This unusual, but very useful, "how-not-to" book is available in a second edition which eliminates most involuntary mistakes.
Undergraduate mathematics students and instructors.
Introduction. Note to Teachers. Note to Students. Integrals: The Power of Positive Thinking. Differentiating Right from Wrong. More Integrals (That's about the Size of It). Derivatives Again, and the Fine Art of Being Crude. Reducing to Special Cases. Dimensions. Symmetry (The Same Thing Over and Over). The "What Did You Expect?" Method. Some Common Errors. Suggested Reading.