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18.100A Introduction to Analysis (MIT) 18.100A Introduction to Analysis (MIT)

Description

Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the pla Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the pla

Subjects

mathematical analysis | mathematical analysis | estimations | estimations | limit of a sequence | limit of a sequence | limit theorems | limit theorems | subsequences | subsequences | cluster points | cluster points | infinite series | infinite series | power series | power series | local and global properties | local and global properties | continuity | continuity | intermediate-value theorem | intermediate-value theorem | convexity | convexity | integrability | integrability | Riemann integral | Riemann integral | calculus | calculus | convergence | convergence | Gamma function | Gamma function | Stirling | Stirling | quantifiers and negation | quantifiers and negation | Leibniz | Leibniz | Fubini | Fubini | improper integrals | improper integrals | Lebesgue integral | Lebesgue integral | mathematical proofs | mathematical proofs | differentiation | differentiation | integration | integration

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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24.805 Topics in Theory of Knowledge: A Priori Knowledge (MIT) 24.805 Topics in Theory of Knowledge: A Priori Knowledge (MIT)

Description

The seminar will explore the phenomenon of a priori knowledge. We'll consider some notable attempts to account for a priori knowledge in the history of philosophy (e.g., by Plato, Descartes, Hume, and Kant), some influential critiques of the notion; we will end by considering some contemporary approaches to the a priori. The seminar will explore the phenomenon of a priori knowledge. We'll consider some notable attempts to account for a priori knowledge in the history of philosophy (e.g., by Plato, Descartes, Hume, and Kant), some influential critiques of the notion; we will end by considering some contemporary approaches to the a priori.

Subjects

a priori knowledge | a priori knowledge | Plato | Plato | Descartes | Descartes | Hume | Hume | Kant | Kant | Leibniz | Leibniz | Locke | Locke | Hume and the Positivists | Hume and the Positivists | history of philosophy | history of philosophy

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.100A Introduction to Analysis (MIT)

Description

Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the pla

Subjects

mathematical analysis | estimations | limit of a sequence | limit theorems | subsequences | cluster points | infinite series | power series | local and global properties | continuity | intermediate-value theorem | convexity | integrability | Riemann integral | calculus | convergence | Gamma function | Stirling | quantifiers and negation | Leibniz | Fubini | improper integrals | Lebesgue integral | mathematical proofs | differentiation | integration

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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Isaac Newton and his enemies

Description

Authors:  Professor David Wolfe David Wolfe, Emeritus Professor of Physics, University of New Mexico and Director, Oppenheimer Institute for Science and International Co-operation Clicked 295 times. Last clicked 01/24/2015 - 21:11. Teaching & Learning Context:  <p>These audio lectures will be of interest to anyone interested in learning more about Isaac Newton and physics from a historical perspective.</p>

Subjects

Centre for Higher Education Development | Centre for Open Learning | Audio | Audio Lectures | English | Post-secondary | calculus | David Wolfe | Isaac Newton | Leibniz | Newton | physics | podcasts | Robert Hooke

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http://creativecommons.org/licenses/by-nd/2.5/za/

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24.805 Topics in Theory of Knowledge: A Priori Knowledge (MIT)

Description

The seminar will explore the phenomenon of a priori knowledge. We'll consider some notable attempts to account for a priori knowledge in the history of philosophy (e.g., by Plato, Descartes, Hume, and Kant), some influential critiques of the notion; we will end by considering some contemporary approaches to the a priori.

Subjects

a priori knowledge | Plato | Descartes | Hume | Kant | Leibniz | Locke | Hume and the Positivists | history of philosophy

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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