>
</ul>
</details>
<h3 id="fourteen">Week Fourteen · November 18</h3>
<details>
<summary>Mon/Tuesday – The Average Value of a Function </summary>
<ul>
<li>§5.5 Average Value of a Function </li>
<li>Notes: <a href="https://tutorial.math.lamar.edu/Classes/CalcI/AvgFcnValue.aspx"><cite>Average Function Value</cite>, Paul Dawkins</a></li>
</ul>
</details>
<details>
<summary>Wednes/Thursday – <strong>Third Midterm Exam</strong> </summary>
<ul>
<li>Narrative Summary: <a href="summary/#integration">Integration Basics</a></li>
<li>Past Midterm Exams:
<ul class="inline">
<li> <a href="midterms/2022Fall-Midterm3.pdf">2022Fall</a> </li>
<li> <a href="midterms/2023Fall-Midterm3.pdf">2023Fall</a> </li>
<li> <a href="midterms/2024Spring-Midterm3.pdf">2024Spring</a> </li>
<li> <a href="midterms/2024Fall-Midterm3.pdf">2024Fall</a> </li>
</ul>
</li>
</ul>
</details>
<h3 id="fifteen">Week Fifteen · November 25</h3>
<ul>
<li>Thanksgiving Break, No Class</li>
</ul>
<h3 id="sixteen">Week Sixteen · December 2</h3>
<ul>
<li><a href="https://org.coloradomesa.edu/~mapierce2/revision/">Revision Week</a>, No Lecture</li>
</ul>
<h2 id="final">Final Exam</h2>
<ul>
<li>Monday Dec 9 @ 1pm</li>
</ul>
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