story_board

ユーザーが地図をスクロールするとMapViewの更新が止まってしまいますので、storyboardのMapViewのプロパティでスクロールを禁止します。

map_screen

拡大縮小はできますのでアプリによってはこちらのほうが便利な場合もあるかと思います。

import UIKit
import MapKit
import CoreLocation

class ViewController: UIViewController , CLLocationManagerDelegate, MKMapViewDelegate{

    @IBOutlet weak var mapView: MKMapView!
    var locationManager : CLLocationManager?
    
    override func viewDidLoad() {
        super.viewDidLoad()
        // Do any additional setup after loading the view, typically from a nib.
        
        mapView.setUserTrackingMode(MKUserTrackingMode.FollowWithHeading, animated: true)
        mapView.setCenterCoordinate(mapView.userLocation.coordinate, animated: true)
        
        if CLLocationManager.locationServicesEnabled() {
            locationManager = CLLocationManager()
            locationManager?.delegate = self
            locationManager?.startUpdatingLocation()
        }
    }

    override func didReceiveMemoryWarning() {
        super.didReceiveMemoryWarning()
        // Dispose of any resources that can be recreated.
    }

    // MARK: - CLLocationManager delegate
    func locationManager(manager: CLLocationManager, didChangeAuthorizationStatus status: CLAuthorizationStatus) {
        switch status {
        case .NotDetermined:
            locationManager?.requestWhenInUseAuthorization()
        case .Restricted, .Denied:
            break
        case .Authorized, .AuthorizedWhenInUse:
            break
        }
    }
}