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A01 Introduction to linear systems
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Classroom Contents
A Second Course in Differential Equations
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- 1 A01 Introduction to linear systems
- 2 A02 Independence of the solution set
- 3 A03 Eigenvalues
- 4 A04 Eigenvectors
- 5 A05 Explanation of the matrix format of a system of linear differential equations
- 6 A06 Example problem including the Wronskian
- 7 A07 Repeated real eigenvalues
- 8 A08 Example problem of repeated real eigenvalues
- 9 A09 Example problem of multiplicity two
- 10 A10 Example problem of multiplicity three
- 11 A11 Eigenvalues with complex numbers
- 12 A12 Changing the notation
- 13 A13 More Example Problems
- 14 A14 Nonhomegeneous linear systems solved by undetermined coefficients
- 15 A15 More about undetermined coefficients
- 16 A16 The method of variation of parameters
- 17 A17 Deriving the equation for the particular solution
- 18 A18 Example problem using variation of parameters
- 19 B01 An introduction to numerical methods
- 20 B02 An introduction to the Euler method
- 21 B03 An improvement of the Euler method
- 22 B04 An example problem
- 23 B05 Local truncation errors
- 24 B06 Example problem calculating the error
- 25 B07 Fourth-order Runge Kutta
- 26 B08 Using Python to do numerical calculations
- 27 B09 Installing Python on the Mac
- 28 B10 Constructing code for the Euler Formula
- 29 B11 The improved Euler Formula
- 30 B12 Second order ODEs solved with Python using the Euler formula
- 31 B13 Second order ODE solved with RK4 in Python
- 32 B14 Simplifying a system of higher order ODEs
- 33 B15 Solving a system of first order ODEs with RK4 using Python
- 34 B16 Example problem solving a higher order ODE with the Euler formula
- 35 B17 Example problem solving a system of ODEs with RK4
- 36 B18 Plane autonomous systems
- 37 B19 Example problem of a system of autonomous equations
- 38 B21 Example problem
