Dr. Karen Brucks: New Applications
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en-us2020 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSat, 31 Oct 2020 17:06:09 GMTSat, 31 Oct 2020 17:06:09 GMTNew applications published by Dr. Karen Bruckshttps://www.maplesoft.com/images/Application_center_hp.jpgDr. Karen Brucks: New Applications
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Calculus I: Lesson 21: L'Hospital's Rule
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In this worksheet, we look at L'Hospital's Rule.<img src="https://www.maplesoft.com/view.aspx?si=1592/Calc1_logo.gif" alt="Calculus I: Lesson 21: L'Hospital's Rule" style="max-width: 25%;" align="left"/>In this worksheet, we look at L'Hospital's Rule.https://www.maplesoft.com/applications/view.aspx?SID=1592&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen BrucksCalculus I: Lesson 20: Exponential Growth and Decay
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In this worksheet, we look at exponential growth and decay.<img src="https://www.maplesoft.com/view.aspx?si=1591/Calc1_logo.gif" alt="Calculus I: Lesson 20: Exponential Growth and Decay" style="max-width: 25%;" align="left"/>In this worksheet, we look at exponential growth and decay.https://www.maplesoft.com/applications/view.aspx?SID=1591&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen BrucksCalculus I: Lesson 19: Applications of Inverse Trig Functions
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In this worksheet, we look at applications of inverse trig functions.<img src="https://www.maplesoft.com/view.aspx?si=1590/Calc1_logo.gif" alt="Calculus I: Lesson 19: Applications of Inverse Trig Functions" style="max-width: 25%;" align="left"/>In this worksheet, we look at applications of inverse trig functions.https://www.maplesoft.com/applications/view.aspx?SID=1590&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen BrucksCalculus I: Lesson 18: Inverse Functions
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This worksheet will look at inverse functions.<img src="https://www.maplesoft.com/view.aspx?si=1589/Calc1_logo.gif" alt="Calculus I: Lesson 18: Inverse Functions" style="max-width: 25%;" align="left"/>This worksheet will look at inverse functions.https://www.maplesoft.com/applications/view.aspx?SID=1589&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen BrucksCalculus I: Lesson 17: The Mean Value Theorem
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In this worksheet, we look at the Mean Value Theorem.<img src="https://www.maplesoft.com/view.aspx?si=1588/Calc1_logo.gif" alt="Calculus I: Lesson 17: The Mean Value Theorem" style="max-width: 25%;" align="left"/>In this worksheet, we look at the Mean Value Theorem.https://www.maplesoft.com/applications/view.aspx?SID=1588&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen BrucksCalculus I: Lesson 16: Analysing the Graphs of Functions 2 - Extrema and Asymptotes
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In this worksheet, for each function, we find: intervals of increase or decrease, extrema, intervals of concavity, points of inflection, and asymptotes.<img src="https://www.maplesoft.com/view.aspx?si=1587/Calc1_logo.gif" alt="Calculus I: Lesson 16: Analysing the Graphs of Functions 2 - Extrema and Asymptotes" style="max-width: 25%;" align="left"/>In this worksheet, for each function, we find: intervals of increase or decrease, extrema, intervals of concavity, points of inflection, and asymptotes.https://www.maplesoft.com/applications/view.aspx?SID=1587&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen BrucksCalculus I: Lesson 15: Analysing the Graphs of Functions 1 - Direction and Concavity
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In this worksheet, we graph several functions and find: all critical points, where the function is increasing and where it is decreasing, where the function is concave down and where it is concave up, and all points of inflection.<img src="https://www.maplesoft.com/view.aspx?si=1586/Calc1_logo.gif" alt="Calculus I: Lesson 15: Analysing the Graphs of Functions 1 - Direction and Concavity" style="max-width: 25%;" align="left"/>In this worksheet, we graph several functions and find: all critical points, where the function is increasing and where it is decreasing, where the function is concave down and where it is concave up, and all points of inflection.https://www.maplesoft.com/applications/view.aspx?SID=1586&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen BrucksCalculus I: Lesson 14: Solving Trigonometric Equations
