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Calculus
Untitled (the Wolfram Language for Students - Personal Use Only : www.wolfram.com)

Using Mathematica for calculus

Mathematica is what Wolfram Alpha is based on
(You may be familiar from Math 1A...)

There is very powerful built-in differentiation and integration of expressions:

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Integrate can be used to compute indefinite integrals

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Providing bounds of integration in the form of a list (just like in plotting) can be used to compute definite integrals

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Numerical (approximate results) can be obtained using the N function

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If we want to be fancy, we can use mathematical notation in our code:

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More calculus and series

Mathematica can easily compute partial and repeated derivatives

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Finite and infinite sums can be computed using Sum

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Differential equations

Mathematica can find analytical solutions to many differential equations, both initial value problems and boundary value problems

The function DSolve looks for solutions to differential equations

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We did not specify an initial condition, so the solution has a constant. Specifying the initial condition eliminates the constant

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We can solve a boundary value problem:

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