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+ | ==Course Catalog== | ||
+ | [https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory MAT 3613. Differential Equations I]. (3-0) 3 Credit Hours. | ||
+ | |||
+ | Prerequisite: Completion of or concurrent enrollment in [[MAT2233]]. Basic notions of differential equations, solution of first-order equations and linear equations with constant coefficients, nth-order initial value problems, Laplace transforms, and may include additional topics such as power series solutions of differential equations, linear systems, and stability. Generally offered: Fall, Spring, Summer. Differential Tuition: $150. | ||
+ | |||
+ | ==Text== | ||
+ | [https://login.libweb.lib.utsa.edu/login?url=http://link.springer.com/content/pdf/10.1007%2F978-3-319-02129-4.pdf Ahmad, S., & Ambrosetti, A. (2014). textbook on Ordinary Differential Equations (Vol. 73). Springer] | ||
==Topics List== | ==Topics List== | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
Line 5: | Line 12: | ||
|Week I | |Week I | ||
|| | || | ||
− | * Ahmad and Ambrosetti 2014, | + | * Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3 |
− | |||
− | |||
− | |||
− | |||
− | |||
|| | || | ||
− | * | + | * [[Order of Differential Equations]] |
− | |||
− | |||
− | |||
− | |||
− | |||
|| | || | ||
− | * Integration techniques | + | * Integration techniques |
− | + | :- [[Direct Integration]] | |
− | + | :- [[Integration by Substitution]] | |
− | + | :- [[Integration by Parts]] | |
− | + | :- [[Partial Fractions]] | |
− | |||
|| | || | ||
− | * Explain the basic | + | * Explain the basic notion of the order of a differential equation. |
− | * Determine separable differential equations of the first order. Apply direct methods to evaluate exact solutions of separable differential equations of the first order. | + | |- |
− | * | + | |Week I |
− | * | + | || |
− | * | + | * Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3 |
− | * | + | || |
+ | * [[Solutions of Differential Equations]] | ||
+ | || | ||
+ | * Integration techniques | ||
+ | :- [[Direct Integration]] | ||
+ | :- [[Integration by Substitution]] | ||
+ | :- [[Integration by Parts]] | ||
+ | :- [[Partial Fractions]] | ||
+ | || | ||
+ | * Explain the basic notion of solutions of differential equations. | ||
+ | |- | ||
+ | |Week I | ||
+ | || | ||
+ | * Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3 | ||
+ | || | ||
+ | * [[Initial Value Problem|Initial Value Problem (IVP)]] | ||
+ | || | ||
+ | * Integration techniques | ||
+ | :- [[Direct Integration]] | ||
+ | :- [[Integration by Substitution]] | ||
+ | :- [[Integration by Parts]] | ||
+ | :- [[Partial Fractions]] | ||
+ | || | ||
+ | * Explain the basic notion of the initial values problem. | ||
+ | |- | ||
+ | |Week I | ||
+ | || | ||
+ | * Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3 | ||
+ | || | ||
+ | * [[Cauchy Problem]] | ||
+ | || | ||
+ | * Integration techniques | ||
+ | :- [[Direct Integration]] | ||
+ | :- [[Integration by Substitution]] | ||
+ | :- [[Integration by Parts]] | ||
+ | :- [[Partial Fractions]] | ||
+ | || | ||
+ | * Explain the Cauchy Problem | ||
+ | * Explain the basic notion of existence and uniqueness of a solution to the Cauchy Problem. | ||
+ | |- | ||
+ | |Week I | ||
+ | || | ||
+ | * Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3 | ||
+ | || | ||
+ | * [[Separation of Variables (1st Order)]] | ||
+ | || | ||
+ | * Integration techniques | ||
+ | :- [[Direct Integration]] | ||
