Differential Equations

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Here is review material for an undergraduate course on differential equations based on Guterman and Nitecki’s Differential Equations: A First Course.


Page 7, Example 1.2.2 – On the fifth line, the right-hand side of the expression should read -1/2 ln|(t+1)/(t-1)| + C. Note that there is a multiplicative factor of -1/2 that was missing.

Error Propagation Calculator

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Error Propagation Calculator (Excel)

How to Use:

Step 1 – Download the file above, open it in Excel (choose “enable content” or “enable macros” if prompted), and press the huge button shown below. If you get an error message about macros despite this, go to the bottom of this page to learn how to solve the issue:Step 1

Step 2 – Input your numbers into the 4 boxes. (Note: if any of these images are too small, click on them to enlarge them).


Step 3 – Choose the mathematical operation you desired to do for “a” and “b.” A pop-up window will reveal the results of the calculation and the resulting propagated error.


Step 4 – Since nobody wants to write out numbers manually, the results of Step 3 will be temporarily saved to the two small text boxes at the bottom of the window (highlighted in the following picture). They can be copied and pasted from here.


Step 5 (Optional) – If you wish to perform another calculation based on the results you just obtained, you do not have to re-input the numbers yourself. Press one of the “Substitute last answer” blue boxes to have the program copy the answer to the input boxes.



If you have trouble opening the program, it’s likely because you have macros disabled in your Excel settings. To solve this, go to File, then Options (may be different for older versions of Excel). Navigate to “Trust Center” (shown below), and click “Trust Center Settings.” Finally, under “Macro Settings,” select “Enable all macros” if they are currently disabled.


Physical Chemistry I

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Here is review material for a first semester course on physical chemistry for undergraduates based on Levine’s Physical Chemistry.

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