Mathematical Analysis (often called Advanced Calculus) is generally found by students to be one of their hardest courses in Mathematics. This text uses the so-called sequential approach to continuity, differentiability and integration to make it easier to understand the subject.Topics that are generally glossed over in the standard Calculus courses are given careful study here. For example, what exactly is a 'continuous' function? And how exactly can one give a careful definition of 'integral'? The latter question is often one of the mysterious points in a Calculus course - and it is quite difficult to give a rigorous treatment of integration! The text has a large number of diagrams and helpful margin notes; and uses many graded examples and exercises, often with complete solutions, to guide students through the tricky points. It is suitable for self-study or use in parallel with a standard university course on the subject.
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Book Description
A down-to-earth advanced Calculus text. It has a large number of diagrams and helpful margin notes; and uses many graded examples and exercises, often with complete solutions, to guide students through the tricky points. Suitable for self-study or use in parallel with a standard university course on the subject.
About the Author
David Brannan is Professor, Dean and Director of Studies of the Maths & Computing Faculty at the Open University
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Most Helpful Customer Reviews
25 of 27 people found the following review helpful:
5.0 out of 5 stars
Excellent first intro to Analysis,
By A. Cox "Artist, Musician, Physicist and Cook" (New York, NY United States) - See all my reviews
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This review is from: A First Course in Mathematical Analysis (Hardcover)
This book pretty much copies the Real Analysis part of the Open University's excellent course 'Into to Pure Mathematics' which also covered Group Theory and Linear Algebra . If you're new to Analysis I cannot more highly recommend another book, though I would also recommend Spivak's Calculus which is at the same level, and pretty much covers the same material. I did the course (and have the book) and found it a breeze, all due to the excellently presented material, and the many examples, where like the SUMS books (of which I recommend most), all answers are givern in detail; which is important when you start more advanced maths (sic) and especially when you're teaching yourself! However it is only an introduction, but will prepare you for more advanced Analysis books like Rudin, Royden and my new favourite Knapp and his 2 Real Analysis books. Personally I wish they would produce more of the OU Maths courses in book format, as the material that I have read and studied has rarely been bettered in the standard books. Maybe this is a start of a new trend with the OU, I hope!
5 of 6 people found the following review helpful:
5.0 out of 5 stars
The best introductory text on analysis that I've seen.,
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This review is from: A First Course in Mathematical Analysis (Hardcover)
This book is a gem.
As the author states in the introduction, this is a student friendly book - the notes in the margins are really useful, the worked examples are clear and well thought out while the book has a good flow to it. A lot of thought has been put into this text and it shows. The bottom line is that I learnt a lot from this book and now feel ready to tackle more advanced texts.
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First Sentence:
In this book we study the properties of real functions defined on intervals of the real line (possibly the whole real line) and whose image also lies on the real line. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
basic null sequence, kth bracket, power series anxn, punctured neighbourhood, continuous inverse function, nth root function, odd subsequence, limit limf, null sequences, rearranging inequalities, rearranged series, tangent approximation, sequential definition, standard partition, repeated bisection, intermediate value theorem, final inequality, nth partial sum, partition points, following power series, convergent infinite series, maximum element Key Phrases - Capitalized Phrases (CAPs): (learn more)
Combination Rules, Squeeze Rule, Composition Rule, Sum Rule, Triangle Inequality, Product Rule, Multiple Rule, Inverse Function Rule, Mean Value Theorem, Monotone Convergence Theorem, Rolle's Theorem, Comparison Test, Ratio Test, Quotient Rule, Binomial Theorem, Taylor's Theorem, Proof Let, Stirling's Formula, Reciprocal Rule, Least Upper Bound Property, Definition Let, Mathematical Induction, Solution Let, Alternating Test, Non-null Test New!
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Front Cover | Table of Contents | First Pages | Index | Surprise Me!
In this book we study the properties of real functions defined on intervals of the real line (possibly the whole real line) and whose image also lies on the real line. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
basic null sequence, kth bracket, power series anxn, punctured neighbourhood, continuous inverse function, nth root function, odd subsequence, limit limf, null sequences, rearranging inequalities, rearranged series, tangent approximation, sequential definition, standard partition, repeated bisection, intermediate value theorem, final inequality, nth partial sum, partition points, following power series, convergent infinite series, maximum element Key Phrases - Capitalized Phrases (CAPs): (learn more)
Combination Rules, Squeeze Rule, Composition Rule, Sum Rule, Triangle Inequality, Product Rule, Multiple Rule, Inverse Function Rule, Mean Value Theorem, Monotone Convergence Theorem, Rolle's Theorem, Comparison Test, Ratio Test, Quotient Rule, Binomial Theorem, Taylor's Theorem, Proof Let, Stirling's Formula, Reciprocal Rule, Least Upper Bound Property, Definition Let, Mathematical Induction, Solution Let, Alternating Test, Non-null Test New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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