Math 287 Course Syllabus

Course Syllabus:  Math 287 Syllabus-51419-Spring 18-1.docx

Meet Your Instructor:

 Hi, my name is Dr. George Sweeney. I am a full-time professor here at Santa Ana College.  I have a PhD in Math Education from the joint doctoral program at San Diego State and UC San Diego.  I also have a master's degree in Math from Cal Poly Pomona and a bachelor's from UCLA.  My fields of specialty are in research methodologies, Statistics, Linear Algebra, and Data Science.  I am Bronze, Silver, and Gold certified in Canvas in-person and online teaching. My dissertation was on teaching and learning in Linear Algebra, and I have done research and been published in research in trigonometry, differential equations, physical chemistry and calculus.  I love to teach and do mathematics.  I am currently learning some new computer programming languages.  I also enjoy meditating, making music, reading, playing with my kids, and hanging out with my wife.  I have been married for 13 years and I have two children, 2 1/2 and 5.

Course Description:  

Course Description: This is a joint Linear Algebra and Differential Equations class.  Both disciplines are very important for a variety of sciences and engineering.  In general, differential equations are the underpinning of engineering, while linear algebra is the foundation for computer science and statistics.  If you want to excel in your chosen discipline, this class can provide a very valuable introduction to a powerful set of tools and concepts that will last you a lifetime.

I love both linear algebra and differential equations.  I also love teaching it.  It is challenging. The mathematical ideas are advanced and show up in many different places.  You will have to work very hard in this class.  It is advanced.  You will also find that we will engage in mathematics in ways that you have never before, like using proofs and engaging with applications.  I look forward to working together very much.  I know that I can expect a lot from our experience together.  Let’s do some math!

Textbook Information: Goode and Annin. Differential Equations and Linear Algebra, 4th ed. Pearson/Prentice Hall, 2017, ISBN: 0-321-96467-5.

Additional Course Information: 

Course Learning Objectives: 

1. Create and analyze mathematical models using ordinary differential equations
2. Verify solutions of differential equations
3. Identify the type of a given differential equation and select and apply the appropriate analytical technique for finding the solution of first order and selected higher order ordinary differential equations
4. Apply the existence and uniqueness theorems for ordinary differential equations
5. Find power series solutions to ordinary differential equations
6. Determine the Laplace Transform and inverse Laplace Transform of functions
7. Solve Linear Systems of ordinary differential equations
8. Find solutions of systems of equations using various methods appropriate to lower division linear algebra
9. Use bases and orthonormal bases to solve problems in linear algebra
10. Find the dimension of spaces such as those associated with matrices and linear transformations
11. Find eigenvalues and eigenvectors and use them in applications
12. Prove basic results in linear algebra using appropriate proof-writing techniques such as linear independence of vectors; properties of subspaces; linearity, injectivity and surjectivity of functions; and properties of eigenvectors and eigenvalues