Score: 3. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it. This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience.
Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related topics such as determinants, eigenvalues, and differential equations. Table of Contents: l. The Algebra of Matrices 2. Linear Equations 3. Vector Spaces 4. Determinants 5. Linear Transformations 6. Eigenvalues and Eigenvectors 7. Inner Product Spaces 8.
Applications to Differential Equations For the second edition, the authors added several exercises in each chapter and a brand new section in Chapter 7. The exercises, which are both true-false and multiple-choice, will enable the student to test his grasp of the definitions and theorems in the chapter. The new section in Chapter 7 illustrates the geometric content of Sylvester's Theorem by means of conic sections and quadric surfaces.
Two prefaces. Answer section. Matrix Algebra Author : James E. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices.
Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Concrete, easy-to-understand examples m. Balancing theory and applications, the book is written in a conversational style and combines a traditional presentation with a focus on student-centered learning.
Theoretical, computational, and applied topics are presented in a flexible yet integrated way. Stressing geometric understanding before computational techniques, vectors and vector geometry are introduced early to help students visualize concepts and develop mathematical maturity for abstract thinking. Additionally, the book includes ample applications drawn from a variety of disciplines, which reinforce the fact that linear algebra is a valuable tool for modeling real-life problems.
Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. Its prerequisites are minimal, and the order of its presentation promotes an intuitive approach to calculus. Algebraic concepts receive an unusually strong emphasis.
Numerous exercises appear throughout the text. This reference book provides the background in matrix algebra necessary to do research and understand the results in these areas. Essentially self-contained, the book is best-suited for a reader who has had some previous exposure to matrices. Solultions to the exercises are available in the author's "Matrix Algebra: Exercises and Solutions.
Score: 5. Advanced Topics In Introductory Probability. Stochastic Processes 1. Advanced Maths for Chemists. Partial differential equations and operators. Study notes for Statistical Physics. Linear algebra c Essential Group Theory. Linear Algebra III. Analytical Trigonometry with Applications. Mathematical Models in Portfolio Analysis. Theoretical Probability Distributions. Exercises in Statistical Inference. Complex Functions Theory c Examples of Sequences. Random variables II.
Elementary Analytic Functions. Global Analysis. Random variables I. Linear and Convex Optimization. Integration and differential equations. Differential Equations with YouTube Examples.
Ordinary differential equations of first order. Discrete Dynamical Systems. Complex Functions Examples c Integral Operators. Sequences and Power Series. Stochastic Processes 2. An Introduction to Group Theory. Fourier Series and Systems of Differential Stability Analysis via Matrix Functions Method. Examples of General Elementary Series. Stability, Riemann Surfaces, Conformal Mappings. Real Functions in One Variable - Elementary Examples of Differential Equations of Second Introductory Nonparametrics.
Real Functions in One Variable - Complex Real Functions in One Variable - Simple Examples of Power Series. A Short Course in Predicate Logic. Fibonacci Numbers and the Golden Ratio. Hilbert Spaces and Operators on Hilbert Spaces.
Stability of Weakly Connected Nonlinear Systems. Real Functions in One Variable - Integrals Second-order ordinary differential equations.
Complex Functions c My Horror Chamber. Discrete Distributions. Descent and Interior-point Methods. Examples of Applications of The Power Series Advanced stochastic processes: Part I. Methods for finding Zeros in Polynomials. Examples of Fourier series. Topological and Metric Spaces, Banach Spaces Continuous Distributions.
Real Functions in One Variable - Taylor's Real Functions in One Variable. Calculus of Residua. Examples of Eigenvalue Problems. Spectral Theory. Random variables III. Examples of Systems of Differential Equations
0コメント