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A Primer for Mathematical Analysis / by David Borthwick.
Springer Nature - Springer Mathematics and Statistics (R0) eBooks 2025 English International Available online
View online- Format:
- Book
- Author/Creator:
- Borthwick, David, Author.
- Series:
- Synthesis Lectures on Mathematics & Statistics, 1938-1751
- Language:
- English
- Subjects (All):
- Mathematics.
- Mathematical analysis.
- Functions of real variables.
- Functions of complex variables.
- Functional analysis.
- Analysis.
- Real Functions.
- Several Complex Variables and Analytic Spaces.
- Integral Transforms and Operational Calculus.
- Functional Analysis.
- Local Subjects:
- Mathematics.
- Analysis.
- Real Functions.
- Several Complex Variables and Analytic Spaces.
- Integral Transforms and Operational Calculus.
- Functional Analysis.
- Physical Description:
- 1 online resource (VIII, 119 p. 18 illus., 16 illus. in color.)
- Edition:
- 1st ed. 2025.
- Place of Publication:
- Cham : Springer Nature Switzerland : Imprint: Springer, 2025.
- Summary:
- This book presents a concise introduction to real and complex number systems and metric space theory. The goal is to help students bridge the gap between undergraduate courses in advanced calculus and graduate level material in analysis or related subjects such as differential geometry or probability. The unifying feature in all of these subject areas is the predominance of the limit, and metric space theory is the mathematical language in which limits are formulated. To understand analysis at a graduate level, students need to develop fluency in this language. To facilitate this development, exercises are incorporated into the main text, with many key results posed as problems. Solutions are provided to help readers fill in any gaps. This book: Covers the most crucial prerequisites for graduate level analysis, including metric space theory Contains plentiful exercises to help develop proficiency in the key ideas and techniques, with solutions provided Features a self-contained presentation designed for students to review or study on their own.
- Contents:
- Real Numbers
- Complex Numbers and Series
- Metric Topology
- Functions on Metric Spaces. Solutions to Exercises
- Index.
- ISBN:
- 9783031917134
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