Calculus, Volume 1Gilbert Strang's Calculus textbook is ideal both as a course companion and for self study. The author has a direct style. His book presents detailed and intensive explanations. Many diagrams and key examples are used to aid understanding, as well as the application of calculus to physics and engineering and economics. The text is well organized, and it covers single variable and multivariable calculus in depth. An instructor's manual and student guide are available online at http: //ocw.mit.edu/ans7870/ 
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Mathematical inbreeding is an inherent issue if one author is referenced or studied exclusively. While I was originally taught Calculus with George Thomas' excellent text on Calculus, I found that upon review Gilbert Strang packed a little more meat on the bones so to speak, in his introductory text and consequently gained much insight unattainable otherwise. I found the problems and exercises relevant and non trivial enough to keep me from whizzing through the book too fast. I also chuckled at the author's dry sense of humor. This text is a must for any Math maven.
M. Conrad Kabay
The book is really good. It lets u link with physics while studying mathematics.
Contents
Introduction to Calculus  1 
Derivatives  44 
Applications of the Derivative  91 
The Chain Rule  154 
Integrals  177 
Exponentials and Logarithms  228 
Techniques of Integration  282 
Applications of the Integral  311 
Infinite Series  366 
Vectors and Matrices  397 
Motion along a Curve  446 
Partial Derivatives  471 
Multiple Integrals  521 
Vector Calculus  549 
Mathematics after Calculus  597 
Polar Coordinates and Complex Numbers  348 