Homework

The homework associated to this course will have two components: an online and handwritten homework component.
Each will count as half of the final homework grade.

The online problems cover the more routine aspects of the class. You can think of these problems as a first check of your understanding. The written homework problems are usually more conceptual. They will help you understand the concepts more completely and are often motivated by problems from the Life Sciences.

Online Homework: The online homework can be accessed through the following website https://webwork.as.uky.edu/webwork2/MA138S24
Your username is your Link Blue user ID (use capital letters!) and your password is your student ID number.

With the online assignments you can try (most) problems as many times as you like. The system will tell you if your answer is correct or not. There is also a way to email the TA a question from each of the problem. We encourage you to use this system for online homework questions since it provides the TA with additional information about the problem you are working on. Please keep in mind that you will not get an instantaneous response to your email questions. We will always do our best to respond within 24 hours and you will probably get a faster response if you email during normal business hours. (Don't wait until the last minute!)
Also remember that more specific questions will get more informative responses from us.

Handwritten Homework: When submitting a written homework you will be required to follow these guidelines:

All pages for each assignment must be included in a single PDF file.
You must either (a) have all problems in numerical order or (b) start every problem on the left side of the page
so that the TA can easily find the problems that s/he chooses to grade.

You will be penalized one point for each unsatisfied item listed above on every handwritten assignment.

