"TypeError: undefined is not a function" when requiring jQuery-ui in node.js using Express

I am trying to set up a small node.js webserver which will use jQuery and jQuery-ui. I have used Express to set up a small project and then installed all packages I need using npm <package-name> install --save. Please bear in mind that I am new to the JavaScript world, so I might be doing silly things, but I could not find anyone with the same issue (just related).

Express has set up the project like this:

$ ls
app.js  bin  node_modules  npm-debug.log  package.json  public  routes  views

The folder node_modules now contain:

$ ls node_modules
body-parser  cookie-parser  debug  express  jade  jquery  jquery-ui  morgan  serve-favicon

My app.js file is as set up by Express except that I now include jQuery and jQuery-ui, like this:

$ cat app.js
var express = require('express');
var path = require('path');
var favicon = require('serve-favicon');
var logger = require('morgan');
var cookieParser = require('cookie-parser');
var bodyParser = require('body-parser');
var jQuery = require('jquery');
var jQueryUi = require('jquery-ui');

var routes = require('./routes/index');
var users = require('./routes/users');

var app = express();
// The rest is omitted here for brevity. Default settings from Express.

Running node bin/www now shows the error

/home/oystein/QAWebApp3/node_modules/jquery-ui/jquery-ui.js:15
$.extend( $.ui, {
  ^
TypeError: undefined is not a function
    at /home/oystein/QAWebApp3/node_modules/jquery-ui/jquery-ui.js:15:3
    at Object.<anonymous> (/home/oystein/QAWebApp3/node_modules/jquery-ui/jquery-ui.js:316:3)
    at Module._compile (module.js:460:26)
    at Object.Module._extensions..js (module.js:478:10)
    at Module.load (module.js:355:32)
    at Function.Module._load (module.js:310:12)
    at Module.require (module.js:365:17)
    at require (module.js:384:17)
    at Object.<anonymous> (/home/oystein/QAWebApp3/app.js:8:16)
    at Module._compile (module.js:460:26)

This error seems to originate from the file jquery-ui.js, which looks like this:

var jQuery = require('jquery');

/*! jQuery UI - v1.10.3 - 2013-05-03
* http://jqueryui.com
* Includes: jquery.ui.core.js, jquery.ui.widget.js, jquery.ui.mouse.js, jquery.ui.draggable.js, jquery.ui.droppable.js, jquery.ui.resizable.js, jquery.ui.selectable.js, jquery.ui.sortable.js, jquery.ui.effect.js, jquery.ui.accordion.js, jquery.ui.autocomplete.js, jquery.ui.button.js, jquery.ui.datepicker.js, jquery.ui.dialog.js, jquery.ui.effect-blind.js, jquery.ui.effect-bounce.js, jquery.ui.effect-clip.js, jquery.ui.effect-drop.js, jquery.ui.effect-explode.js, jquery.ui.effect-fade.js, jquery.ui.effect-fold.js, jquery.ui.effect-highlight.js, jquery.ui.effect-pulsate.js, jquery.ui.effect-scale.js, jquery.ui.effect-shake.js, jquery.ui.effect-slide.js, jquery.ui.effect-transfer.js, jquery.ui.menu.js, jquery.ui.position.js, jquery.ui.progressbar.js, jquery.ui.slider.js, jquery.ui.spinner.js, jquery.ui.tabs.js, jquery.ui.tooltip.js
* Copyright 2013 jQuery Foundation and other contributors; Licensed MIT */
(function( $, undefined ) {

var uuid = 0,
    runiqueId = /^ui-id-\d+$/;

// $.ui might exist from components with no dependencies, e.g., $.ui.position
$.ui = $.ui || {};

$.extend( $.ui, {
    version: "1.10.3",

    keyCode: {
        BACKSPACE: 8,
        COMMA: 188,
        DELETE: 46,
        DOWN: 40,
// Lots of other defines...
})( jQuery ); // End of block on line 316

My guess is some inclusion problems. The error kicks in at line 15, $.extend( $.ui, {, but the message tells me to look at the line (function( $, undefined ) {. What is the best way to solve this?

Oh, and package.json looks like this:

{
  "name": "QAWebApp3",
  "version": "0.0.0",
  "private": true,
  "scripts": {
    "start": "node ./bin/www"
  },
  "dependencies": {
    "body-parser": "^1.12.3",
    "cookie-parser": "^1.3.4",
    "debug": "^2.1.3",
    "express": "^4.12.3",
    "jade": "^1.9.2",
    "jquery": "^2.1.3",
    "jquery-ui": "^1.10.5",
    "morgan": "^1.5.2",
    "serve-favicon": "^2.2.0"
  }
}