MA 341 Syllabus with Matlab/Maple

http://www4.ncsu.edu/eos/users/w/white/www/white/ma341/ma341hp.htm

This syllabus was used during the Spring 2001 semester by R. E. White, 515-7478, HA308, white@math.ncsu.edu. The textbook was Differential Equations and Boundary Value Problems (Third Edition) by Nagle, Saff and Snider. Below are links to transparencies, which are in 18 point font and about five slides were presented in the last 10 minutes of each lecture. These transparencies are often associated with examples in this text. They illustrate the use of Matlab/Maple calculations in ODEs, and when coupled with the one credit course MA 302 on Applications and Numerical Solution of ODEs, can empower the student with the necessary computational tools to solve nontrivial systems of differential equations.

Lecture	Sections in NSS	Topics	Matlab/Maple Calculations
1	1.1,1.2	Solutions and Initial Value Problems	Solution of ODEs via dsolve
2	1.3	Direction Fields	Tangent Vectors via quiver
3	1.4	Phase Lines	Solution of ODEs via Direction Fields
4	2.1,2.2	Separable Equations	Separation of Variables and dsolve
5	3.2	Application to Mixing and Populations	Application to Mixing and Populations
6	2.3	First Order Linear Equations	Linear Method and Cooling
7	3.2,3.3	Applications to Heat Transfer and Falling Mass	Application to Heating and Falling Mass
8	1.5	Euler Approximations	Euler's Method and m-files
9	3.5	Improved Euler Approximations	Improved Euler Method and m-files
10	4.1,4.2,4.3	Second Order Linear Equations	Mass-Spring Problem y'' + y = sin(wt)
11	4.5	Homogeneous Solution for Constant Coefficients	Applications to Heat Diffusion and Mass-Spring with Damping
12	4.6	Constant Coefficients - Complex Roots	Application to Truck and Shock Absorbers
13		Review
14		Test One
15	4.7	Non-homogeneous Equations	Homogeneous and Particular Solutions
16	4.8	Undetermined Coefficients	Examples of Particular Solutions; Happy Valentine's Day
17	4.8	Undetermined Coefficients	More Examples of Particular Solution
18	4.9	Variation of Parameters	Variation of Parameters and Numerical Integration
19	4.11	Application to Mass-Spring	Variable Damping and Stiffness for the Homogeneous Equation
20	4.12	Resonance of Mass-Spring	Mass-Spring with External Force and Resonance
21	5.5	Application to Circuits	Tuning a LRC Circuit
22	5.1,5.2	Systems in the Plane	Solution of System via quiver, dsolve and improved Euler
23	5.3	Elimination Method	Application of Systems to Mixing and Population
24	5.5,5.6	Applications to Mixing Tanks, Springs ,Circuits	Coupled Mass-Spring
25		Review
26		Test Two
27	7.1,7.2	Laplace Transforms - Introduction and Definition	Laplace Transform via laplace and ilaplace
28	7.3	Basic Properties	More Laplace Transform Rules
29	7.4	Inverse Transforms	Solution of ODE via Laplace Transforms
30	7.5	Solving Initial Value Problems	More Laplace Transforms and ODEs
31	7.6	Discontinuous Functions	Laplace Transforms and Discontinuities
32	7.7	Convolution, Periodic Function and Systems	Laplace Transforms and Systems
33	9.1,9.2	Introduction to Linear Algebra	Matrix Row Operations via *
34	9.3	Matrices and Vectors	Inverse Matrix via inv; Least Squares via \
35	9.4	Linear Systems of ODEs	Eigenvectors and Eigenvectors via eig
36	9.5	Eigenvalues and Eigenvectors	More Eigenvectors and Eigenvectors
37	9.5	Homogeneous Systems and Real Eigenvalues	Solution of ODE Systems via Eigenvalues
38	9.6	Homogeneous Systems and Complex Eigenvalues	ODE Solution via Complex Eigenvalues
39	9.7	Particular Solution via Undetermined Coefficients	Steady State Particular Solution
40	9.7	Particular Solution via Variation of Parameters	Solution of System via Variation of Parameters
41		Review
42		Test Three
43		Review
44		Review
45		Review
		FINAL EXAM