David calvis - Study guides, Class notes & Summaries
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MA 262: 5.5 Review- Nonhomogeneous Differential Equations & Undetermined Coefficients, Variation of Parameters
- Class notes • 2 pages • 2024
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Review of lesson 5.5 for MA 262 (Linear Algebra & Differential Equations) at Purdue University. Content based on class textbook Differential Equations & Linear Algebra by C. Henry Edwards and David E. Penney (ISBN: 9780536264923). 
5.5 covers methods to solve nonhomogeneous differential equations (DEs), namely the method of undetermined coefficients and variation of parameters. Content includes the general form of a nonhomogeneous DE, the general form of a solution to a nonhomogeneous DE (comple...
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MA 262: 6.1 Review- Introduction to Eigenvalues
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Review of lesson 6.1 for MA 262 (Linear Algebra & Differential Equations) at Purdue University. Content based on class textbook Differential Equations & Linear Algebra by C. Henry Edwards and David E. Penney (ISBN: 9780536264923). 
6.1 introduces eigenvalue and eigenvalues for a singular matrix (i.e. not linear system). Covers definitions of eigenvalues and eigenvectors, derivation of equations for eigenvectors/values, eigenspaces, and dimension of eigenspaces. 
Includes example problems.
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MA 262: 4.2 Review- The Vector Space R^n & Subspaces
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Review of lesson 4.2 for MA 262 (Linear Algebra & Differential Equations) at Purdue University. Content based on class textbook Differential Equations & Linear Algebra by C. Henry Edwards and David E. Penney (ISBN: 9780536264923). 
4.2 covers vector spaces and subspaces in further detail (from 4.1) with multiple example cases for more complex evaluations (drawn from previous exams). Includes definition of vector spaces/subspaces, distinction between trivial and proper subspaces, procedure to ex...
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MA 262: 4.1 Review- Vector Spaces
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Review of lesson 4.1 for MA 262 (Linear Algebra & Differential Equations) at Purdue University. Content based on class textbook Differential Equations & Linear Algebra by C. Henry Edwards and David E. Penney (ISBN: 9780536264923). 
4.1 defines vector spaces and various pertinent concepts to evaluate their existence. These include the definition and meaning of linear independence/dependence, linear combinations, span, null space, and requirements to be a vector space (closure under vector multipl...
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MA 262: 5.4 Review- Mechanical Vibrations
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Review of lesson 5.4 for MA 262 (Linear Algebra & Differential Equations) at Purdue University. Content based on class textbook Differential Equations & Linear Algebra by C. Henry Edwards and David E. Penney (ISBN: 9780536264923). 
5.4 covers the application of differential equations (DEs) to describe mechanical vibrations, including mass-spring-dashpot systems, masses on springs, simple pendulums, free damped motion, free undamped motion, and overdamped and underdamped cases. 
Derivation of ap...
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MA 262: 3.6 Review- Determinants
- Class notes • 2 pages • 2024
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Review of lesson 3.6 for MA 262 (Linear Algebra & Differential Equations) at Purdue University. Content based on class textbook Differential Equations & Linear Algebra by C. Henry Edwards and David E. Penney (ISBN: 9780536264923). 
3.6 covers determinants. Specific concepts include cofactor expansion formula/procedure, Cramer's rule (definition and applications), row and column properties, and matrix transposes.
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MA 262: 5.1 Review- Introduction to 2nd-Order Linear Equations
- Class notes • 2 pages • 2024
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Review of lesson 5.1 for MA 262 (Linear Algebra & Differential Equations) at Purdue University. Content based on class textbook Differential Equations & Linear Algebra by C. Henry Edwards and David E. Penney (ISBN: 9780536264923). 
5.1 introduces the concept of 2nd-order linear differential equations, including definitions, general form, homogeneous equations vs. nonhomogeneous equations, the principle of superposition for homogeneous equations, existence and uniqueness of solutions, the Wronsk...
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MA 262: 4.3 Review- Linear Combinations & Independence of Vectors
- Class notes • 1 pages • 2024
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Review of lesson 4.3 for MA 262 (Linear Algebra & Differential Equations) at Purdue University. Content based on class textbook Differential Equations & Linear Algebra by C. Henry Edwards and David E. Penney (ISBN: 9780536264923). 
4.3 covers criteria for linear independence/dependence and procedure to express a given vector as a linear combination of vectors. Reviews concepts of span, relationship between span and linear combinations, and the Rank-Nullity theorem.
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MA 262: 3.5 Review- Inverses of Matrices
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Review of lesson 3.5 for MA 262 (Linear Algebra & Differential Equations) at Purdue University. Content based on class textbook Differential Equations & Linear Algebra by C. Henry Edwards and David E. Penney (ISBN: 9780536264923). 
3.5 covers inverse matrices, including definitions, significance of invertibility, criteria for invertibility, and the procedure to obtain an inverse matrix.
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Answers for Hand-Written Questions in MA266 @ Purdue
- Exam (elaborations) • 14 pages • 2022
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This document contains the solutions for some questions in Differential Equations and Boundary Value Problems Chapter 1, section 1.2 and 1.3
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