ColoState   Spring 2026   MATH 340

Textbook:  William E. Boyce, Richard C. DiPrima, Douglas B. Meade,
Elementary Differential Equations and Boundary Value Problems,
Wiley,11th ed.,  ISBN-13: 978-1-119-25600-7 (or ISBN-10: 1119256003) 

List of Topics for Study (or A Tentative Weekly Schedule)
Classes start on Tue.Jan.20 and end on Fri.May 8;
Spring Break March 14-22 (Sat.-Sun.)

Week 1
Ch.1. Introduction 
-- Modeling (Falling object, Predator-prey system, Newton's cooling law); 
-- Direction fields;  
-- Solutions and classification of ODEs.

Week 2 & 3
Ch.2. First-Order ODEs  (Sec.1,2,3,5,6)
-- 1st order linear ODEs (Integrating factor); 
-- Separable ODEs;
-- Exact ODEs (Integrating factor);
-- Modelling by 1st order ODEs (Mixing, Newton's cooling law);
-- Use of dfield (Java or Matlab)

Week 4 & 5  
Ch.3. Second-Order Linear ODEs
-- Solutions of 2nd linear homo. ODEs w/ const. coeff. (Sec.1,3,4)
-- Solutions of 2nd linear NonHomo. ODEs w/ const. coeff. (Sec.5)
-- Method of undetermined coefficients
-- Mechanical vibrations (undamped/damped free vibrations) (Sec.7)
-- Forced periodic vibrations (beat, resonance) (Sec.8)
-- Wronskian, Linear combinations, Superposition principle (Sec.2)
-- Method of variation of parameters (Sec.6)

Week 6 
Ch.4. Higher-Order Linear ODEs, Review, Midterm#1  
-- Study Ch.4, Sec.2,3 (but not Sec.1)
-- Review (Up to Ch.4 Sec.3)
-- Midterm#1 on topics up to Ch.4 Sec.3
-- Thu. Feb.26th, 5pm,  Midterm#1,  Location TBD. 
-- No class on Fri. Feb.27th 

Week 7,8,9,10
Ch.7. Systems of 1st order ODEs
-- Study/Review Linear Algebra (Sec.2,3) for about 1 week  
-- Sec.5,6,8 for about 2 weeks
Spring Break (Mar.14-22) happens in the middle
-- Sec.1,4,7 for about 1 week
-- Use of pplane software

Week 11
Ch.7 Sec.9, Catch-up, Review, Midterm#2 
-- Ch.7 Sec.9 and catch-up 
-- Review for Ch.7 Sec.1-8
-- Midterm#2 on topics in Ch.7 Sec.1-8 
-- Thu. Apr.9th, 5pm,  Midterm #2,  Location TBD
-- No class on Fri. Apr.10th

Week 12 & 13
Ch.6 Laplace transforms and their use for ODE IVPs
(Mainly Sec. 1 & 2)
-- Review of improper integrals
-- Definition & examples of Laplace transforms
-- Properties of Laplace transform
-- Inverse Laplace transforms
-- A table of direct & inv. Laplace trans. of common functions
-- Solving 1st order ODE IVPs by direct & inv. Laplace trans.
-- Solving 2nd order ODE IVPs by direct & inv. Laplace trans.
Topics we have to skip due to time constraints
* Laplace transform of step/discontinuous/impulse functions;
* ODEs with discontinuous forcing terms 

Week 14
Ch.9.
-- Planar linear systems and classification (Sec.1)  
-- Autonomous systems and stability (Sec.2)
-- Locally linear systems (Sec.3)
-- Predator-prey systems (Sec.5)

Week 15
Optional topics & suggestions for further study
-- SIR model for infectious disease
-- Explicit and implicit Euler methods (Ch.8 Sec.1&2)
Review for Final Exam

Final Exam (Cumulative)
Monday May 11th, 7:30am--09:30am, Location TBD

Last modified by James Liu on Thu.01/01/2026