## Techniques in Ordinary Differential Equations (804-255) at Madison College, Fall 2010 |

**Final Exam will be Wednesday 12/15/2010 from 1:30 PM to 3:20 PM in room 337AB.**- Brief Course Description
- Course Information ( Syllabus, etc. )
- Course Components ( Homework, Quizzes, Labs, Tests, Grades, Lesson Plans )
- Reference Sites
- Handouts
- LECTURE NOTES
- Course Schedule
- Past Semesters

This course presents techniques for solving and approximating solutions to ordinary differential equations. Topics will include solving first order differential equations, solving second- and higher-order linear differential equations, Laplace and Fourier transforms, systems of first order linear differential equations, numerical methods, and Sturm-Liouville Theory.

- Differential Equations Syllabus (for Fall 2010)
- Differential Equations Course Description and Schedule
- Differential Equations Course Outline

- Wolfram Alpha ( http://www.wolframalpha.com/ )
- Wolfram MathWorld, created by Eric Weisstein ( http://mathworld.wolfram.com/ )
- The Wolfram Integrator ( http://integrals.wolfram.com/index.jsp )
- Wolfram Step-by-Step Derivatives ( http://library.wolfram.com/webMathematica/Education/WalkD.jsp )
- The Math Forum ( http://mathforum.org/ )
- Calc 101 ( http://www.calc101.com/ )
- odetoolkit at Harvey Mudd College ( http://odetoolkit.hmc.edu/index.html )
- The Khan Academy ( http://www.khanacademy.org/ )

