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AMS 361, Applied Calculus IV: Differential Equations

Catalog Description: Homogeneous and inhomogeneous linear differential equations; systems of linear differential equations; solution with power series and Laplace transforms; partial differential equations and Fourier series. May not be taken for credit in addition to the equivalent MAT 303.

PrerequisiteAMS 161 or MAT 127 or 132 or 142

4 credits

AMS 361 Instructor webpage

Required Textbook:
"Lectures, Problems and Solutions for Ordinary Differential Equations" by Yuefan Deng, World Scientific, Second Edition; October 14, 2017;
ISBN: 978-981-3226-13-5 (paperback)

Lecture notes will also be provided.

Recommended Only Textbook:
"Elementary Differential Equations and Boundary Value Problems" by C. Henry Edwards & David E. Penney, 6th edition, Pearson Education, Inc., 2008; ISBN: 978-0136006138

1.   Exact methods and homogeneous linear differential equations -- 6 classes
2.  Methods of approximate solution of differential equations –-  6 classes
3.  Nonhomogeneous linear differential equations –-  6 classes.
4.  Systems of linear differential equations and matrices -- 6 classes
5.  Solutions with Laplace transforms –- 6 classes.
6.  Solutions with power series and special functions -- 4 classes
7.  Partial differential equations and separation of variables – 4 classes.
8.  Examinations and Review – 4 classes.


Learning Outcomes for AMS 361, Applied Differential Equations

1.) Build differential equations models of phenomena in:
        * physical sciences;
        * biological sciences;
        * engineering.

2.) Demonstrate skill with solution methods for first-order ordinary differential equations.
        * linear equations;
        * separable and exact nonlinear equations.

3.) Demonstrate skill with solution methods of second- and higher order ordinary differential equations.
        * homogeneous equations with constant coefficients;
        * non-homogenous equations;
        * methods of undetermined coefficients and variation of parameters;
        * series solutions;
        * using the theory Laplace transforms to solve differential equations.
 
4.) Demonstrate skill with the theory for solving systems of first-order linear differential equations.
        * mastery of necessary tools of matrix algebra;
        * basic theory of vector-valued solutions;
        * solving homogeneous linear system with constant coefficients, including complex and repeated eigenvalues;

5.) Use computer software techniques to validate analytical solutions, and to visualize solutions of differential equations.

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