Watch these short videos about creating custom solutions with SharePoint 2010 Application Development, which match the materials of the course # 10175A.
Reference: http://msdn.microsoft.com/en-us/sharepoint/hh298298.aspx

Module 1:
Getting Started: Building Web Parts in SharePoint 2010

Videos

1 – 2 – 3 – 4 – 5
Module 2: What
Developers Need to Know About SharePoint 2010

Videos

1 –  2 –  3 –  4 –  5 –  6 – 7 –  8 – 9 –  10
Module 3:
Building Blocks for Web Part Development in SharePoint 2010

Videos

1 – 2 – 3 – 4
Module 4:
Accessing SharePoint 2010 Data and Objects with Server-Side APIs

Videos

1 – 2 – 3 – 4 –5 – 6
Module 5:
Accessing SharePoint 2010 Data and Objects with Client-Side APIs

Videos

1 – 2 – 3 – 4 – 5 – 6
Module 6:
Accessing External Data with Business Connectivity Services in SharePoint 2010

Videos

1 – 2 – 3 – 4 – 5 – 6
Module 7:
Developing Business Processes with SharePoint 2010 Workflows

Videos

1 – 2 – 3 – 4 – 5
Module 8:
Creating Silverlight User Interfaces for SharePoint 2010 Solutions

Videos

1 – 2 – 3 – 4 – 5
Module 9:
Sandboxed Solutions for Web Parts in SharePoint 2010

Videos

1 – 2 – 3 – 4 – 5
Module 10:
Creating Dialog Boxes and Ribbon Controls for SharePoint 2010

Videos

1 – 2 – 3 – 4 – 5