Shape of Nature (The Great Courses)

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How do you measure the size of a black hole? The motion of individual particles at the subatomic level? The possible shape of space-time itself? In short: How do you mathematically describe the world around you? The answer lies in the fascinating ways mathematicians use geometry and topology to study and understand the shape of […]

Coding the Matrix: Linear Algebra course (Anki)

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Anki is a flashcard tool which incorporates sophisticated research to maximize your study efficiency. You can import public “decks” of flashcards, such as this one. Cards are customizable! When this deck is imported into the desktop program, cards will appear as if you made them yourself. About this Flashcard Deck… Flash cards from course of […]

Alternate coordinate systems (bases) (Khan Academy)

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We explore creating and moving between various coordinate systems. (1) Orthogonal complements Orthogonal complements dim(v) + dim(orthogonal complement of v) = n Representing vectors in rn using subspace members Orthogonal complement of the orthogonal complement Orthogonal complement of the nullspace Unique rowspace solution to Ax = b Rowspace solution to Ax = b example (2) […]

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 […]