Camera script

Hi, I would like the camera to follow the player. So far I have kind of made it work, but only to an extent; the camera does not follow the player while jumping and "lags" behind the player for most parts until it simply stops following the player altogether. I borrowed the script that came with the free Unity download

 using UnityEngine;
 using System.Collections;
 
 public class CameraFollow : MonoBehaviour 
 {
 
     public float xMargin = 1f;        // Distance in the x axis the player can move before the camera follows.
     public float yMargin = 1f;        // Distance in the y axis the player can move before the camera follows.
     public float xSmooth = 8f;        // How smoothly the camera catches up with it's target movement in the x axis.
     public float ySmooth = 8f;        // How smoothly the camera catches up with it's target movement in the y axis.
     public Vector2 maxXAndY;        // The maximum x and y coordinates the camera can have.
     public Vector2 minXAndY;        // The minimum x and y coordinates the camera can have.
     
     
     private Transform player;
     
     
     void Awake ()
     {
         // Setting up the reference.
         player = GameObject.FindGameObjectWithTag("Player").transform;
     }
     
     
     bool CheckXMargin()
     {
         // Returns true if the distance between the camera and the player in the x axis is greater than the x margin.
         return Mathf.Abs(transform.position.x - player.position.x) > xMargin;
     }
     
     
     bool CheckYMargin()
     {
         // Returns true if the distance between the camera and the player in the y axis is greater than the y margin.
         return Mathf.Abs(transform.position.y - player.position.y) > yMargin;
     }
     
     
     void FixedUpdate ()
     {
         TrackPlayer();
     }
     
     
     void TrackPlayer ()
     {
         // By default the target x and y coordinates of the camera are it's current x and y coordinates.
         float targetX = transform.position.x;
         float targetY = transform.position.y;
         
         // If the player has moved beyond the x margin...
         if(CheckXMargin())
             // ... the target x coordinate should be a Lerp between the camera's current x position and the player's current x position.
             targetX = Mathf.Lerp(transform.position.x, player.position.x, xSmooth * Time.deltaTime);
         
         // If the player has moved beyond the y margin...
         if(CheckYMargin())
             // ... the target y coordinate should be a Lerp between the camera's current y position and the player's current y position.
             targetY = Mathf.Lerp(transform.position.y, player.position.y, ySmooth * Time.deltaTime);
         
         // The target x and y coordinates should not be larger than the maximum or smaller than the minimum.
         targetX = Mathf.Clamp(targetX, minXAndY.x, maxXAndY.x);
         targetY = Mathf.Clamp(targetY, minXAndY.y, maxXAndY.y);
         
         // Set the camera's position to the target position with the same z component.
         transform.position = new Vector3(targetX, targetY, transform.position.z);
     }
 }

Does anyone know how to make the camera keep track of my player on both the x and y axis and tracks the player spot on - the player are not supposed to move to the end of the screen before the camera follows.