Math 287 Differential Equations and Linear Algebra

Mathematics

Author: SeanS Smith
Publisher: Santa Ana College
Source: LibreTexts
Language: EN
Category: Basic Sciences

Read online Download PDF (open licence)

Contents· 151 sections

01: First Chapter
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: Matrices
3.01: Matrix Arithmetic
3.02: Multiplication of Matrices
3.03: The ijth Entry of a Product
3.04: Properties of Matrix Multiplication
3.05: The Transpose
3.06: The Identity and Inverses
3.07: Finding the Inverse of a Matrix
3.08: Elementary Matrices
3.09: More on Matrix Inverses
3.10: LU Factorization
3.E: Exercises
04: Determinants
4.01: Basic Techniques
4.02: Properties of Determinants
4.03: Finding Determinants using Row Operations
4.04: Applications of the Determinant
4.E: Exercises
05: R
5.01: Vectors in R
5.02: Vector Algebra
5.03: Geometric Meaning of Vector Addition
5.04: Length of a Vector
5.05: Geometric Meaning of Scalar Multiplication
5.06: Parametric Lines
5.07: The Dot Product
5.08: Planes in R
5.09: The Cross Product
5.10: Spanning Linear Independence and Basis in R
5.11: Orthogonality
5.12: Applications
5.E: Exercises
06: Vector Spaces
6.01: Algebraic Considerations
6.02: Spanning Sets
6.03: Linear Independence
6.04: Subspaces and Basis
6.05: Sums and Intersections
6.06: Linear Transformations
6.07: Isomorphisms
6.08: The Kernel and Image of a Linear Map
6.09: The Matrix of a Linear Transformation
6.E: Exercises
07: Linear Transformations
7.01: Linear Transformations
7.02: The Matrix of a Linear Transformation I
7.03: Properties of Linear Transformations
7.04: Special Linear Transformations in R
7.05: One-to-One and Onto Transformations
7.06: Isomorphisms
7.07: The Kernel and Image of A Linear Map
7.08: The Matrix of a Linear Transformation II
7.09: The General Solution of a Linear System
7.E: Exercises
08: Spectral Theory
8.01: Eigenvalues and Eigenvectors of a Matrix
8.02: Diagonalization
8.03: Applications of Spectral Theory
8.04: Orthogonality
8.E: Exercises
09: First Order Equations
9.01: Linear First Order Equations
9.1E: Linear First Order Equations (Exercises)
9.02: Separable Equations
9.2E: Separable Equations (Exercises)
9.03: Existence and Uniqueness of Solutions of Nonlinear Equations
9.3E: Existence and Uniqueness of Solutions of Nonlinear Equations (Exercises)
9.04: Transformation of Nonlinear Equations into Separable Equations
9.4E: Transformation of Nonlinear Equations into Separable Equations (Exercises)
9.05: Exact Equations
9.5E: Exact Equations (Exercises)
9.06: Integrating Factors
9.6E: Integrating Factors (Exercises)
10: Numerical Methods
10.01: Euler's Method
10.1E: Eulers Method (Exercises)
10.02: The Improved Euler Method and Related Methods
10.2E: The Improved Euler Method and Related Methods (Exercises)
10.03: The Runge-Kutta Method
10.3E: The Runge-Kutta Method (Exercises)
11: Applications of First Order Equations
11.01: Growth and Decay
11.1E: Growth and Decay (Exercises)
11.02: Cooling and Mixing
11.2E: Cooling and Mixing (Exercises)
11.03: Elementary Mechanics
11.3E: Elementary Mechanics (Exercises)
11.04: Autonomous Second Order Equations
11.4E: Autonomous Second Order Equations (Exercises)
11.05: Applications to Curves
11.5E: Applications to Curves (Exercises)
12: Linear Second Order Equations
12.01: Homogeneous Linear Equations
12.1E: Homogeneous Linear Equations (Exercises)
12.02: Constant Coefficient Homogeneous Equations
12.2E: Constant Coefficient Homogeneous Equations (Exercises)
12.03: Nonhomogeneous Linear Equations
12.3E: Nonhomgeneous Linear Equations (Exercises)
12.04: The Method of Undetermined Coefficients I
12.4E: The Method of Undetermined Coefficients I (Exercises)
12.05: The Method of Undetermined Coefficients II
12.5E: The Method of Undetermined Coefficients II (Exercises)
12.06: Reduction of Order
12.6E: Reduction of Order (Exercises)
12.07: Variation of Parameters
12.7E: Variation of Parameters (Exercises)
13: Applications of Linear Second Order Equations
13.01: Spring Problems I
13.1E: Spring Problems I (Exercises)
13.02: Spring Problems II
13.2E: Spring Problems II (Exercises)
13.03: The RLC Circuit
13.3E: The RLC Circuit (Exercises)
13.04: Motion Under a Central Force
13.4E: Motion Under a Central Force (Exercises)
14: Linear Higher Order Differential Equations
14.01: Introduction to Linear Higher Order Equations
14.1E: Introduction to Linear Higher Order Equations (Exercises)
14.02: Higher Order Constant Coefficient Homogeneous Equations
14.2E: Higher Order Constant Coefficient Homogeneous Equations (Exercises)
14.03: Undetermined Coefficients for Higher Order Equations
14.3E: Undetermined Coefficients for Higher Order Equations (Exercises)
14.04: Variation of Parameters for Higher Order Equations
14.4E: Variation of Parameters for Higher Order Equations (Exercises)
15: Laplace Transforms
15.01: Introduction to the Laplace Transform
15.1E: Introduction to the Laplace Transform (Exercises)
15.02: The Inverse Laplace Transform
15.2E: The Inverse Laplace Transform (Exercises)
15.03: Solution of Initial Value Problems
15.3E: Solution of Initial Value Problems (Exercises)
15.04: The Unit Step Function
15.4E: The Unit Step Function (Exercises)
15.05: Constant Coefficient Equations with Piecewise Continuous Forcing Functions
15.5E: Constant Coefficient Equations with Piecewise Continuous Forcing Functions (Exercises)
15.06: Convolution
15.6E: Convolution (Exercises)
15.07: Constant Coefficient Equations with Impulses
15.7E: Constant Coefficient Equations with Impulses (Exercises)
15.08: A Brief Table of Laplace Transforms