| 청구기호 |
QA184.2 .S565 2008 |
| 형태사항 |
1 electronic text (x, 132 p. : ill.) : digital file.
|
| 언어 |
English |
| 일반주기 |
Part of: Synthesis digital library of engineering and computer science.
Title from PDF t.p. (viewed on October 15, 2008).
Series from website.
Includes index.
|
| 내용 |
Linear algebra -- Vectors in Rn -- Dot product and angle between vectors in Rn -- Subspaces and linear dependence of vectors -- Gaussian elimination and the linear dependence lemma -- The basis theorem -- Matrices -- Rank and the rank-nullity theorem -- Orthogonal complements and orthogonal projection -- Row echelon form of a matrix -- Inhomogeneous systems -- Analysis in Rn -- Open and closed sets in Euclidean space -- Bolzano-Weierstrass, limits and continuity in Rn -- Differentiability -- Directional derivatives, partial derivatives, and gradient -- Chain rule -- Higher-order partial derivatives -- Second derivative test for extrema of multivariable function -- Curves in Rn -- Submanifolds of Rn and tangential gradients -- More linear algebra -- Permutations -- Determinants -- Inverse of a square matrix -- Computing the inverse -- Orthonormal basis and Gram-Schmidt -- Matrix representations of linear transformations -- Eigenvalues and the spectral theorem -- More analysis in Rn -- Contraction mapping principle -- Inverse function theorem -- Implicit function theorem -- Introductory lectures on real analysis -- Lecture 1: The real numbers -- Lecture 2: Sequences of real numbers and the Bolzano-Weierstrass theorem -- Lecture 3: Continuous functions -- Lecture 4: Series of real numbers -- Lecture 5: Power series -- Lecture 6: Taylor series representations -- Lecture 7: Complex series, products of series, and complex exponential series -- Lecture 8: Fourier series -- Lecture 9: Pointwise convergence of trigonometric Fourier series.
|
| 주제 |
Algebras, Linear.
Mathematical analysis.
|
| ISBN |
9781598298024 (electronic bk.)
9781598298017 (pbk.)
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| 기타 표준번호 |
10.2200/S00147ED1V01Y200808MAS003 |
