Introduction to Analysis (eBook)

Robert C. Gunning (Autor)

eBook Download: PDF

2018
384 Seiten
Princeton University Press (Verlag)
978-1-4008-8941-9 (ISBN)

Infos

An essential undergraduate textbook on algebra, topology, and calculusAn 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 variablesIntroduces students to basic topologyCovers topics in linear algebra, including matrices, determinants, Jordan normal form, and bilinear and normal mappingsDiscusses differential forms and Stokes's theorem in n dimensionsAlso covers the Riemann integral, integrability, improper integrals, and series expansions

Autor

Robert C. Gunning is professor of mathematics at Princeton University. His books include Lectures on Riemann Surfaces and Lectures on ComplexAnalytic Varieties (both Princeton).

Produkt-Details

• Erscheint lt. Verlag: 20.3.2018
• Zusatzinfo: 25 b/w illus.
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Schlagworte: algebraic extension • analytic function • Antiderivative • Arzelà–Ascoli theorem • associative property • axiomatic system • Axiom of choice • Baire category theorem • Basis (linear algebra) • bilinear map • Binomial series • Calculation • Cardinality • Cauchy Sequence • Change of basis • Characterization (mathematics) • commutative property • Compact space • complex number • Conjugate transpose • continuous function • Continuous function (set theory) • coordinate system • corollary • Diagram (category theory) • Differentiable function • differential form • Dimension (vector space) • Divergence Theorem • dot product • Eigenvalues and Eigenvectors • Endomorphism • Equation • equivalence class • equivalence relation • Fubini's Theorem • functional equation • Function composition • Group homomorphism • Heine–Borel theorem • holomorphic function • Homeomorphism • I0 • Identity element • Identity matrix • Implicit function • Infimum and supremum • Injective function • Inner product space • integral domain • Integration by parts • Interior (topology) • intermediate value theorem • Interval (mathematics) • Invertible matrix • Jacobian matrix and determinant • Lebesgue integration • Limit point • Linear map • Linear subspace • Mathematical Induction • Maxima and minima • mean value theorem • Measure (mathematics) • Metric Space • Natural number • Neighbourhood (mathematics) • Open set • Orientability • Orthonormal basis • Permutation • Permutation Matrix • polynomial • power series • Rational number • ratio test • real number • Representation Theory • Riemann integral • Root test • Self-adjoint • set theory • Special case • Stokes' theorem • Stone–Weierstrass theorem • submanifold • Subring • subsequence • Subset • Summation • Taylor series • Theorem • Topological space • Topology • Transitive relation • transpose • Variable (mathematics) • Vector Space • Weierstrass M-test • Weierstrass Theorem
• ISBN-10: 1-4008-8941-3 / 1400889413
• ISBN-13: 978-1-4008-8941-9 / 9781400889419