+ | :- [[Integration by Substitution]] | ||
+ | :- [[Integration by Parts]] | ||
+ | :- [[Partial Fractions]] | ||
+ | || | ||
+ | * Determine separable differential equations of the first order. | ||
+ | * Apply direct methods to evaluate exact solutions of separable differential equations of the first order. | ||
+ | |- | ||
+ | |Week II | ||
+ | || | ||
+ | * Ahmad and Ambrosetti 2014, Chaps. 1 and 3 | ||
+ | || | ||
+ | * [[Homogeneous Differential Equations|Homogeneous Differential Equations (1st Order)]] | ||
+ | || | ||
+ | * Integration techniques | ||
+ | :- [[Direct Integration]] | ||
+ | :- [[Integration by Substitution]] | ||
+ | :- [[Integration by Parts]] | ||
+ | :- [[Partial Fractions]] | ||
+ | || | ||
+ | * Determine homogeneous differential equations of the first order. | ||
+ | * Apply direct methods to evaluate exact solutions of homogeneous differential equations of the first order (substitutions). | ||
+ | * Use some differential equations as mathematical models in biology, population dynamics, mechanics and electrical circuit theory problems. | ||
|- | |- | ||
|Week II | |Week II | ||
|| | || | ||
− | * Ahmad and Ambrosetti 2014, | + | * Ahmad and Ambrosetti 2014, Chaps. 1 and 3 |
− | |||
− | |||
|| | || | ||
− | * | + | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]] |
− | |||
− | |||
|| | || | ||
− | * Integration techniques | + | * Integration techniques |
− | + | :- [[Direct Integration]] | |
− | + | :- [[Integration by Substitution]] | |
+ | :- [[Integration by Parts]] | ||
+ | :- [[Partial Fractions]] | ||
|| | || | ||
− | * Determine | + | * Determine linear differential equations of the first order. |
− | * | + | * Use some differential equations as mathematical models in biology, population dynamics, mechanics and electrical circuit theory problems. |
− | * | + | |- |
+ | |Week II | ||
+ | || | ||
+ | * Ahmad and Ambrosetti 2014, Chaps. 1 and 3 | ||
+ | || | ||
+ | * [[Integrating Factor]] | ||
+ | || | ||
+ | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]] | ||
+ | || | ||
+ | * Apply integrating factor to solve linear differential equations of the first order. | ||
+ | * Use some differential equations as mathematical models in biology, population dynamics, mechanics and electrical circuit theory problems. | ||
+ | |- | ||
+ | |Week III | ||
+ | || | ||
+ | * Ahmad and Ambrosetti 2014, Ch. 3 | ||
+ | || | ||
+ | * [[Bernoulli Equations (1st Order)]] | ||
+ | || | ||
+ | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]] | ||
+ | || | ||
+ | * Determine Bernoulli of the first order. | ||
+ | * Apply direct methods to evaluate exact solutions of Bernoulli of the first order. | ||
|- | |- | ||
|Week III | |Week III | ||
|| | || | ||
− | * Ahmad and Ambrosetti 2014, Ch. | + | * Ahmad and Ambrosetti 2014, Ch. 3 |
− | |||
− | |||
|| | || | ||
− | * | + | * [[Exact Differential Equations|Exact Differential Equations (1st Order)]] |
− | |||
− | |||
|| | || | ||
− | * | + | * [[Integrating Factor]] for exact equations. |
− | * | + | * [[Partial Derivatives]] |
− | |||
|| | || | ||
− | * Determine | + | * Determine Exact Differential Equations of the first order. |
− | + | * Apply direct methods to evaluate exact solutions of Exact Differential Equations of the first order. | |
− | + | * Use the integrating factor technique for exact equations. | |
|- | |- | ||
|Week IV | |Week IV | ||
|| | || | ||
− | * Ahmad and Ambrosetti 2014, | + | * Ahmad and Ambrosetti 2014, Chaps. 1-3 |
− | |||
|| | || | ||
− | |||
