Math C285: Linear Algebra and Diffrential Equations (Tran)

Mathematics

Tác giả: Chau D. Tran
Nhà xuất bản: Coastline College
Nguồn: LibreTexts
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

Đọc trực tuyến Tải PDF (nguồn mở)

Mục lục· 148 mục

01: Systems of Equations
1.01: Systems of Equations Geometry
1.02: Systems of Equations Algebraic Procedures
1.03: Gaussian Elimination
1.04: Uniqueness of the Reduced Row-Echelon Form
1.05: Rank and Homogeneous Systems
1.06: Balancing Chemical Reactions
1.07: Dimensionless Variables
1.08: An Application to Resistor Networks
1.09: Exercises
02: Systems of Equations
2.01: Systems of Equations Geometry
2.02: Systems of Equations Algebraic Procedures
2.03: Gaussian Elimination
2.04: Uniqueness of the Reduced Row-Echelon Form
2.05: Rank and Homogeneous Systems
2.06: Balancing Chemical Reactions
2.07: Dimensionless Variables
2.08: An Application to Resistor Networks
2.09: Exercises
03: Determinants
3.01: Basic Techniques
3.02: Properties of Determinants
3.03: Finding Determinants using Row Operations
3.04: Applications of the Determinant
3.E: Exercises
04: R
4.01: Vectors in R
4.02: Vector Algebra
4.03: Geometric Meaning of Vector Addition
4.04: Length of a Vector
4.05: Geometric Meaning of Scalar Multiplication
4.06: Parametric Lines
4.07: The Dot Product
4.08: Planes in R
4.09: The Cross Product
4.10: Spanning Linear Independence and Basis in R
4.11: Orthogonality
4.12: Applications
4.E: Exercises
05: Linear Transformations
5.01: Linear Transformations
5.02: The Matrix of a Linear Transformation I
5.03: Properties of Linear Transformations
5.04: Special Linear Transformations in R
5.05: One-to-One and Onto Transformations
5.06: Isomorphisms
5.07: The Kernel and Image of A Linear Map
5.08: The Matrix of a Linear Transformation II
5.09: The General Solution of a Linear System
5.E: Exercises
06: Complex Numbers
6.01: Complex Numbers
6.02: Polar Form
6.03: Roots of Complex Numbers
6.04: The Quadratic Formula
6.E: Exercises
07: Spectral Theory
7.01: Eigenvalues and Eigenvectors of a Matrix
7.02: Diagonalization
7.03: Applications of Spectral Theory
7.04: Orthogonality
7.E: Exercises
08: Some Curvilinear Coordinate Systems
8.01: Polar Coordinates and Polar Graphs
8.02: Spherical and Cylindrical Coordinates
8.E: Exercises
09: Vector Spaces
9.01: Algebraic Considerations
9.02: Spanning Sets
9.03: Linear Independence
9.04: Subspaces and Basis
9.05: Sums and Intersections
9.06: Linear Transformations
9.07: Isomorphisms
9.08: The Kernel and Image of a Linear Map
9.09: The Matrix of a Linear Transformation
9.E: Exercises
10: Some Prerequisite Topics
10.01: Sets and Set Notation
10.02: Well Ordering and Induction
11: Introduction
11.01: Notes About These Notes
11.02: Introduction to Differential Equations
11.03: Classification of Differential Equations
11.04: First order ODEs
11.E: Introduction (Exercises)
12: First order ODEs
12.01: Integrals as solutions
12.02: Slope fields
12.03: Separable Equations
12.04: Linear equations and the integrating factor
12.05: Existence and Uniqueness of Solutions of Nonlinear Equations
12.5E: Existence and Uniqueness of Solutions of Nonlinear Equations (Exercises)
12.06: Substitution
12.07: Autonomous equations
12.08: Numerical methods- Eulers method
12.09: Exact Equations
12.10: First Order Linear PDE
12.E: First order ODEs (Exercises)
13: Applications of First Order Equations
13.01: Growth and Decay
13.1E: Growth and Decay (Exercises)
13.02: Cooling and Mixing
13.2E: Cooling and Mixing (Exercises)
13.03: Elementary Mechanics
13.3E: Elementary Mechanics (Exercises)
14: Higher order linear ODEs
14.01: Second order linear ODEs
14.02: The Method of Undetermined Coefficients I
14.2E: The Method of Undetermined Coefficients I (Exercises)
14.03: The Method of Undetermined Coefficients II
14.3E: The Method of Undetermined Coefficients II (Exercises)
14.04: Constant coefficient second order linear ODEs
14.05: Higher order linear ODEs
14.06: Reduction of Order
14.6E: Reduction of Order (Exercises)
14.07: Variation of Parameters
14.7E: Variation of Parameters (Exercises)
14.08: Mechanical Vibrations
14.09: Nonhomogeneous Equations
14.10: Forced Oscillations and Resonance
14.E: Higher order linear ODEs (Exercises)
15: Fourier series and PDEs
15.01: Boundary value problems
15.02: The Trigonometric Series
15.03: More on the Fourier Series
15.04: Sine and Cosine Series
15.05: Applications of Fourier Series
15.06: PDEs Separation of Variables and The Heat Equation
15.07: One Dimensional Wave Equation
15.08: DAlembert Solution of The Wave Equation
15.09: Steady State Temperature and the Laplacian
15.10: Dirichlet Problem in the Circle and the Poisson Kernel
15.E: Fourier Series and PDEs (Exercises)
16: Power series methods
16.01: Power Series
16.02: Series Solutions of Linear Second Order ODEs
16.03: Singular Points and the Method of Frobenius
16.E: Power series methods (Exercises)
17: Nonlinear Systems
17.01: Linearization Critical Points and Equilibria
17.02: Stability and Classication of Isolated Critical Points
17.03: Applications of Nonlinear Systems
17.04: Limit cycles
17.05: Chaos
17.06: Appendix B- Table of Laplace Transforms
17.E: Nonlinear Equations (Exercises)