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\n\"AP\n\n
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\nLesson Planet Curated\n
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\nAP Calculus AB\n

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\n\nFor Students\n\n11th - 12th\n
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\nPrepare high school mathematicians for the AP Calculus AB exam with a collection of 38 videos that can be used to introduce the topics or as a review. The videos focus on two processes; differentiating a function and integrating a...\n
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\n\n47\nItems in Unit\n\n
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\n\"AP\n\n
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\nLesson Planet Curated\n
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\nAP Calculus AB Unit 7: Differential Equations\n

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\n\nFor Teachers\n\n11th - 12th\n
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\nAs with the other units in the Flipped Classroom Calculus course, the Differential Equations Unit follows the College Board’s course and exam description. Topics are introduced with an instructional video demonstrating how to approach...\n
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\n\"Differentiation\n\n
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\nCurated OER\n
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\nDifferentiation Computations\n

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\nFor this calculus worksheet, 11th graders solve problems using differential equations and computations. They apply properties of trig functions and simplify their answers. There are 9 questions.\n
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\n\"Reductions\n\n
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\nCurated OER\n
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\nReductions of Order\n

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\nIn this calculus learning exercise, students identify functions as linear or nonlinear, homogeneous versus nonhomogeneous by using the reduction power theorem. There are 5 questions.\n
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Interactive
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\n\"Differential\n\n
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\nCK-12 Foundation\n
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\nDifferential Equations Representing Growth and Decay: Rice Legend\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nThe legend of a wise man who asks a king for rice as a reward presents a context to study exponential solutions to differential equations. Pupils move quantities of rice to a chessboard and calculate the amount of rice for each day. To...\n
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Instructional Video9:50
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\n\"Power\n\n
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\nKhan Academy\n
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\nPower Rule Introduction (Old) Taking derivatives, Differential Calculus\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nThis video covers the differential notation dy/dx and generalizes the rule for finding the derivative of any polynomial. It also extends the notion of the derivatives covered in the Khan Academy videos, \"Calculus Derivatives 2Ó and...\n
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Instructional Video9:02
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\n\"Calculus:\n\n
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\nKhan Academy\n
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\nCalculus: Derivative of x^(x^x)\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nSal starts by showing how to find dy/dx of y = x2 and then moves on to show the solution to the more complicated implicit differentiation problem of finding the derivative of y in terms of x of y = x ^ x ^ x.\n
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Instructional Video8:49
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\n\"Product\n\n
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\nProduct Rule, Taking Derivatives, Differential Calculus\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nSal defines the product rule and then shows two examples of its use. He then shows an example of finding the derivative using the chain and product rules together.\n
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Instructional Video11:05
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\n\"The\n\n
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\nKhan Academy\n
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\nThe derivative of f(x)=x^2 for any x Taking derivatives, Differential Calculus\n

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\nBy defining the formal definition of a derivative, f(x), Sal can find the general form of the derivate function for the example f(x) = x2. He continues to stress the importance of an intuitive understanding of derivative functions.\n
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Instructional Video5:07
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\n\"Proof:\n\n
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\nKhan Academy\n
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\nProof: d/dx(sqrt(x)) Taking Derivatives Differential Calculus\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nUsing the definition of a limit, Sal proves that the derivative of x or x1/2 equals _ x-1/2.\n
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Instructional Video11:32
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\n\"Introduction\n\n
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\nIntroduction to Limits, Limits, Differential Calculus\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nSal begins his explanation of limits with a few basic examples and takes a more intuitive point of view before looking at a formal mathematical definition in later videos. He starts by introducing the notation for limits and describes...\n
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Instructional Video9:26
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\n\"Calculus:\n\n
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\nCalculus: Derivatives 1\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nSal defines the term derivative by taking the listener on a well-organized tour of the slope. First, he reviews the concept of the slope of a line from algebra, then extends this idea to look at the slope of the curve by first examining...\n
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Instructional Video9:32
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\n\"Calculus:\n\n
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\nCalculus: Derivatives 2\n

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\nSal continues where he left off with the last video, \"Derivatives 1, Ó by looking at the equation y = x^2 and examining the slope of the second line at a specific point, and again defining the limit as x approaches zero to get the slope...\n
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Instructional Video8:07
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\n\"Equation\n\n
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\nKhan Academy\n
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\nEquation of a Tangent Line, Taking Derivatives, Differential Calculus\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nUsing a specific example, Sal shows how to find the equation of a tangent line to a given function at a specific point. Specifically, he solves the problem of finding the tangent line to the function f(x) = xex at x = 1. This problem...\n
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Instructional Video11:32
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\n\"Introduction\n\n
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\nIntroduction to Limits, Limits, Differential Calculus\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nSal begins his explanation of limits with a few basic examples and takes a more intuitive point of view before looking at a formal mathematical definition in later videos. He starts by introducing the notation for limits and describes...\n
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Instructional Video8:58
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\n\"Limit\n\n
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\nKhan Academy\n
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\nLimit Examples (Part 1), Limits, Differential Calculus\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nOne example is finding the limit as x approaches -1 of (2x+2)/(x+1), solved by simplifying the expression and then explored intuitively by looking at the left and right-hand limits. The second example of finding the limit as x approaches...\n
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Instructional Video4:40
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\n\"Proof:\n\n
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\nKhan Academy\n
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\nProof: d/dx(e^x) = e6x\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nUsing the derivative of ln x, the chain rule, and the definition of a limit, Sal shows proof that the derivative of ex = ex. Note: The video titled \"Proof of Derivatives of Ln(x) and e^x,Ó clearly explains this proof.\n
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Instructional Video9:52
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\n\"Proof:\n\n
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\nKhan Academy\n
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\nProof: d/dx(ln x)=1/x\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nUsing the definition of a limit, various properties of logarithms, and a definition of e, Sal shows the proof of the derivative of ln x = 1/x. Note: The video titled \"Proof of Derivatives of Ln(x) and e^x,Ó has a more straightforward...\n
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Instructional Video7:03
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\n\"Proof:\n\n
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\nKhan Academy\n
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\nProof: d/dx(x^n)\n

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\nUsing the binomial theorem and definition of a limit, Sal shows a proof that the derivative of xn equals nxn-1.\n
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Instructional Video7:38
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\n\"Introduction\n\n
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\nIntroduction to Limits 2, Limits, Precalculus\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nSal explains limits by looking at a basic example of a discontinuous function and takes a more intuitive point of view before looking at a formal mathematical definition in later videos. He starts by introducing the notation for limits...\n
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Worksheet
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\n\"Worksheet\n\n
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\nCurated OER\n
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\nWorksheet 31\n

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\n\nFor Students\n\n12th - Higher Ed\n
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\nIn this math worksheet, students find the solutions to the differential equations. They also investigate the application of recognizing the parts of the equation.\n
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Worksheet
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\nWorksheet 30\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nIn this math instructional activity, students solve the differential equation by means of a power series about the point x0 = 2. Then they find the recurrence relation and the first four terms.\n
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Worksheet
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\n\"Worksheet\n\n
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\nWorksheet 20\n

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\n\nFor Students\n\n10th - 12th\n
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\nIn this math worksheet, they write down and solve a differential equation governing the motion of an underdamped spring. Then they find the solution to the initial value problem.\n
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Worksheet
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\nWorksheet 13\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nFor this math worksheet, students find the solution for the Euler equation. Then they simplify the two differential for the functions of g and yp.\n
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