* Overview of the solutions methods discussed so far (Chapters 1-3). | * Overview of the solutions methods discussed so far (Chapters 1-3). | ||
|| | || | ||
− | * Integration techniques | + | * Integration techniques |
− | * First-order differential equations | + | :- [[Direct Integration]] |
+ | :- [[Integration by Substitution]] | ||
+ | :- [[Integration by Parts]] | ||
+ | :- [[Partial Fractions]] | ||
+ | * [[Partial Derivatives]] | ||
+ | * First-order differential equations: | ||
+ | :- [[Separation of Variables (1st Order)]] | ||
+ | :- [[Homogeneous Differential Equations|Homogeneous Differential Equations (1st Order)]] | ||
+ | :- [[Linear Differential Equations|Linear Differential Equations (1st Order)]] | ||
+ | :- [[Bernoulli Equations (1st Order)]] | ||
+ | :- [[Exact Differential Equations|Exact Differential Equations (1st Order)]] | ||
|| | || | ||
* Determine the type of different classes of differential equations of the first order: separable, linear, homogeneous, Bernoulli, exact. | * Determine the type of different classes of differential equations of the first order: separable, linear, homogeneous, Bernoulli, exact. | ||
Line 86: | Line 173: | ||
|| | || | ||
* Ahmad and Ambrosetti 2014, Ch. 5 | * Ahmad and Ambrosetti 2014, Ch. 5 | ||
− | |||
|| | || | ||
− | * | + | * [[Linear Independence of Functions]]. |
− | * | + | || |
+ | * [[Linear Independence of Vectors]]. | ||
+ | || | ||
+ | * Understanding of Linear Independence of Functions. | ||
+ | |- | ||
+ | |Week V | ||
+ | || | ||
+ | * Ahmad and Ambrosetti 2014, Ch. 5 | ||
+ | || | ||
+ | * [[Linear Independence of Functions|Linear Dependence of Functions]]. | ||
+ | || | ||
+ | * [[Linear Dependence of Vectors]]. | ||
+ | || | ||
+ | * Understanding of Linear Dependence of Functions. | ||
+ | |- | ||
+ | |Week V | ||
+ | || | ||
+ | * Ahmad and Ambrosetti 2014, Ch. 5 | ||
+ | || | ||
+ | * [[Wronskian]] | ||
+ | || | ||
+ | * [[Linear Independence of Functions]]. | ||
+ | * [[Linear Independence of Functions|Linear Dependence of Functions]]. | ||
+ | * [[Determinant]]. | ||
+ | || | ||
+ | * Showing linear independence of two functions using the Wronskian. | ||
+ | * Showing linear independence of two solutions of Linear Second-Order ODEs using the Wronskian. | ||
+ | |- | ||
+ | |Week VI | ||
+ | || | ||
+ | * Ahmad and Ambrosetti 2014, Ch. 5 | ||
+ | || | ||
+ | * [[Reduction of the Order]] | ||
+ | || | ||
+ | * [[Wronskian]]. | ||
+ | * [[Quadratic Equations]]. | ||
+ | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]]. | ||
+ | * [[Solutions of Linear Systems]]. | ||
+ | || | ||
+ | * Apply of the reduction of the order technique for second-order ODEs with a given solution. | ||
+ | |- | ||
+ | |Week VI | ||
+ | || | ||
+ | * Ahmad and Ambrosetti 2014, Ch. 5 | ||
+ | || | ||
+ | * [[Homogeneous Differential Equations|Linear Homogeneous Equations]] | ||
|| | || | ||
− | * Linear | + | * [[Wronskian]]. |
− | * | + | * [[Quadratic Equations]]. |
+ | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]]. | ||
+ | * [[Solutions of Linear Systems]]. | ||
|| | || | ||
− | * | + | * Determine homogeneous classes of differential equations of the second and higher order. |
− | + | * Determine linear and non-linear classes of differential equations of the second and higher order. | |
|- | |- | ||
|Week VI | |Week VI | ||
|| | || | ||
* Ahmad and Ambrosetti 2014, Ch. 5 | * Ahmad and Ambrosetti 2014, Ch. 5 | ||
− | |||
− | |||
− | |||
− | |||
− | |||
|| | || | ||
− | * | + | * [[Abel’s Theorem]] |
− | |||
− | |||