Section	Online/Handwritten assigned problems (with due dates)
6.3	The online assignment is due on Tuesday, January 16, 11 pm
6.3	# 1, 3, 5, 7, 19
	The handwritten homework set 6.3 is due on Canvas on Tuesday, January 16, 11 pm
7.1	The online assignment is due on Friday, January 19, 11 pm
7.1	# 35, 38, 47, 49, 51, 53, 55, 57
7.2	The online assignment is due on Tuesday, January 23, 11 pm
7.2	# 32, 35, 39, 41, 45, 49, 67
	The handwritten homework sets 7.1 and 7.2 are due on Canvas on Tuesday, January 23, 11 pm
7.3	The online assignment is due on Tuesday, January 30, 11 pm
7.3	# 26, 45, 71, 75, 81
	The handwritten homework set 7.3 is due on Canvas on Tuesday, January 30, 11 pm
7.4	The online assignment is due on Tuesday, February 6, 11 pm
7.4	# 9, 29, 32, 37, 39, 43
	The handwritten homework set 7.4 is due on Canvas on Tuesday, February 6, 11 pm
8.1	The online assignment is due on Friday, February 16, 11 pm
8.1	# 9, 17, 25, 28, 33, 41, 45, 51
	The handwritten homework set 8.1 is due on Canvas Friday, February 16, 11 pm
	Direction fields and SAGE: In this supplementary set of notes we discuss the notion of a direction (or slope) field of a differential equation. SAGE is a free open-source mathematics software system. It is easy to plot direction (slope) fields of a differential equation using SAGE. This set of notes summarizes the details of the solutions of interesting models for the Life Sciences (the exponential and logistic growth models; the Lotka-Volterra predator-prey model; the Von Bertalanffy individual growth model and the Solow economic growth model). This YouTube video How Wolves Change Rivers is a good motivation to introduce the Lotka-Volterra predator-prey model. This is a 2014 follow-up article on the New York Times: Is the Wolf a Real American Hero?
8.2	The online assignment is due on Friday, February 23, 11 pm
8.2	# 79, 80, 89, 90, 91, 93
	The handwritten homework set 8.2 is due on Canvas on Friday, February 23, 11 pm
9.1	A useful software to perform Gaussian Elimination: click here. The online assignment is due on Friday, March 1, 11 pm
9.1	# 5, 27, 29, 31, 35
	The handwritten homework set 9.1 is due on Canvas on Friday, March 1, 11 pm
9.2	The online assignment is due on Tuesday, March 5, 11 pm
9.2	# 7, 23, 31, 35, 39, 43, 45, 49, 51, 63, 67
	The handwritten homework set 9.2 is due on Canvas on Tuesday, March 5, 11 pm
9.3	The online assignment is due on Friday, March 22, 11 pm
9.3	# 38, 39, 41, 45, 69, 71, 73
	The handwritten homework set 9.3 is due on Canvas on Friday, March 22, 11 pm
	Fibonacci's numbers, a population model, and powers of matrices: The goal of these notes is to illustrate an application of large powers of matrices. Our primary tools are the eigenvalues and eigenvectors of the matrix. We illustrate this with two familiar examples.
Suppl.	The online assignment for the supplement on curve fitting - least squares approximation is due on Tuesday, March 26, 11pm
	There is no handwritten homework set for the supplement on curve fitting - least squares approximation
	Curve fitting - least squares approximation: These notes explain how to find the "best" possible solution to a system of linear equations that has too many equations with respect to the number of variables. This is a typical issue in the Life Sciences.
10.1	The online assignment is due on Friday, March 29, 11 pm
10.1	# 4, 12, 15, 17, 23, 25
	The handwritten homework set 10.1 is due on Canvas on Friday, March 29, 11 pm
10.2	The online assignment is due on Tuesday, April 2, 11pm
10.2	# 3, 7, 11, 17, 19, 25
10.3	The online assignment is due on Friday, April 5, 11 pm
10.3	# 9, 13, 19, 23, 27, 29, 33, 41, 47, 49
	The handwritten homework sets 10.2 and 10. 3 are due on Canvas on Friday, April 5, 11 pm
10.4	The online assignment is due on Tuesday, April 9, 11 pm
10.4	# 3, 7, 19, 27
	The handwritten homework set 10.4 is due on Canvas on Tuesday, April 9, 11 pm
10.4	# 29, 31, 35, 37, 39, 43
11.1	# 9, 13, 17
	The handwritten homework sets 10.4 and 11.1 are due on Canvas on Tuesday, April 16, 11 pm
	Direction fields of systems of linear differential equations: we analize the behavior of several types of linear differential equations acoording to the corresponding eigenvalues (see plots associated with DE1-DE6). The direction fields have been plotted using the software Maple.
11.1	The online assignment is due on Friday, April 19, 11 pm
11.1	# 31, 35, 37, 47, 49, 51
	The handwritten homework set 11.1 is due on Canvas on Friday, April 19, 11 pm
11.2	The online assignment is due on Wednesday, April 24, 11 pm
11.2	# 1, 5, 19, 20
11.3	# 9, 13, 15, 17, 19, 23 In Section 11.3/Lecture 42 we follow the description of the graphical approach for 2x2 systems as in the 3rd Edition of the textbook of Dr. Claudia Neuhauser (see pp. 627-629). You can find the scanned version of Section 11.3 here. Also, the written homework assignment is based on the 3rd edition.
	The handwritten homework sets 11.2 and 11.3 are due on Canvas on Wednesday, April 24, 11 pm
	Direction fields of systems of nonlinear linear differential equations: we illustrate the classic Lotka-Volterra predator-prey model -- see the plots associated with DE1-DE2. In DE3 we illustrate a modified Lotka-Volterra model in which the prey grows according to the logistic model; we illustrate various types of population dynamics related to the Lotka-Volterra competing species model -- see plots associated with DE4-DE6. In DE4 species 1 (=x(t)) and 2 (=y(t)) cohexist; in DE5 either species 1 or 2 wins depending on the initial condition; in DE6 one of the two species outcompetes the other; we illustrate the Fitzhugh-Nagumo model (an approximation to the original Hodgkin-Huxley model) for neuron activity -- see plots associated with DE7; we illustrate the motion of a pendulum in the presence of air resistence -- see plots associated with DE8; In the plots associated with DE9-DE10 we give two systems of nonlinear differential equations which have the same linearization at the equilibrium (0,0). In DE9 the origin is an unstable spiral whereas in DE10 the origin is a stable spiral. These examples illustrate the failure of the linearization criterion when the eigenvalues at the equilibrium are purely imaginary. All direction fields and plots have been created using the software Maple.