Mr. Integral

THE BIG IDEA

Laplace Transforms

Can we turn a changing-time problem into algebra?

The Laplace transform converts derivatives into algebraic expressions while retaining initial data. Delays, impulses and convolution then describe inputs that are awkward to handle directly in time.

Begin the first lesson →See the lesson route ↓

5 lessons · No deadlines or locked lessons

SEE THE CONNECTIONS

How the ideas fit together.

A map of the main ideas. Follow a node to its lesson.

  1. Start with01Transform rules
  2. solving and inverting gives02Initial-value solutions
  3. time shifts introduce03Delayed inputs
  4. isolating input from output defines04System response

YOUR LEARNING ROUTE

One idea at a time.

Read the explanation, use the visualization, then try the check before opening its reasoning.

Keep the unit cheat sheet handy →
Lessons in this unit5 lessons
  1. 01Laplace Transforms and Their DomainCompute elementary transforms and retain the initial-value terms in derivatives.
  2. 02Laplace Inversion and Initial-Value ProblemsSolve transformed algebra and reconstruct the time response by recognizable pairs.
  3. 03Delayed Inputs and ConvolutionRepresent switched forcing and combine an input with an impulse response.
  4. 04Impulse Inputs and Jump ConditionsUse impulse area to determine which state or derivative jumps.
  5. 05Transfer Functions, Poles and ResponseSeparate a system’s zero-state input response from its initial-condition response.