11.10 Systems of Equations, Eigenvalues, and Eigenvectors.

Fundamental Math and Physics for Scientists and Engineers; Copyright; Contents; Chapter 1 Introduction; Chapter 2 Problem Solving; 2.1 Analysis; 2.2 Test-Taking Techniques; 2.2.1 Dimensional Analysis; Chapter 3 Scientific Programming; 3.1 Language Fundamentals; 3.1.1 Octave Programming; Chapter 4 Elementary Mathematics; 4.1 Algebra; 4.1.1 Equation Manipulation; 4.1.2 Linear Equation Systems; 4.1.3 Factoring; 4.1.4 Inequalities; 4.1.5 Sum Formulas; 4.1.6 Binomial Theorem; 4.2 Geometry; 4.2.1 Angles; 4.2.2 Triangles; 4.2.3 Right Triangles; 4.2.4 Polygons; 4.2.5 Circles.

4.3 Exponential, Logarithmic Functions, and Trigonometry4.3.1 Exponential Functions; 4.3.2 Inverse Functions and Logarithms; 4.3.3 Hyperbolic Functions; 4.3.4 Complex Numbers and Harmonic Functions; 4.3.5 Inverse Harmonic and Hyperbolic Functions; 4.3.6 Trigonometric Identities; 4.4 Analytic Geometry; 4.4.1 Lines and Planes; 4.4.2 Conic Sections; 4.4.3 Areas, Volumes, and Solid Angles; Chapter 5 Vectors and Matrices; 5.1 Matrices and Matrix Products; 5.2 Equation Systems; 5.3 Traces and Determinants; 5.4 Vectors and Inner Products; 5.5 Cross and Outer Products; 5.6 Vector Identities.

5.7 Rotations and Orthogonal Matrices5.8 Groups and Matrix Generators; 5.9 Eigenvalues and Eigenvectors; 5.10 Similarity Transformations; Chapter 6 Calculus of a Single Variable; 6.1 Derivatives; 6.2 Integrals; 6.3 Series; Chapter 7 Calculus of Several Variables; 7.1 Partial Derivatives; 7.2 Multidimensional Taylor Series and Extrema; 7.3 Multiple Integration; 7.4 Volumes and Surfaces of Revolution; 7.5 Change of Variables and Jacobians; Chapter 8 Calculus of Vector Functions; 8.1 Generalized Coordinates; 8.2 Vector Differential Operators; 8.3 Vector Differential Identities.

8.4 Gauss ́s and Stokes ́ Laws and Green ́s Identities8.5 Lagrange Multipliers; Chapter 9 Probability Theory and Statistics; 9.1 Random Variables, Probability Density, and Distributions; 9.2 Mean, Variance, and Standard Deviation; 9.3 Variable Transformations; 9.4 Moments and Moment-Generating Function; 9.5 Multivariate Probability Distributions, Covariance, and Correlation; 9.6 Gaussian, Binomial, and Poisson Distributions; 9.7 Least Squares Regression; 9.8 Error Propagation; 9.9 Numerical Models; Chapter 10 Complex Analysis; 10.1 Functions of a Complex Variable.

10.2 Derivatives, Analyticity, and the Cauchy-Riemann Relations10.3 Conformal Mapping; 10.4 Cauchy ́s Theorem and Taylor and Laurent Series; 10.5 Residue Theorem; 10.6 Dispersion Relations; 10.7 Method of Steepest Decent; Chapter 11 Differential Equations; 11.1 Linearity, Superposition, and Initial and Boundary Values; 11.2 Numerical Solutions; 11.3 First-Order Differential Equations; 11.4 Wronskian; 11.5 Factorization; 11.6 Method of Undetermined Coefficients; 11.7 Variation of Parameters; 11.8 Reduction of Order; 11.9 Series Solution and Method of Frobenius.

This text summarizes the core undergraduate physics curriculum together with the mathematics frequently encountered in engineering and physics calculations, focusing on content relevant to practical applications. Covers major undergraduate physics topics including the complete Physics GRE subject examination syllabusOverview of key results in undergraduate applied mathematics and introduces scientific programmingPresents simple, coherent derivations and illustrations of fundamental concepts.

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