Differential Equations Review Sheets & Study Guides

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Diff Eqs Review Packet


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.

Physical Chemistry I Lab Review Sheets & Study Guides

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Error Propagation Calculator (v. 3):

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.


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 3

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 4

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.

Step 5


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.


Note: Make sure that you keep as many digits as possible throughout your error propagation calculations to get full credit on Chem 33 lab calculations.

Last Update: 9/28/12

Physical Chemistry I Review Sheets & Study Guides

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Want an easy way to take printscreens and save them? Try Greenshot.

P-Chem Review Packet

Tufts P-Chem I Syllabus (Fall 2012)

Organic Chemistry I Review Sheets & Study Guides

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Orgo I Review Packet

Orgo I Overview

Chemistry Principles (Chem 2) Review Sheets & Study Guides

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Here is study material for Chemistry Principles (otherwise known as General Chemistry II) based on the material taught at Tufts University and the Chemistry: Central Science book by Pearson. Chemistry, as most sciences, requires a lot of practice to understand the concepts fully. With that being said, these review sheets do not cover everything. They should be read and understood, but they are the basics. The only way to truly learn chemistry is to get out there and do it!

Chapter 13 – Properties of Solutions

Chapter 14 – Chemical Kinetics

Chapter 15 – Chemical Equilibrium

Chapter 16 – Acids and Bases

Chapter 19 – Thermochemistry

Chapter 23 – Coordination Compounds

Chemistry Fundamentals (Intro Chem) Review Sheets & Study Guides

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Hey there. Here are review sheets for Chemistry Fundamentals, otherwise known as Intro Chem. Intro chem has a lot of material, so these review sheets are not 100% comprehensive. They require you to know the basics, and then they cover the nuances and specifics for each chapter. Below are the review sheets I made for Chem 1 at Tufts University based off the Chemistry: The Central Science, 12th Edition book. There are a few “random notes” for exams attached to this post. These are just that: random notes I needed to remember but had trouble recalling for an exam. Perhaps you’ll feel the same way.

Also, if you are looking for more review material, please do check out my AP Chemistry Review Sheets posts (http://sites.tufts.edu/andrewrosen/category/high-school-review-sheets/ap-chemistry/). Yes, college chemistry is more difficult, but those review sheets will give you a very good overview of the basics if you need it.

Units 1-3: Introduction; Atoms, Molecules, and Ions; Stoichiometry

Unit 4: Reactions in Aqueous Solution

Unit 5: Thermochemistry

Unit 6: Electronic Structure of Atoms

Unit 7: Periodic Properties of the Elements

Unit 8: Basic Concepts of Chemical Bonding – Part I

Unit 8: Basic Concepts of Chemical Bonding – Part II

Unit 9: Molecular Geometry and Bonding Theories

Unit 10: Gases

Unit 11: Liquids and Intermolecular Forces

Unit 12: Solids and Modern Materials – Part I

Unit 12: Solids and Modern Materials – Part II

Random Exam 1 Tips

Random Final Tips

Intro to Psychology (Psy 1) Review Sheets & Study Guides

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These review sheets were made by me and are specifically tailored for Tufts University’s Intro to Pscyhology (Psy 1) course that used Psychology, 8th edition by Gleitman, Gross, and Reisberg.

Prologue – What is Psychology

Chapter 1 – Research Methods

Chapter 3 – Part 1 – The Brain and Nervous System

Chapter 3 – Part 2 – The Brain and Nervous System

Chapter 4 – Sensation

Chapter 5 (I) – Perception

Chapter 5 (II) and Anderson Excerpt- Perception

Chapter 6 – Consciousness

Chapter 7 – Learning

Chapter 8 – Memory

Chapter 9 and 13 (I) – Thinking and Social Psychology

Chapter 10 (I) – Language

Chapter 10 (II) – Language

Chapter 10 (III) and Chapter 14 – Language and Development

Chapter 12 – Motivation and Emotion

Chapter 13 (II) – Social Psychology

Chapter 13 (III) – Social Psychology

Chapter 14 – Development

Chapter 15 – Personality

Chapter 16 – Psychopathology

Chapter 17 – Treatment of Mental Disorders

The following website is also a good source of information, especially if you’re using this specific textbook. It contains study guides for each chapter by the publisher, and it contains multiple choice question “quizzes” to do for each chapter. You can find it at: http://www.wwnorton.com/college/psych/psychology8/welcome.aspx

Calculus II (Applied) Review Sheets & Study Guides

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Here are review sheets for (Applied) Calculus II

Approximation of Higher Degrees

Arc Length

Differential Equations

Improper Integration

Integration by Parts

Linear Approximations

More Integral Properties

Newton’s Method

Numerical Integration

Partial Fractions

Physical Applicatoins


Regions Between Curves

Symmetric Integration

Trig Substitutions

Velocity and Net Change

Volumes by Integration


Alternating Series

Infinite Series

Sequences and Series Overview


The Divergence and Integral Tests

The Ratio and Comparison Tests

The following notes are not created by me, but I think you might find them helpful if you’re in need of them. They are made by Paul Dawkins of “Paul’s Online Math Notes,” and they are of stellar quality. You can download the PDF for the entire course here: http://tutorial.math.lamar.edu/downloadfile.aspx?file=B,2,N

For some more basic review material, you can check out my AP Calculus BC Review Sheets at http://sites.tufts.edu/andrewrosen/2012/03/03/ap-calculus-bc-and-ab-review-sheets/

Calc III (Multivariable Calculus) Review Sheets & Study Guides

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Calculus: Early Transcendentals by Briggs and Cochran

Chapter 11 – Vectors and Vector-Valued Functions


11.1 – Vectors in the Plane, 11.2 – Vectors in Three Dimensions, 11.3 – Dot Products, 11.4 – Cross Products, 11.5 – Lines and Curves in Space, 11.6 – Calculus of Vector-Valued Functions, 11.7 – Motion in Space, and 11.8 – Length of Curves

Chapter 12 - Functions of Several Variables


12.1 – Planes and Surfaces, 12.2 – Graphs and Level Curves, 12.4 – Partial Derivatives, 12.5 – The Chain Rule, 12.6 – Directional Derivatives and the Gradient, 12.7 – Tangent Planes and Linear Approximations, 12.8 – Maximum/Minimum Problems, 12.9 – Lagrange Multipliers

Chapter 13 - Multiple Integration


13.1 – Double Integrals over Rectangular Regions, 13.2 – Double Integrals over General Regions, 13.3 – Double Integrals in Polar Coordinates, 13.4 – Triple Integrals, 13.5 – Triple Integrals in Cylindrical and Spherical Coordinates

Chapter 14, Part I - Vector Fields


14.1 – Vector Fields and Integrals, 14.2 – Line Integrals, 14.3 – Conservative Fields

Chapter 14, Part II - Vector Calculus – Part II


14.4 – Green’s Theorem, 14.5 – Divergence and Curl, 14.6 – Surface Integrals, 14.7 – Stokes’ Theorem, 14.8 - Divergence Theorem

This is an excellent Calc III review sheet made by my friend Tyler Silber, a student at the University of Connecticut. You can find it here:

Calc III Review by Tyler

Also, this will help you with computing double integrals. It’s a Wolfram|Alpha widget to easily find the answer to a double integral. It can be found at: http://www.wolframalpha.com/widgets/view.jsp?id=f5f3cbf14f4f5d6d2085bf2d0fb76e8a

This review sheet is created by Paul Dawkins of “Paul’s Online Math Notes.” You can download a PDF of his Calc III review sheets at the following domain of his: http://tutorial.math.lamar.edu/downloadfile.aspx?file=B,11,N

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