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In this lesson, we show how to solve equations for x that contain trig functions. Our general method will be to move all terms over to the left-hand side of the equation and find the roots of the resulting equation. We'll find these roots both analytically (by solving) and graphically by inspecting the plot and seeing where the curve crosses the x-axis.<img src="https://www.maplesoft.com/view.aspx?si=1585/Calc1_logo.gif" alt="Calculus I: Lesson 14: Solving Trigonometric Equations" style="max-width: 25%;" align="left"/>In this lesson, we show how to solve equations for x that contain trig functions. Our general method will be to move all terms over to the left-hand side of the equation and find the roots of the resulting equation. We'll find these roots both analytically (by solving) and graphically by inspecting the plot and seeing where the curve crosses the x-axis.https://www.maplesoft.com/applications/view.aspx?SID=1585&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen BrucksCalculus I: Lesson 13: Quadratic Approximation
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In this worksheet, we'll look at quadratic approximation.<img src="https://www.maplesoft.com/view.aspx?si=1584/Calc1_logo.gif" alt="Calculus I: Lesson 13: Quadratic Approximation" style="max-width: 25%;" align="left"/>In this worksheet, we'll look at quadratic approximation.https://www.maplesoft.com/applications/view.aspx?SID=1584&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen BrucksCalculus I: Lesson 12: Linear Approximation
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In this worksheet, we'll look at linear approximation.<img src="https://www.maplesoft.com/view.aspx?si=1583/Calc1_logo.gif" alt="Calculus I: Lesson 12: Linear Approximation" style="max-width: 25%;" align="left"/>In this worksheet, we'll look at linear approximation.https://www.maplesoft.com/applications/view.aspx?SID=1583&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen BrucksCalculus I: Lesson 11: Implicit Functions and Implicit Differentiation
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Usually when we speak of functions, we are talking about explicit functions of the form y = f(x). Sometimes we have instead an equation in x and y, for example, x + y + xy = sin(x + y), which may not be solvable for y. The solutions to this equation are a set of points {(x,y)} which implicitly define a relation between x and y which we will call an implicit function . Implicit functions are often not actually functions in the strict definition of the word, because they often have multiple y values for a single x value. They do have graphs and derivatives however.
This worksheet explores implicit functions and implicit differentiation.<img src="https://www.maplesoft.com/view.aspx?si=1582/Calc1_logo.gif" alt="Calculus I: Lesson 11: Implicit Functions and Implicit Differentiation" style="max-width: 25%;" align="left"/>Usually when we speak of functions, we are talking about explicit functions of the form y = f(x). Sometimes we have instead an equation in x and y, for example, x + y + xy = sin(x + y), which may not be solvable for y. The solutions to this equation are a set of points {(x,y)} which implicitly define a relation between x and y which we will call an implicit function . Implicit functions are often not actually functions in the strict definition of the word, because they often have multiple y values for a single x value. They do have graphs and derivatives however.
This worksheet explores implicit functions and implicit differentiation.https://www.maplesoft.com/applications/view.aspx?SID=1582&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen BrucksCalculus I: Lesson 10: Max and Min Problems 3
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In this worksheets, the examples continue exploring max and min problems.<img src="https://www.maplesoft.com/view.aspx?si=1581/Calc1_logo.gif" alt="Calculus I: Lesson 10: Max and Min Problems 3" style="max-width: 25%;" align="left"/>In this worksheets, the examples continue exploring max and min problems.https://www.maplesoft.com/applications/view.aspx?SID=1581&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen BrucksCalculus I: Lesson 9: Max and Min Problems 2
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In this worksheet, we'll look at problems, where we first get a numerical solution and then a precise solution.<img src="https://www.maplesoft.com/view.aspx?si=1580/Calc1_logo.gif" alt="Calculus I: Lesson 9: Max and Min Problems 2" style="max-width: 25%;" align="left"/>In this worksheet, we'll look at problems, where we first get a numerical solution and then a precise solution.https://www.maplesoft.com/applications/view.aspx?SID=1580&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen BrucksCalculus I: Lesson 8: Max and Min Problems 1
