Library resources have been vetted, whether by professionals working in the field, or by librarians responsible for evaluating material specific to that discipline. All libraries offer access to these types of resources.
Like Google, library databases calculate the number of times a particular word or phrase appears in a resource's metadata. Unlike Google, the results you'll find in a library database are limited to vetted material, are not displayed according to click rankings, and you'll never see advertisements.
You are already busy! By searching against the library's collections, you reduce the amount of time and energy required to evaluate resources.
I <3 Google. Really. It is chock full of information.
But Google and library databases are very different types of resources.
The money-making potential for a given topic can seriously skew your Google search results.
If you decide you'd like to use Google for your initial search, please take this information into account. When in doubt, use Google Scholar. Google Scholar searches against patents/trademarks, governmental organizations, and the indexes and contents notes of peer reviewed material.
This multi-disciplinary database has records for nearly 18,000 periodicals - journals, magazines, and newspapers - of which nearly 16,000 are peer reviewed. It provides full text for more than 5,000 journals, and you can use Journal Finder to locate articles that do not have a PDF readily available.
Electronic archive and distribution server for research papers in the areas of physics and related disciplines, mathematics, nonlinear sciences, computer science and quantitative biology.
Scientific literature digital library and search engine that focuses primarily on the literature in computer and information science. CiteSeer aims to improve the dissemination and feedback of the scientific literature and to provide improvements in functionality, usability, availability, cost, comprehensiveness, efficiency, and timeliness in the access of scientific and scholarly knowledge.
Project Euclid offers access to a growing platform of high-quality, peer-reviewed journals, monographs, and conference proceedings in the fields of theoretical and applied mathematics and statistics.
Wolfram Alpha is a computational knowledge engine or answer engine developed by Wolfram Research. It is an online service that answers factual queries directly by computing the answer from externally sourced "curated data", rather than providing a list of documents or web pages that might contain the answer as a search engine might.