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Elementary Differential Equations and Boundary Value Problems (Custom Edition for the Math. Dept. of the
University of Missouri-Columbia) Ninth Edition by William E. Boyce and Richard C. DiPrima
Planar Systems of Differential Equations (contained in the Custom Edition for the Math.
Dept. of the
University of Missouri-Columbia)
There will be 3 midterm exams (100 points each), homework/quizzes (100 points) and one comprehensive final exam (150 points). The maximum total for the course will be 550 points.
Sections Covered |
Homework |
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| Elementary Differential Equations and Boundary Value Problems | ||
| 2.1: | Linear Equations; Method of Integrating Factors | 2(c),6(c),8(c),13,16 |
| 2.2: | Separable Equations | 3,6,7,10(a,c),22 |
| 2.3: | Modeling with First Order Equations | 1,3,7,21,23 |
| 2.6: | Exact Equations and Integrating Factors | 3,5,11,12,19,29 |
| 3.1: | Homogeneous Equations with Constant Coefficients | 7,14,17,20,23 |
| 3.2: | Fundamental Solutions of Linear Homogeneous Equations | 4,8,12,13,15,16,17,19,23,24,27,31,32,34,36 |
| 3.3: | Complex Roots of the Characteristic Equation | 7,12,16,18,19,27 |
| 3.4: | Repeated Roots; Reduction of Order | 1,2,7,12,15,25,32 |
| 3.5: | Non-homogeneous Equations; Method of Undetermined Coefficients | 2,4,8,16,17 |
| 3.6: | Variation of Parameters | 7,12,13,17 |
| 3.7: | Mechanical and Electrical Vibrations (Mechanical Vibrations only) | 7,9,13,17,26(a,b) |
| 3.8: | Forced Vibrations | 5,7,11,12 |
| 6.1: | Definition of the Laplace Transform | 1,2,3,5(c),7,13,14,16,18 |
| 6.2: | Solution of Initial Value Problems | 7,8,9,11,20,21,24 |
| 6.3: | Step Functions | 1,3,11,13,15,20,22,23,30,31 |
| 6.4: | Differential Equations with Discontinuous Forcing Functions | 1,2,4,6,8,11,14,16(a,b) |
| 6.5: | Impulse Functions | 1,3,5,11,14(a,b) |
| 6.6: | The Convolution Integral | 4,6,8,10,13,15 |
| 2.7: | Numerical Approximations: Euler's Method | |
| 8.1: | The Euler or Tangent Line Method | 3(a,b,c,d),4(a,b,c,d),9(a,b,c,d),22 |
| Planar Systems of Differential Equations | ||
| 1. | Introduction | 1.1-1.2 |
| 2. | Some Concepts from Matrix Theory and Linear Algebra 2.1 Notations and Basic Definitions 2.2 Determinants, Inverses, Linear Dependence, Eigenvalues and Eigenvectors |
2.1,2.2(1,4,6,7),2.3(1),2.4(3),2.5(1,2,3) |
| 3. | General Theory of Linear 2x2 Systems (for those interested in the details) | 3.1,3.3,3.4 |
| 4. | Case 1 | 4.1,4.2,4.4 |
| 5. | Case 2 | 5.1,5.2,5.3 |
| 6. | Case 3 | 6.1,6.2,6.5 |
| 7. | Solutions of Nonhomogeneous Systems | 2.6(1,3),7.1,7.3,7.4 |
| 8. | Qualitative Methods | 8.1,8.2,8.3 |
| 9. | Linearization of a Nonlinear System at an Isolated Rest Point | Optional |
Mathematics Department |
Phone (573) 882-6221
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© 2009 — Curators of the University of Missouri |
