Matrix transformations (Khan Academy)

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Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations. (1) Functions and linear transformations A more formal understanding of functions Vector transformations Linear transformations Visualizing linear transformations Matrix from visual representation of transformation Matrix vector products as linear transformations Linear transformations as matrix vector products Image […]

Vectors and spaces (Khan Academy)

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Let’s get our feet wet by thinking in terms of vectors and spaces. (1) Vectors Vector intro for linear algebra Real coordinate spaces Adding vectors algebraically & graphically Multiplying a vector by a scalar Vector examples Scalar multiplication Unit vector notation Unit vectors Add & subtract vectors Add vectors: magnitude & direction to component Parametric […]

Laplace transform (Khan Academy)

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Transforms and the Laplace transform in particular. Convolution integrals. (1) Laplace transform Laplace transform 1 Laplace transform 2 L{sin(at)} – transform of sin(at) Part 2 of the transform of the sin(at) (2) Properties of the Laplace transform Laplace as linear operator and Laplace of derivatives Laplace transform of cos t and polynomials “Shifting” transform by […]

Second order linear equations (Khan Academy)

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Linear differential equations that contain second derivatives (1) Linear homogeneous equations 2nd order linear homogeneous differential equations 1 2nd order linear homogeneous differential equations 2 2nd order linear homogeneous differential equations 3 2nd order linear homogeneous differential equations 4 (2) Complex and repeated roots of characteristic equation Complex roots of the characteristic equations 1 Complex […]

First order differential equations (Khan Academy)

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Differential equations with only first derivatives. (1) Intro to differential equations Differential equation introduction Finding particular linear solution to differential equation Introduction to differential equations and initial value problems Creating a slope field Slope field to visualize solutions Differential equation from slope field Slope fields (2) Separable equations Separable differential equations introduction Particular solution to […]

Derivative applications (Khan Academy)

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The reason we study calculus, and the reason it was invented, is for its many uses in real-world problems. In particular, derivatives let us optimize functions and study their rates of change. Here we cover optimization, rates of change, L’Hopital’s rule, the mean value theorem, and more! (1) Equations of normal and tangent lines Equation […]

Taking derivatives (Khan Academy)

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Calculating derivatives. Power rule. Product and quotient rules. Chain Rule. Implicit differentiation. Derivatives of common functions. (1) Introduction to differential calculus Newton, Leibniz, and Usain Bolt (2) Using secant line slopes to approximate tangent slope Slope of a line secant to a curve Slope of a secant line example 1 Slope of a secant line […]

Limits (Khan Academy)

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Limit introduction, squeeze theorem, and epsilon-delta definition of limits (1) Limits Preparing for AP Calculus? Intro to limits Inferring limit from numerical data Estimating limit numerically Finding limits numerically (2) Estimating limits from graphs One-sided limits from graphs One-sided limits from graphs Two-sided limit at a point of discontinuity Two-sided limits from graphs Determining which […]

Trigonometric equations and identities (Khan Academy)

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Learn how to solve trigonometric equations and how to use trigonometric identities to solve various problems. (1) Trig identity reference Trig identity reference (2) The inverse trigonometric functions Intro to arcsine Intro to arctangent Intro to arccosine Evaluate inverse trig functions Restricting domains of functions to make them invertible Domain & range of inverse tangent […]

Graphs of trigonometric functions (Khan Academy)

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Learn how to graph trigonometric functions and how to interpret those graphs. Learn how to construct trigonometric functions from their graphs or other features. (1) The graphs of sine, cosine, and tangent Graph of y=sin(x) Graph of y=tan(x) Intersection points of y=sin(x) and y=cos(x) (2) Introduction to amplitude, midline, and extrema of sinusoidal functions Features […]