Mechanical Engineering is a very broad topic.
Important topics for Industrial Designers are: Applied Physics, Materials, Mechanics, Simulation and Finite Element Analysis.
Applied Physics: Young & Freedman, University Physics, 13th edition.
Mechanics: Fenner R.T., Mechanics of Solids, CRC Press.
Materials: Ashby, Shercliff, Cebon, Materials: engineering, science, processing and design, Butterworth Heinemann.
Khan academy website (self study website): http://www.khanacademy.org/science/physics
Good software tools:
Computer Aided Design & Finite Element Analysis: SolidWorks
Mathematical packages: MatLab, Mathematica
Simulation packages: Simulink,NetLogo
CES Edupack is a materials database which contains data about approximately 3000 materials. The database contains mechanical, electrical, optical, cost price, eco, typical application and producers data.
Below you find presentations I regularly give about:
Materials selection presentation
Material behavior presentation
TRIZ (creative thinking) presentation
Most above mentioned software packages are made freely available for Industrial Design students. Simulink (as part of Matlab) and SolidWorks are available from the TU/e PC software page.