Topics that will be covered in a particular lecture will appear a day or two before the lecture.
I expect you to have read the relavent sections in the book before the lecture and to be prepared to answer questions about the material.
The theorem is presented along with an everyday explanation of what it means....
View the lesson Section 8 - Graphing Solutions of Differential Equations In this section, we learn how the solution to first order differential equations even if we do not know the solution ahead of time.
All of this software is available in most computing labs around the university, including the mathematics computing lab.
Wolfram Alpha is available through most web browsers and there is even an app for it for your phones or tablets.We use the technique of isoclines in order to plot the general solution of the ODE....View the lesson Section 9 - Applications of Differential Equations: Mixing Problems In this section, we apply the techniques and theory of solving differential equations to the problems involving mixtures.You will also be asked to use this or similar software, such as Wolfram Alpha, Maple, MATLAB (through the symbolic toolbox), or Chebfun, on the homework assignments.The purpose here is to help you build a qualitative understanding of partial differential equations and to aid you with some tedious computations for the homework problems.View the lesson Section 6: Exact Differential Equations In this section, we learn how to identify and test if an ordinary differential is "exact" in nature.If it is exact, we learn how to solve it by using the constraints placed upon Exact Differential Equations. View the lesson Section 7 - Existence and Uniqueness Theorem In this section, we learn about the existence and uniqueness theorem of ordinary differential equations.These problems will require us to read the problem and use the information in the problem statement to set up a differential equations that we can then solve....View the lesson Section 10 - Applications of Differential Equations: Newton's Law of Cooling In this section, we apply the techniques and theory of solving differential equations to the problems involving Newton's Law of Cooling.Section 8.12: Constructing the Green's function for a Sturm-Liouville problem Section 9.1: Boundary value problems: Laplace's and Poisson's equation Section 9.7-9.8: Solving Poisson's equation on a rectangle Your submitted homework should show all necessary work you used to solve the problems.Mathematical statements should be complete (or nearly complete) sentences and the reasoning and logic underlying all arguments should be clearly spelled out.