Analysis Flashcards by Aiden Dawes

Q

How to find the derivative from first principles the old way

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Q

How to find the derivative from first principles the new way

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Q

What is the product rule

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Q

What is the quotient rule

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Q

What is the chain rule

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Q

What is a continuous function

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Q

How to determine extrema

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Q

What is a partial derivative

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Q

How to find the gradient of a multivariable function

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Q

What is the Hessian

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Q

How to use the Hessian to determine the type of a critical point

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Q

How to find the derivative of a function in a direction

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Q

What is a complex number

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Q

What is an imaginary number

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Q

How does integration relate to infinitessimals

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Q

How is a complex number expressed as a vector

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Q

How is a complex number expressed in polar form

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Q

How is a complex number expressed on the Argand diagram

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Q

How are complex numbers expressed in Euler form

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Q

How to take the roots of a complex number using Euler form

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Q

What is the conjugate of a complex number and how can it be used to simplify fractions

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Q

What is a differential equation

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Q

What is an ordinary differential equation

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Q

What is a linear ODE

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What is a linear homogeneous ODE

How to solve ODE's using an Ansatz (guess)

How to solve ODE's normally

What is the Fundamental Theorem of Calculus

How does solving integrals using u-substitution work

What is the order of a differential equation

What is the taylor series of a function

What is the Euler approximation

What is L'Hopital's rule

Formula for integration by parts

What is the form for a first order inhomogeneous equation

How to solve inhomogeneous equations using the integrating factor

How to solve inhomogeneous equations using a Particular Solution

What are numerical solutions to mathematical problems and why are they used?

How does Euler's method work

What is a 2nd order ODE

How can you solve 2nd order ODEs

How to sole a 2nd order ODE with repeated roots for the guess

How to solve a 2nd order ODE with imaginary roots for the guess

How to optimise functions numerically

How does gradient descent work

What is the cost function in neural networks

Why and how to use the downhill simplex

How to decompose a function into partial fractions

How to use the Laplaz transform