− | |||
− | |||
− | |||
|| | || | ||
− | * Wronskian. | + | * [[Wronskian]]. |
− | * | + | * [[Quadratic Equations]]. |
− | * | + | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]]. |
− | * | + | * [[Solutions of Linear Systems]]. |
− | * | + | || |
− | * | + | * Determine Wronskian for a second-order ODE with 2 given solutions. |
+ | |- | ||
+ | |Week VI | ||
+ | || | ||
+ | * Ahmad and Ambrosetti 2014, Ch. 5 | ||
+ | || | ||
+ | * [[Fundamental Solutions]] | ||
+ | || | ||
+ | * [[Wronskian]]. | ||
+ | * [[Quadratic Equations]]. | ||
+ | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]]. | ||
+ | * [[Solutions of Linear Systems]]. | ||
|| | || | ||
− | |||
* Determine fundamental solutions. | * Determine fundamental solutions. | ||
+ | |- | ||
+ | |Week VI | ||
+ | || | ||
+ | * Ahmad and Ambrosetti 2014, Ch. 5 | ||
+ | || | ||
+ | * [[Linear Differential Equations|Linear Non-homogeneous Equations]] | ||
+ | || | ||
+ | * [[Wronskian]]. | ||
+ | * [[Quadratic Equations]]. | ||
+ | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]]. | ||
+ | * [[Solutions of Linear Systems]]. | ||
+ | || | ||
+ | * Determine non-homogeneous classes of differential equations of the second and higher order. | ||
+ | * Determine linear and non-linear classes of differential equations of the second and higher order | ||
+ | |- | ||
+ | |Week VI | ||
+ | || | ||
+ | * Ahmad and Ambrosetti 2014, Ch. 5 | ||
+ | || | ||
+ | * [[Variation Of Parameters (2nd Order)|Variation of Parameters (2nd Order)]] | ||
+ | || | ||
+ | * Integration techniques | ||
+ | :- [[Direct Integration]] | ||
+ | :- [[Integration by Substitution]] | ||
+ | :- [[Integration by Parts]] | ||
+ | :- [[Partial Fractions]] | ||
+ | * [[Quadratic Equations]]. | ||
+ | * [[Solutions of Linear Systems]]. | ||
+ | || | ||
* Apply of the variation of parameters technique for second-order ODEs. | * Apply of the variation of parameters technique for second-order ODEs. | ||
− | |||
− | |||
− | |||
|- | |- | ||
|Week VII | |Week VII | ||
|| | || | ||
* Ahmad and Ambrosetti 2014, Ch. 5 | * Ahmad and Ambrosetti 2014, Ch. 5 | ||
− | |||
|| | || | ||
− | * Variation of | + | * [[Variation Of Parameters (2nd Order)|Variation of Parameters (2nd Order)]] (continued) |
− | * Method of | + | || |
+ | * Integration techniques | ||
+ | :- [[Direct Integration]] | ||
+ | :- [[Integration by Substitution]] | ||
+ | :- [[Integration by Parts]] | ||
+ | :- [[Partial Fractions]] | ||
+ | * [[Quadratic Equations]]. | ||
+ | * [[Solutions of Linear Systems]]. | ||
+ | || | ||
+ | * Apply variation of parameters technique for second-order ODEs. | ||
+ | |- | ||
+ | |Week VII | ||
+ | || | ||
+ | * Ahmad and Ambrosetti 2014, Ch. 5 | ||
+ | || | ||
+ | * [[Method of Undetermined Coefficients (2nd Order)]] | ||
|| | || | ||
− | * | + | * [[Quadratic Equations]]. |
− | + | * [[Systems of Linear Equations]]. | |
|| | || | ||
− | * Apply | + | * Apply method of undetermined coefficients technique for second-order ODEs. |
− | |||
|- | |- | ||
|Week VIII | |Week VIII | ||
|| | || | ||
− | * | + | * Ahmad and Ambrosetti 2014, Ch. 5 |
|| | || | ||
− | * | + | * [[Non-linear 2nd Order ODEs]] |
|| | || | ||
− | * | + | * [[Algebraic Equations]] |
+ | * [[Reduction of the Order]] | ||
+ | * Integration techniques | ||
+ | :- [[Direct Integration]] | ||
+ | :- [[Integration by Substitution]] | ||
+ | :- [[Integration by Parts]] | ||
+ | :- [[Partial Fractions]] | ||
|| | || | ||
− | * | + | * Methods for nonlinear second-order ODEs. |
