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雷达卡
Author(s): Jeffrey R. Chasnov
Hong Kong University of Science and Technology
A Short Mathematical Review
0: A Short Mathematical Review
0.1: The Trigonometric Functions
0.2: The Exponential Function and the Natural Logarithm
0.3: Definition of the Derivative
0.4: Differentiating a Combination of Functions
0.5: Differentiating Elementary Functions
0.6: Definition of the Integral
0.7: The Fundamental Theorem of Calculus
0.8: Definite and Indefinite Integrals
0.9: Indefinite Integrals of Elementary Functions
0.10: Substitution
0.11: Integration by Parts
0.12: Taylor Series
0.13: Functions of Several Variables
0.14: Complex Numbers I. Linear Algebra
1: Matrices
1.1: Definition of a Matrix
1.2: Addition and Multiplication of Matrices
1.3: General Notation, Transposes, and Inverses
1.3: The Identity Matrix and the Zero Matrix
1.4: Rotation Matrices and Orthogonal Matrices
1.6: Matrix Representation of Complex Numbers
1.7: Permutation Matrices
1.8: Projection Matrices
2: Systems of Linear Equations
2.1: Gaussian Elimination
2.2: When There is No Unique Solution
2.3: Reduced Row Echelon Form
2.4: Computing Inverses
2.5: LU Decomposition
3: Vector Spaces
3.1: Vector Spaces
3.2: Linear Independence
3.3: Span, Basis, and Dimension
3.4: Inner Product Spaces
3.5: Vector Spaces of a Matrix
3.6: Gram-Schmidt Process
3.7: Orthogonal Projections
3.8: QR Factorization
3.9: The Least-Squares Problem
3.10: 3. 10-Solution of the Least-Squares Problem
4: Determinants
4.1: Two-by-Two and Three-by-Three Determinants
4.2: Laplace Expansion and Leibniz Formula
4.3: Properties of the Determinant
4.4: Use of Determinants in Vector Calculus
5: Eigenvalues and Eigenvectors
5.1: The Eigenvalue Problem5.2: Matrix Diagonalization
5.3: Symmetric and Hermitian Matrices II. Differential Equations
6: Introduction to ODEs
6.1: The Simplest Type of Differential Equation
7: First-Order ODEs
7.1: The Euler Method
7.2: Separable Equations
7.3: Linear Equations
7.4: Applications
8: Second-Order ODEs, Constant Coefficients
8.1: The Euler Method
8.3: The Wronskian
8.2: The Principle of Superposition
8.4: Homogeneous linear second-order ode with con-stant coefficients
8.5: Difference Equations
8.6: Inhomogenous ODEs
8.7: Resonance
8.8: Applications
8.9: Damped Resonance
9: Series Solutions of homogeneous linear second-order differential equations
9.1: Ordinary Points
10: Systems of Linear Differential Equations
10.1: Distinct Real Eigenvalues
10.2: Solution by Diagonalization
10.3: Solution by the Matrix Exponential
10.4: Distinct Complex-Conjugate Eigenvalues
10.5: Repeated Eigenvalues with One Eigenvector
10.6: Normal Modes
11: Nonlinear Differential Equations
11.1: Fixed Points and Stability
о 11.2: Bifurcation Theory
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Applied Linear Algebra and Differential Equations-Hong Kong University (2024).pdf
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