[SalesForce] Calling a static resource resource javascript functoin from lightning component

Usually the static resource files are cached in the browser. So in case you make minor change in the files they are not reflected immediately.

So to always get the latest changes in the browser, you can either do Ctrl+F5 or update VF page with the verison number in the resource.

Before Change:

<script type="text/javascript" src="{!URLFOR($Resource.myStaticResource, 'myApp/js/sequenceOrder.js')}"></script>

after Change:

<script type="text/javascript" src="{!URLFOR($Resource.myStaticResource, 'myApp/js/sequenceOrder.js?ver=001')}"></script>

Just increment the version in the parameter and that will fetch the changes in the view. I haven't worked with Lightning components, but this what works out for me in VF.

you could attach your utility methods to the global window object(SecureWindow) and use it in your controller.

Static Resource: TestScript

(function(w){
    "use strict"; //Optional because LC on LockerService active runs in strict mode

    var utilMethods = {
        "method1":method1,
        "method2":method2
    };

    function method1(){
        console.log("method1 called");
    } 

    function method2(){
        console.log("method2 called");
    }

    w.myUtil = utilMethods;

})(window);

Component:

<ltng:require scripts="{!$Resource.TestScript}" afterScriptsLoaded="{!c.afterScriptsLoaded}" />
<ui:button label="Do job" press="{!c.doJob}"/>

Controller.js:

doJob : function(cmp){
     myUtil.method1(); // Print method1 called
     myUtil.method2(); // Print method2 called
}