+ | * Apply reduction of the order method to some nonlinear second-order ODEs. | ||
+ | |- | ||
+ | |Week VIII | ||
+ | || | ||
+ | * Ahmad and Ambrosetti 2014, Ch. 5 | ||
+ | || | ||
+ | * [[Variation Of Parameters|Variation of Parameters (Higher Order)]] | ||
+ | || | ||
+ | * [[Variation Of Parameters|Variation of Parameters (2nd Order)]] | ||
+ | || | ||
+ | * Apply variation of parameters technique for higher-order ODEs | ||
+ | |- | ||
+ | |Week VIII | ||
+ | || | ||
+ | * Ahmad and Ambrosetti 2014, Ch. 5 | ||
+ | || | ||
+ | * [[Method of Undetermined Coefficients|Method of Undetermined Coefficients (Higher Order)]] | ||
+ | || | ||
+ | * [[Method of Undetermined Coefficients (2nd Order)]] | ||
+ | || | ||
+ | * Apply method of undetermined coefficients technique for higher-order ODEs | ||
|- | |- | ||
|Week IX | |Week IX | ||
|| | || | ||
− | * | + | * Ahmad and Ambrosetti 2014, Ch. 6 |
+ | || | ||
+ | * [[Linear Differential Equations|Linear Differential Equations (Higher Order)]] | ||
+ | || | ||
+ | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]] | ||
+ | * [[Variation Of Parameters|Variation of Parameters (Higher Order)]]. | ||
+ | * [[Method of Undetermined Coefficients|Method of Undetermined Coefficients (Higher Order)]]. | ||
+ | || | ||
+ | * Methods for linear higher-order ODEs | ||
+ | |- | ||
+ | |Week X | ||
+ | || | ||
+ | * Ahmad and Ambrosetti 2014, Chaps. 5, 6 | ||
|| | || | ||
− | * | + | * Overview of the solutions methods for second and higher order differential equations. |
|| | || | ||
− | * | + | * [[Algebraic Equations]] |
+ | * Direct methods for second and higher-order ODEs: | ||
+ | :- [[Variation Of Parameters|Variation of Parameters (Higher Order)]] | ||
+ | :- [[Method of Undetermined Coefficients|Method of Undetermined Coefficients (Higher Order)]] | ||
|| | || | ||
− | * | + | * Evaluate the exact solutions of important classes of differential equations such as second order differential equations as well as some higher order differential equations. |
|- | |- | ||
|Week X | |Week X | ||
|| | || | ||
− | * Ahmad and Ambrosetti 2014, | + | * Ahmad and Ambrosetti 2014, Chaps. 10 |
− | |||
− | |||
|| | || | ||
− | * | + | * [[Power Series Solutions]] |
− | |||
− | |||
|| | || | ||
− | * | + | * [[Power Series Induction]] |
− | |||
− | |||
|| | || | ||
− | + | Apply power series method to evaluate solutions of first-order and second-order ODEs. | |
− | |||
− | |||
|- | |- | ||
|Week XI | |Week XI | ||
|| | || | ||
− | * Ahmad and Ambrosetti 2014, | + | * Ahmad and Ambrosetti 2014, Chaps. 10 |
− | |||
− | |||
|| | || | ||
− | * | + | * [[Power Series Solutions]] (continued) |
− | |||
− | |||
|| | || | ||
− | * | + | * [[Power Series Induction]] |
− | |||
− | |||
|| | || | ||
− | + | Apply power series method to evaluate solutions of first-order and second-order ODEs. | |
− | |||
− | |||
|- | |- | ||
|Week XII | |Week XII | ||
|| | || | ||
− | * Ahmad and Ambrosetti 2014, Ch. | + | * Ahmad and Ambrosetti 2014, Ch. 11 |
− | |||
− | |||
− | |||
− | |||
− | |||
|| | || | ||
− | * | + | * [[Laplace Transform]] |
− | |||
− | |||
− | |||
− | |||
− | |||
|| | || | ||
− | * | + | * [[Functions]] of Single Variable. |
− | * | + | * [[Continuity]] of functions of single variables. |
− | * | + | * [[Derivatives]] of functions of single variables. |
− | * | + | * [[Improper Integrals]] of functions of single variables with infinite limits. |
− | |||
− | |||
|| | || | ||
− | * Definition and main properties of the | + | * Definition and main properties of the L-transform. |
