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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What is an ordinary differential equation

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What is a linear ODE

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What is a linear homogeneous ODE

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

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How to solve ODE’s normally

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What is the Fundamental Theorem of Calculus

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How does solving integrals using u-substitution work

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What is the order of a differential equation

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Q

What is the taylor series of a function

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Q

What is the Euler approximation

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Q

What is L’Hopital’s rule

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Q

Formula for integration by parts

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What is the form for a first order inhomogeneous equation

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How to solve inhomogeneous equations using the integrating factor

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How to solve inhomogeneous equations using a Particular Solution

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

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Q

How does Euler’s method work

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What is a 2nd order ODE

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How can you solve 2nd order ODEs

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

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

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How to optimise functions numerically

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How does gradient descent work

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What is the cost function in neural networks

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Q

Why and how to use the downhill simplex

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Q

How to decompose a function into partial fractions

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Q

How to use the Laplaz transform

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