MATH 2066 Course Outline
Differential Equations
September 2010

Course Organization

Required Textbook: A First Course in Differential Equations, with Modeling Applications, 9th Edition
Author: Dennis Zill
Publisher: Brooks/Cole, 9th edition, ISBN: 978-0-495-10824-5

Prerequisite: Math 1037 and Math 1057

Instructor: Dr. Barry G. Adams
Office: FA-378
Phone: 675-1151 x 2323
Email: badams 'at' laurentian 'dot' ca

Lecture Times: Mon-Wed-Fri: 8:30 - 9:30 in Room: C-204
Test Time 8:05 - 9:20 in Room C-204

Office Hours: Mon 9:30 am - 2:00 pm
Office Hours: Tue 12:00 am - 2:00 pm
Office Hours: Wed 9:30 am - 2:00 pm

There are also free tutoring sessions in F-215 on Tuesdays from 17:30 - 19:30

Grading Scheme

Grading Scheme: The final grade will be determined on the basis of

5 Assignments (Best 4 of 5) 30% Sept 24, Oct 8, Oct 22, Nov 12, Nov 26

Term test 20% Nov 3 (75 minutes)

Final exam (3 hours) 50% Scheduled by registrar

NOTE: The term test time is 8:05 am - 9:20 am (75 minutes)

Course Outline

Chapter 1: Introduction to Differential Equations (2 lectures)

terminology, classification, explicit and implicit solutions, families of solutions, systems, initial value problems, existence and uniqueness, mathematical models: population dynamics, radioactive decay, Newton's law of cooling/warming, spread of a disease, chemical reactions, draining a tank, mixtures, series circuits, falling bodies, air resistance, suspended cables.

Chapter 2: First-Order Differential Equations (5 lectures)

omit section 2.6
direction fields, autonomous first-order DE's, one-dimensional phase portrait (phase line), population models, solution curves of autonomous DE's, attractors and repellers\\ separable variables, initial value problems, solutions defined by integrals, linear equations, solution using integrating factors, general solution, exact equations and integrating factors, method of substitution.

Chapter 3: Modeling with First-Order Differential Equations (3 lectures)

Solutions to some linear models from chapters 1 and 2, nonlinear models, logistic equation, chemical reactions, modeling with systems of first order DE's, predator-prey and competition models (to be solved later).

Chapter 4: Higher-Order Differential Equations (7 lectures)

omit sections 4.5 and 4.7
Linear equations: Initial value and boundary value problems, existence and uniqueness of solutions, homogeneous equations, superposition principle, linear dependence and independence, Wronskian, fundamental sets, general solution of homogeneous equations, nonhomogeneous equations, reduction of order, constant coefficient case and undetermined coefficients, variation of parameters, solving linear systems by elimination, simple nonlinear DE's.

Chapter 5: Modeling with Higher-Order Differential Equations (4 lectures)

mass/spring systems and simple harmonic motion, damping, driven motion, series circuit analogue, deflection of beams, simple nonlinear models.

Chapter 7: The Laplace Transform (6 lectures)

definitions, simple examples, inverse transforms and derivative transforms. partial fractions, solving first and second order IVP's, unit step functions, translation theorems, derivatives of transforms, convolutions, periodic functions, Dirac delta function, solving systems of linear DE's

Chapter 8: Systems of Linear First-Order Differential Equations (6 lectures)

linear algebra review, matrix form of linear systems, linear independence, Wronskian, fundamental set, solution of homogeneous constant coefficient systems using eigenvalues and eigenvectors, solution of nonhomogeeous linear systems, variation of parameters, matrix exponential.

Course Notes and Software

DFIELD is a java applet that plots direction fields and solution curves for first-order differential equations:

Tutorial on using DFIELD: dfield.pdf

PPOINT is a java applet that plots phase plane solution curves for a system of two first-order differential equations x' = f(t,x,y) and y' = g(t,x,y) and also shows graphs of x and y as functions of time.