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In the next three lessons, we demonstrate the solution process for various optimization problems using derivatives.<img src="https://www.maplesoft.com/view.aspx?si=1579/Calc1_logo.gif" alt="Calculus I: Lesson 8: Max and Min Problems 1" style="max-width: 25%;" align="left"/>In the next three lessons, we demonstrate the solution process for various optimization problems using derivatives.https://www.maplesoft.com/applications/view.aspx?SID=1579&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen BrucksCalculus I: Lesson 7: Differentiation Rules
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In this worksheet, we will review the definition of the derivative of a function, look at Maple's commands for differentiation, and use them to verify the basic differentiation formulas.<img src="https://www.maplesoft.com/view.aspx?si=1578/Calc1_logo.gif" alt="Calculus I: Lesson 7: Differentiation Rules" style="max-width: 25%;" align="left"/>In this worksheet, we will review the definition of the derivative of a function, look at Maple's commands for differentiation, and use them to verify the basic differentiation formulas.https://www.maplesoft.com/applications/view.aspx?SID=1578&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen BrucksCalculus I: Lesson 6: Finding the Equation of a Tangent Line
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In this worksheet, first we'll demonstrate graphically the meaning of a tangent line in an animation. Afterwards, we'll show how to find the equation of a line tangent to a function at a given point.<img src="https://www.maplesoft.com/view.aspx?si=1577/Calc1_logo.gif" alt="Calculus I: Lesson 6: Finding the Equation of a Tangent Line" style="max-width: 25%;" align="left"/>In this worksheet, first we'll demonstrate graphically the meaning of a tangent line in an animation. Afterwards, we'll show how to find the equation of a line tangent to a function at a given point.https://www.maplesoft.com/applications/view.aspx?SID=1577&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen BrucksCalculus I: Lesson 5: Tangent Lines and Differentiability
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In this worksheet, you will look at tangent lines, and differentiability.<img src="https://www.maplesoft.com/view.aspx?si=1576/Calc1_logo.gif" alt="Calculus I: Lesson 5: Tangent Lines and Differentiability" style="max-width: 25%;" align="left"/>In this worksheet, you will look at tangent lines, and differentiability.https://www.maplesoft.com/applications/view.aspx?SID=1576&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen BrucksCalculus I: Lesson 4: Definition of the Derivative
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In this worksheet, you will see how to solve two problems: the mathematical problem of finding the tangent line to the graph of a function, and the physical problem of defining the velocity of a moving object. Although these problems might seem unrelated at first, it will turn out that they both lead to the same mathematical concept: the derivative of a function.<img src="https://www.maplesoft.com/view.aspx?si=1575/Calc1_logo.gif" alt="Calculus I: Lesson 4: Definition of the Derivative" style="max-width: 25%;" align="left"/>In this worksheet, you will see how to solve two problems: the mathematical problem of finding the tangent line to the graph of a function, and the physical problem of defining the velocity of a moving object. Although these problems might seem unrelated at first, it will turn out that they both lead to the same mathematical concept: the derivative of a function.https://www.maplesoft.com/applications/view.aspx?SID=1575&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen BrucksCalculus I: Lesson 3: Continuity and Limits at Infinity II
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In this worksheet, we'll continue looking at continuity, and limits at infinity.<img src="https://www.maplesoft.com/view.aspx?si=1574/Calc1_logo.gif" alt="Calculus I: Lesson 3: Continuity and Limits at Infinity II" style="max-width: 25%;" align="left"/>In this worksheet, we'll continue looking at continuity, and limits at infinity.https://www.maplesoft.com/applications/view.aspx?SID=1574&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen BrucksCalculus I: Lesson 2: Continuity and Limits at Infinity I
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In this worksheet, we'll look at continuity, and limits at infinity.<img src="https://www.maplesoft.com/view.aspx?si=1573/Calc1_logo.gif" alt="Calculus I: Lesson 2: Continuity and Limits at Infinity I" style="max-width: 25%;" align="left"/>In this worksheet, we'll look at continuity, and limits at infinity.https://www.maplesoft.com/applications/view.aspx?SID=1573&ref=FeedWed, 01 Oct 2003 00:00:00 ZDr. Karen BrucksDr. Karen Brucks