− | |||
− | |||
− | |||
− | |||
− | |||
|- | |- | ||
|Week XIII | |Week XIII | ||
|| | || | ||
− | * Ahmad and Ambrosetti 2014, Ch. | + | * Ahmad and Ambrosetti 2014, Ch. 11 |
− | |||
|| | || | ||
− | * | + | * [[Inverse Laplace Transform]] |
− | |||
|| | || | ||
− | * | + | * [[Laplace Transform]] |
− | * | + | * [[Complex Derivatives]] |
|| | || | ||
* Apply the theorem(s) for inverse L-transform. | * Apply the theorem(s) for inverse L-transform. | ||
− | |||
|- | |- | ||
|Week XIV | |Week XIV | ||
|| | || | ||
− | * Ahmad and Ambrosetti 2014, Ch. | + | * Ahmad and Ambrosetti 2014, Ch. 11 |
− | |||
|| | || | ||
− | * | + | * [[Laplace Transform to ODEs]] |
− | |||
|| | || | ||
− | * | + | * [[Linear Differential Equations|Linear Equations]] |
− | * | + | * [[Laplace Transform]] |
+ | * [[Inverse Laplace Transform]] | ||
|| | || | ||
* Apply the Laplace transform as solution technique. | * Apply the Laplace transform as solution technique. | ||
− | |||
|- | |- | ||
− | |Week | + | |Week XIV |
|| | || | ||
− | * Ahmad and Ambrosetti 2014 | + | * Ahmad and Ambrosetti 2014, Ch. 11 |
− | |||
|| | || | ||
− | * | + | * [[Laplace Transform to ODEs|Laplace Transform to Systems of ODEs]] |
− | |||
|| | || | ||
− | * Solutions | + | * [[Solutions of Linear Systems]]. |
− | * | + | * [[Laplace Transform]]. |
+ | * [[Inverse Laplace Transform]]. | ||
|| | || | ||
− | * Apply the | + | * Apply the Laplace transform as solution technique. |
− | |||
|- | |- | ||
− | |Week | + | |Week XV |
|| | || | ||
* Ahmad and Ambrosetti 2014 | * Ahmad and Ambrosetti 2014 | ||
− | |||
|| | || | ||
− | * | + | * Overview of the solutions methods discussed. |
− | |||
|| | || | ||
− | * Solutions | + | * [[Separation of Variables (1st Order)]] |
− | * | + | * [[Homogeneous Differential Equations|Homogeneous Differential Equations (1st Order)]] |
+ | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]] | ||
+ | * [[Integrating Factor]] | ||
+ | * [[Bernoulli Equations (1st Order)]] | ||
+ | * [[Exact Differential Equations|Exact Differential Equations (1st Order)]] | ||
+ | * [[Reduction of the Order]] | ||
+ | * [[Method of Undetermined Coefficients (2nd Order)]] | ||
+ | * [[Non-linear 2nd Order ODEs]] | ||
+ | * [[Variation Of Parameters|Variation of Parameters (Higher Order)]] | ||
+ | * [[Method of Undetermined Coefficients|Method of Undetermined Coefficients (Higher Order)]] | ||
+ | * [[Linear Differential Equations|Linear Differential Equations (Higher Order)]] | ||
+ | * [[Power Series Solutions]] | ||
+ | * [[Laplace Transform to ODEs]] | ||
+ | * [[Laplace Transform to ODEs|Laplace Transform to Systems of ODEs]] | ||
|| | || | ||
* Apply all solutions methods discussed. | * Apply all solutions methods discussed. | ||
− | |||
|} | |} |
Latest revision as of 12:24, 27 November 2021
Course Catalog
MAT 3613. Differential Equations I. (3-0) 3 Credit Hours.
Prerequisite: Completion of or concurrent enrollment in MAT2233. Basic notions of differential equations, solution of first-order equations and linear equations with constant coefficients, nth-order initial value problems, Laplace transforms, and may include additional topics such as power series solutions of differential equations, linear systems, and stability. Generally offered: Fall, Spring, Summer. Differential Tuition: $150.
Text
Ahmad, S., & Ambrosetti, A. (2014). textbook on Ordinary Differential Equations (Vol. 73). Springer
Topics List
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