Learing physics can be a difficult and frustrating experience for many students, particularly those with a weak math background. Here I have collected together a group of resources intended to provide students with tools for learning physics. The tools are intended for students taking either a Calculus based course such as University Physics or a non-calculus course like General Physics. I am also putting together a set of Tutorials on various physics related topics.
In physics we use mathematics as a tool. It is important, when using any tool, to know how to use it and what it is intended for. You do not need to be able to make the tool yourself. Mathematicians tend to focus on the manufacture of their tool sets: rigorous derivations from first principles. Physicists focus on the proper use of mathematics. There are several books aimed at reviewing or presenting usefull mathematics in a practical, user oriented, manner. Here are a couple:
Mathematics for Physics with Calculus by Biman Das, SUNY Potsdam. Publisher: Pearson/Prentice Hall (2004).
Designed for students who plan to take or who are presently taking calculus-based physics courses. This book will develop necessary mathematical skills and help students gain the competence to use precalculus, calculus, vector algebra, vector calculus, and the statistical analysis of experimental data. Students taking intermediate physics, engineering, and other science courses will also find the book useful—and will be able to use the book as a mathematical resource for these intermediate level courses. The book emphasizes primarily the use of mathematical techniques and mathematical concepts in Physics and does not go into their rigorous developments.
A related text for non-calculus based courses is Mathematics for College Physics by the same author and publisher.
Designed for concurrent self-study or remedial math work for students in introductory courses, this text is ideal for students who find themselves unable to keep pace because of a lack of familiarity with necessary mathematical tools. It not only shows them clearly how mathematics is directly applied to physics, but discusses math anxiety in general and how to overcome it. Instead of a rigorous development of the concepts of mathematics (as is found in a typical math book), the text describes the various mathematical concepts and tools (including algebra, trigonometry, geometry, vector, and statistics) and their direct use in solving physics problems. Almost all sections end with worked-out examples and exercises directly from introductory physics.
The laboratory is one of the most important aspects of learning physics. Measurement and experiment are fundamental to all of science and, in particular, to physics. I am working on a set of guidelines for our physics laboratories including material on how to write a lab report. It is a work in progress! Here is an online draft version and a PDF draft to download. A very important set of skills is knowing how to use software systems like Microsoft Excel or MathCAD or Python to analyze and graph data. Here is a page of demos, instructions and tutorials on various methods and techniques.
Central to all quantitative laboraory work is the concept of uncertainty in physical measurements. No laboratory report is complete without an error analysis whose result is the identification and quantitative estimate of the errors in the expermental results. Here is an excellent introduction to the subject:
Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements (Second Edition, 1997) by John R. Taylor, University of Colorado, Boulder. Publisher: University Science Books.
This best-selling text by John Taylor, now released in its second edition, introduces the study of uncertainties to lower division science students. Assuming no prior knowledge, the author introduces error analysis through the use of familiar examples ranging from carpentry to well-known historic experiments. Pertinent worked examples, simple exercises throughout the text, and numerous chapter-ending problems combine to make the book ideal for use in physics, chemistry, and engineering lab courses.
The primary resource for any physics student after his or her instructor should be the materials, both printed and online, that accompany the main course textbook.
For Physics for Scientists and Engineers: A Strategic Approach (2nd Ed), by Randall D. Knight, there is MasteringPhysics with many tutorial, videos, exercises and problems with hints and answers.
For Understanding Physics, First Edition, by Cummings, Laws, Redish, and Cooney, there is a Student Companion Site with a lot of downloadable material including hints and solutions.
For Physics for Scientists and Engineers, 3/E, by Fishbane, Gasiorowicz, and Thornton, there is a very nice Companion Web Site with a host of helpful material. There is also a study guide with solved problems and many examples.
There another group of resources that the physics community has dubbed Physlets, a word coined from physics+applet. A physlet is a small single concept Java applet designed to teach physics. There is a very interesting book of physlet applications written for student use: Physlet® Physics: Interactive Illustrations, Explorations and Problems forIntroductory Physics by Wolfgang Christian and Mario Belloni, Davidson College. This book and CD package furnishes students with a host of interactive, computer-based exercises and study resources that span the entire introductory physics curriculum. Using a practical yet engaging structure, Physlet® Physics presents a wide spectrum of “media-focused” critical thinking and problem-solving exercises, and provides students with an interactive visual representation of the physical phenomena they see in introductory physics textbooks. The animations and graphics provide insight missing from ordinary graphics and text.