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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 or MPE level 9

4 credits

SBC:  STEM+

 

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.