diff --git a/jquery/jquery.d.ts b/jquery/jquery.d.ts
index 866d0de076..5dc88bf795 100644
--- a/jquery/jquery.d.ts
+++ b/jquery/jquery.d.ts
@@ -1024,7 +1024,7 @@ interface JQueryStatic {
      * @param func The function to process each item against. The first argument to the function is the item, and the second argument is the index. The function should return a Boolean value.  this will be the global window object.
      * @param invert If "invert" is false, or not provided, then the function returns an array consisting of all elements for which "callback" returns true. If "invert" is true, then the function returns an array consisting of all elements for which "callback" returns false.
      */
-    grep<T>(array: T[], func: (elementOfArray: T, indexInArray: number) => boolean, invert?: boolean): T[];
+    grep<T>(array: T[], func: (elementOfArray?: T, indexInArray?: number) => boolean, invert?: boolean): T[];
 
     /**
      * Search for a specified value within an array and return its index (or -1 if not found).
@@ -1091,14 +1091,14 @@ interface JQueryStatic {
      * @param array The Array to translate.
      * @param callback The function to process each item against. The first argument to the function is the array item, the second argument is the index in array The function can return any value. Within the function, this refers to the global (window) object.
      */
-    map<T, U>(array: T[], callback: (elementOfArray: T, indexInArray: number) => U): U[];
+    map<T, U>(array: T[], callback: (elementOfArray?: T, indexInArray?: number) => U): U[];
     /**
      * Translate all items in an array or object to new array of items.
      * 
      * @param arrayOrObject The Array or Object to translate.
      * @param callback The function to process each item against. The first argument to the function is the value; the second argument is the index or key of the array or object property. The function can return any value to add to the array. A returned array will be flattened into the resulting array. Within the function, this refers to the global (window) object.
      */
-    map(arrayOrObject: any, callback: (value: any, indexOrKey: any) => any): any;
+    map(arrayOrObject: any, callback: (value?: any, indexOrKey?: any) => any): any;
 
     /**
      * Merge the contents of two arrays together into the first array.