Understanding Calculus

Understanding Calculus is a complete online introductory book that focuses on concepts. Integrated throughout the e-book are many engineering applications aimed at developing the student's scientific approach towards problem solving.

**Tag(s):**
Mathematics

**Publication date**: 31 Dec 2009

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**Views**: 15,714

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**Post time**: 23 Jul 2009 04:39:09

Understanding Calculus

Understanding Calculus is a complete online introductory book that focuses on concepts. Integrated throughout the e-book are many engineering applications aimed at developing the student's scientific approach towards problem solving.

Excerpts from the Preface:

Faraz Hussain wrote:The purpose of this book is to present mathematics as the science of deductive reasoning and not as the art of manipulation. Unfortunately, many students feel mathematics is incomprehensible and is riddled with complex and abstract jargon. My goal is to impose a lasting understanding of and appreciation for calculus on the student.

Unfortunately, students are rarely given any example of practical applications. The curriculum's idea of exercises is nothing more than sheer number-crunching and manipulation of variables. The entire underlying principle of order and beauty upon which calculus is based, is neglected. The problems never call upon the student's ability to think logically. Rather, they require no more than time and persistence, to allow the trial and error method to succeed.

Faraz Hussain wrote:It is all these shortcomings I set out to correct in writing my book. My book is intended to give the student a real for and understanding of what Calculus is truly about. Only by explaining where something has come from will I be able to show where it is going. It does not take more intelligence than that of a parrot to be able to go through a list of theorems and equations; but only when one understands their origins can one correctly and confidently apply them in the real world.

I assume absolutely nothing and neither do I take anything for granted. Each chapter has a definite beginning, followed by logical, elegant and clear proofs, concluded with a brief summary that ties everything together. My only reference has been reason and if you could find just three lines that remotely resemble the lines from any other book, I would feel greatly distressed.

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