Homogeneous linear odes Study guides, Class notes & Summaries
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AU MATH 376 STUDY GUIDE ORDINARY DIFFERENTIAL EQUATIONS NEW UPDATED SOLUTION FOR THE COMING 2022-2023 EXAM Athabasca University
- Exam (elaborations) • 263 pages • 2022
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AU MATH 376 STUDY GUIDE ORDINARY DIFFERENTIAL EQUATIONS NEW UPDATED SOLUTION FOR THE COMING 2022-2023 EXAM Athabasca University 
Contents 
Introduction	1 
Some Preliminary Remarks	2 
Part I: First-order Differential Equations	9 
1	Introducing Ordinary Differential Equations	11 
1.1	Solutions: Complete, General, Particular, Partial	12 
1.2	Methods for Solving Ordinary Differential Equations	14 
1.3	The Fundamental Theorem	15 
1.4	Direction Fields	18 
2	Directly Integrable Ordinary Differential 
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Math 475: Partial Differential Equations
- Exam (elaborations) • 19 pages • 2023
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Math 475: Partial Differential Equations 
Shereen Elaidi 
Fall 2019 Term 
Contents 
1 Introduction 2 
1.1 Domains and Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 
1.1.1 What are the main boundary conditions? . . . . . . . . . . . . . . . . . . . . . 3 
1.2 Classification of PDEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 
2 Diffusion 4 
2.1 Derivation and Setting Up (n = 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
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MAT 275 TOP Exam Questions and CORRECT Answers
- Exam (elaborations) • 2 pages • 2024
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Linear Second Order ODE y(t)''+p(t)y'+q(t)y=g(t) 
Alternate Linear Second Order ODE R(t)y''+P(t)y'+Q(t)y=G(t) 
Homogeneous Linear ODEs y''(t)+p(t)y'+q(t)y=0 or R(t)y''+P(t)y'+Q(t)y=0 
Linear with Constant Coefficients y''(t)+Ay'(t)+By(t)=0 or ay''(t)+by'(t)+cy(t)=0 
Linear with Constant Coefficients Solution y(t)=c1e^r1t+c2e^r2t 
Linear with Complex Characteristic Roots e^a(cos(b)+i*sin(b)) 
If y=0, the system is undamped
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Constant Coefficient Linear ODEs (Homogeneous)
- Class notes • 4 pages • 2023
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These notes cover constant coefficient linear ODEs for homogeneous equations. Includes 5 different root cases with several examples and explanations for each for the Differential Equations class taught by Professor Peter Brady at Stevens Institute of Technology.
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Exam (elaborations) TEST BANK FOR Advanced Engineering Mathematics [Volume 1] By Herbert Kreyszig and Erwin Kreyszig (Student Solutions Manual and Study Guide)
- Exam (elaborations) • 257 pages • 2021
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Exam (elaborations) TEST BANK FOR Advanced Engineering Mathematics [Volume 1] By Herbert Kreyszig and Erwin Kreyszig (Student Solutions Manual and Study Guide) 
P A R T A 
Ordinary 
Differential 
Equations (ODEs) 
Chap. 1 First-Order ODEs 
Sec. 1.1 Basic Concepts. Modeling 
To get a good start into this chapter and this section, quickly review your basic calculus. Take a look at 
the front matter of the textbook and see a review of the main differentiation and integration formulas. Also, 
Appen...
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Exam (elaborations) TEST BANK FOR Advanced Engineering Mathematics [Volume 2] By Herbert Kreyszig and Erwin Kreyszig (Student Solutions Manual and Study Guide)
- Exam (elaborations) • 223 pages • 2021
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Exam (elaborations) TEST BANK FOR Advanced Engineering Mathematics [Volume 2] By Herbert Kreyszig and Erwin Kreyszig (Student Solutions Manual and Study Guide) 
P A R T D 
Complex 
Analysis 
Chap. 13 Complex Numbers and Functions. 
Complex Differentiation 
Complex numbers appeared in the textbook before in different topics. Solving linear homogeneous ODEs 
led to characteristic equations, (3), p. 54 in Sec. 2.2, with complex numbers in Example 5, p. 57, and 
Case III of the table on p. 58. Solv...
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Second Order Differential Equations Homogeneous Linear ODEs
- Presentation • 15 pages • 2022
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notes topic cover second order differential equation, homogeneous linear ODEs, with Textbook references
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Exam (elaborations) TEST BANK FOR Advanced Engineering Mathematics [Volume 2] By Herbert Kreyszig and Erwin Kreyszig (Student Solutions Manual and Study Guide)
- Exam (elaborations) • 223 pages • 2021
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Complex numbers appeared in the textbook before in different topics. Solving linear homogeneous ODEs 
led to characteristic equations, (3), p. 54 in Sec. 2.2, with complex numbers in Example 5, p. 57, and 
Case III of the table on p. 58. Solving algebraic eigenvalue problems in Chap. 8 led to characteristic 
equations of matrices whose roots, the eigenvalues, could also be complex as shown in Example 4, p. 328. 
Whereas, in these type of problems, complex numbers appear almost naturally as compl...
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8. Second and higher order ODEs
- Class notes • 5 pages • 2019
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Picard's Iteration method with example and using matlab to solve. Classification of ODEs: order and linearity. Initial value problem theory: autonomy, deterministism, homogeneous linear ODEs and superposition with proof. Different cases of equation giving examples of the different types and features.
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4. Second and higher order ODEs
- Class notes • 4 pages • 2019
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Solving Linear ODEs: definition of linear/nonlinear and homogeneous/nonhomogeneous. General solution to first order ODE with integrating factor. Example of a first order linear IVP. Explanation to why the General solution formula works. Example of Hormone levels and their rates of changes. Using Matlab to solve ODEs.
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