ma 345 differential equations “fundamentals of differential...

MA 345 Differential EquationsText : “Fundamentals of Differential Equations”

by Nagle, Saff and Snider

Instructor : Dr. E. Jacobs

Office : COAS 301-36

Office HoursMon, Wed, Fri 12:30 - 1:45Tuesday 2:30 - 3:30

e-mail: jacobs50@xecu.net

MA 345-05 Class meeting times

MWF 3:00 - 3:50 in COAS 318Tues 3:45 - 5:00 in COAS 204

Grading System

Exam Average 88%Homework Average 12%

Rules for Exams1. You may not have formulas or notes with you onexams.2. Put away cell phones and smart watches duringexams.3. Make-up exams will only be given for in veryspecial circumstances. Arrangements for a make-upexam must be made within 24 hours of the originalexam.

Rule for Homework1. Homework must be neat. Show work.2. If homework takes more than one sheet of paper,the pages must be stapled.3. Homework must be handed in on time.

AttendanceAttendance is not counted in your grade in the courseexcept for borderline cases.

http://users.xecu.net/jacobs/index345ej.htm

Differential Equation

A differential equation is an equation that involvesthe derivative of an unknown function.

dy

dx− 2y = 0

dy

dx+ y = 0

dy

dx+ y = ex

A differential equation could involve higher orderderivatives

md2y

dt2+ β

dy

dt+ ky = 0

A differential equation could involve partial deriva-tives

∂u

∂t= α2 ∂

2u

∂x2where u = u(x, t)

ih̄∂Ψ

∂t= − h̄2

2m

∂2Ψ

∂x2+ VΨ where Ψ = Ψ(x, t)

Let P = P (t) be the population at time t.

Malthusian Model of Growth

Population grows at a rate proportional to the sizeof the population at any point in time.

Malthusian Model of Growth

Population grows at a rate proportional to the sizeof the population at any point in time.

dPdt is proportional to P at any t

Malthusian Model of Growth

Population grows at a rate proportional to the sizeof the population at any point in time.

dPdt is proportional to P at any t

dP

dt= kP

Let A = A(t) be the amount of money in a bankaccount after t years. The bank pays 1 percent in-terest. Find a formula for A(t).

Let A = A(t) be the amount of money in a bankaccount after t years. The bank pays 1 percent in-terest. Find a formula for A(t).

Interest = (Principal)(rate)(time)

Let A = A(t) be the amount of money in a bankaccount after t years. The bank pays 1 percent in-terest. Find a formula for A(t).

Interest = (Principal)(rate)(time)

dA = A · 0.01 · dt

Let A = A(t) be the amount of money in a bankaccount after t years. The bank pays 1 percent in-terest. Find a formula for A(t).

Interest = (Principal)(rate)(time)

dA = A · (0.01) · dt

dA

dt= 0.01A

Population problem:

dP

dt= kP

Bank account problem:

dA

dt= 0.01A

Let M = M(t) be the mass of a radioactive object

dM

dt= −λM

Population GrowthdP

dt= kP

Bank Account ProblemdA

dt= 0.01A

Radioactive MassdM

dt= −λM

dP

dt= kP

dA

dt= 0.01A

dM

dt= −λM

Find a formula for y = y(x)dy

dx= ky

Spring Problem:

md2y

dt2+ β

dy

dt+ ky = 0

Electrical Circuit Problem:

Ld2Q

dt2+R

dQ

dt+

1

CQ = 0