Leseprobe
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An Introduction to Analysis
Robert C. Gunning
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Naturwissenschaften, Medizin, Informatik, Technik / Analysis
Beschreibung
An essential undergraduate textbook on algebra, topology, and calculus
An Introduction to Analysis is an essential primer on basic results in algebra, topology, and calculus for undergraduate students considering advanced degrees in mathematics. Ideal for use in a one-year course, this unique textbook also introduces students to rigorous proofs and formal mathematical writing--skills they need to excel.
With a range of problems throughout, An Introduction to Analysis treats n-dimensional calculus from the beginning—differentiation, the Riemann integral, series, and differential forms and Stokes's theorem—enabling students who are serious about mathematics to progress quickly to more challenging topics. The book discusses basic material on point set topology, such as normed and metric spaces, topological spaces, compact sets, and the Baire category theorem. It covers linear algebra as well, including vector spaces, linear mappings, Jordan normal form, bilinear mappings, and normal mappings.
Proven in the classroom, An Introduction to Analysis is the first textbook to bring these topics together in one easy-to-use and comprehensive volume.
- Provides a rigorous introduction to calculus in one and several variables
- Introduces students to basic topology
- Covers topics in linear algebra, including matrices, determinants, Jordan normal form, and bilinear and normal mappings
- Discusses differential forms and Stokes's theorem in n dimensions
- Also covers the Riemann integral, integrability, improper integrals, and series expansions
Kundenbewertungen
Axiom of choice, Stokes' theorem, Vector space, Equivalence class, Mean value theorem, Polynomial, Group homomorphism, Limit point, Real number, Ratio test, Heine–Borel theorem, Inner product space, Injective function, Permutation, Special case, Continuous function, Differential form, Intermediate value theorem, Topology, Measure (mathematics), Metric space, Holomorphic function, Arzelà–Ascoli theorem, Characterization (mathematics), Identity element, Analytic function, Function composition, Subset, Infimum and supremum, Topological space, Differentiable function, Summation, Theorem, Integral domain, Open set, Submanifold, Neighbourhood (mathematics), Subsequence, Maxima and minima, Bilinear map, Eigenvalues and eigenvectors, Conjugate transpose, Equivalence relation, Power series, Homeomorphism, Identity matrix, Dimension (vector space), Implicit function, Lebesgue integration, Variable (mathematics), Continuous function (set theory), Orientability, Rational number, Complex number, Orthonormal basis, Diagram (category theory), Baire category theorem, Linear map, Linear subspace, Calculation, Cauchy sequence, Endomorphism, Binomial series, Transitive relation, Fubini's theorem, Integration by parts, Self-adjoint, Basis (linear algebra), Equation, Natural number