- Lecture Notes for Section 1.1 (Some Basic Mathematical Models; Direction Fields)
- Click here to view a pdf of the completed notes for Section 1.1
- Lecture Notes for Section 1.2 (Solutions of Some Differential Equations)
- Click here to view a pdf of the completed notes for Section 1.2
- Lecture Notes for Section 1.3 (Classification of Differential Equations)
- Click here to view a pdf of the completed notes for Section 1.3
- Lecture Notes for Section 1.4 (Historical Remarks)
- Lecture Notes for Section 2.1 (Linear Equations; Method of Integrating Factors)
- Click here to view a pdf of the completed notes for Section 2.1
- Lecture Notes for Section 2.2 (Separable Equations)
- Click here to view a pdf of the completed notes for Section 2.2
- Lecture Notes for Section 2.3 (Modeling with First Order Equations)
- Click here to view a pdf of the completed notes for Section 2.3
- Lecture Notes for Section 2.4 (Differences Between Linear and Nonlinear Equations)
- Click here to view a pdf of the completed notes for Section 2.4
- Lecture Notes for Section 2.5 (Autonomous Equations and Population Dynamics)
- Click here to view a pdf of the completed notes for Section 2.5
- Lecture Notes for Section 2.6 (Exact Equations and Integrating Factors)
- Click here to view a pdf of the completed notes for Section 2.6
- Lecture Notes for Section 2.7 (Numerical Approximations: Euler’s Method)
- Click here to view a pdf of the completed notes for Section 2.7
- Lecture Notes for Section 2.8 (The Existence and Uniqueness Theorem)
- Lecture Notes for Section 2.9 (First Order Difference Equations)
- Lecture Notes for Section 3.1 (Homogeneous Equations with Constant Coefficients)
- Click here to view a pdf of the completed notes for Section 3.1
- Lecture Notes for Section 3.2 (Solutions of Linear Homogeneous Equations; the Wronskian)
- Click here to view a pdf of the completed notes for Section 3.2
- Lecture Notes for Section 3.3 (Complex Roots of the Characteristic Equation)
- Click here to view a pdf of the completed notes for Section 3.3
- Lecture Notes for Section 3.4 (Repeated Roots; Reduction of Order)
- Click here to view a pdf of the completed notes for Section 3.4
- Lecture Notes for Section 3.5 (Nonhomogeneous Equations; Method of Undetermined Coefficients)
- Click here to view a pdf of the completed notes for Section 3.5
- Lecture Notes for Section 3.6 (Variation of Parameters)
- Click here to view a pdf of the completed notes for Section 3.6
- Lecture Notes for Section 3.7 (Mechanical and Electrical Vibrations)
- Click here to view a pdf of the completed notes for Section 3.7
- Lecture Notes for Section 3.8 (Forced Vibrations)
- Click here to view a pdf of the completed notes for Section 3.8
- Lecture Notes for Section 4.1 (General Theory of nth Order Linear Equations)
- Click here to view a pdf of the completed notes for Section 4.1
- Lecture Notes for Section 4.2 (Homogeneous Equations with Constant Coefficients)
- Click here to view a pdf of the completed notes for Section 4.2
- Lecture Notes for Section 4.3 (The Method of Undetermined Coefficients)
- Click here to view a pdf of the completed notes for Section 4.3
- Lecture Notes for Section 4.4 (The Method of Variation of Parameters)
- Click here to view a pdf of the completed notes for Section 4.4
- Lecture Notes for Section 5.1 (Review of Power Series)
- Click here to view a pdf of the completed notes for Section 5.1
- Lecture Notes for Section 5.2 (Series Solutions Near an Ordinary Point, Part I)
- Click here to view a pdf of the completed notes for Section 5.2
- Lecture Notes for Section 5.3 (Series Solutions Near an Ordinary Point, Part II)
- Click here to view a pdf of the completed notes for Section 5.3
- Lecture Notes for Section 5.4 (Euler Equations; Regular Singular Points)
- Click here to view a pdf of the completed notes for Section 5.4
- Lecture Notes for Section 5.5 (Series Solutions Near a Regular Singular Point, Part I)
- Click here to view a pdf of the completed notes for Section 5.5
- Lecture Notes for Section 5.6 (Series Solutions Near a Regular Singular Point, Part II)
- Click here to view a pdf of the completed notes for Section 5.6
- Lecture Notes for Section 5.7 (Bessel’s Equation)
- Click here to view a pdf of the completed notes for Section 5.7
- Lecture Notes for Section 6.1 (Definition of the Laplace Transform)
- Click here to view a pdf of the completed notes for Section 6.1
- Lecture Notes for Section 6.2 (Solution of Initial Value Problems)
- Click here to view a pdf of the completed notes for Section 6.2
- Lecture Notes for Section 6.3 (Step Functions)
- Click here to view a pdf of the completed notes for Section 6.3
- Lecture Notes for Section 6.4 (Differential Equations with Discontinuous Forcing Functions)
- Click here to view a pdf of the completed notes for Section 6.4
- Lecture Notes for Section 6.5 (Impulse Functions)
- Click here to view a pdf of the completed notes for Section 6.5
- Lecture Notes for Section 6.6 (The Convolution Integral)
- Click here to view a pdf of the completed notes for Section 6.6
- Lecture Notes for Section 7.1 (Introduction)
- Click here to view a pdf of the completed notes for Section 7.1
- Lecture Notes for Section 7.2 (Review of Matrices)
- MatrixTools.xls
- Click here to view a pdf of the completed notes for Section 7.2
- Lecture Notes for Section 7.3 (Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors)
- Click here to view a pdf of the completed notes for Section 7.3
- Lecture Notes for Section 7.4 (Basic Theory of Systems of First Order Linear Equations)
- Click here to view a pdf of the completed notes for Section 7.4
- Lecture Notes for Section 7.5 (Homogeneous Linear Systems with Constant Coefficients)
- Click here to view a pdf of the completed notes for Section 7.5
- Lecture Notes for Section 7.6 (Complex Eigenvalues)
- Click here to view a pdf of the completed notes for Section 7.6
- Lecture Notes for Section 7.7 (Fundamental Matrices)
- Lecture Notes for Section 7.8 (Repeated Eigenvalues)
- Lecture Notes for Section 7.9 (Nonhomogeneous Linear Systems)
- Lecture Notes for Section 8.1 (The Euler or Tangent Line Method)
- Lecture Notes for Section 8.2 (Improvements on the Euler Method)
- Lecture Notes for Section 8.3 (The Runge–Kutta Method)
- Lecture Notes for Section 8.4 (Multistep Methods)
- Lecture Notes for Section 8.5 (More on Errors; Stability)
- Lecture Notes for Section 8.6 (Systems of First Order Equations)
- Lecture Notes for Section 9.1 (The Phase Plane: Linear Systems)
- Lecture Notes for Section 9.2 (Autonomous Systems and Stability)
- Lecture Notes for Section 9.3 (Locally Linear Systems)
- Lecture Notes for Section 9.4 (Competing Species)
- Lecture Notes for Section 9.5 (Predator–Prey Equations)
- Lecture Notes for Section 9.6 (Liapunov’s Second Method)
- Lecture Notes for Section 9.7 (Periodic Solutions and Limit Cycles)
- Lecture Notes for Section 9.8 (Chaos and Strange Attractors: The Lorenz Equations)
- Lecture Notes for Section 10.1 (Two-Point Boundary Value Problems)
- Lecture Notes for Section 10.2 (Fourier Series)
- Lecture Notes for Section 10.3 (The Fourier Convergence Theorem)
- Lecture Notes for Section 10.4 (Even and Odd Functions)
- Lecture Notes for Section 10.5 (Separation of Variables; Heat Conduction in a Rod)
- Lecture Notes for Section 10.6 (Other Heat Conduction Problems)
- Lecture Notes for Section 10.7 (TheWave Equation: Vibrations of an Elastic String)
- Lecture Notes for Section 10.8 (Laplace’s Equation)
- Lecture Notes for Section 11.1 (The Occurrence of Two-Point Boundary Value Problems)
- Lecture Notes for Section 11.2 (Sturm–Liouville Boundary Value Problems)
- Lecture Notes for Section 11.3 (Nonhomogeneous Boundary Value Problems)
- Lecture Notes for Section 11.4 (Singular Sturm–Liouville Problems)
- Lecture Notes for Section 11.5 (Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion)
- Lecture Notes for Section 11.6 (Series of Orthogonal Functions: Mean Convergence)

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