Week 1    (Sections :  (1.3, 2.1, 2.2, 2.4) Basic mathematical models. Classification of differential equations. First order linear equations. Separable differential equations. Uniqueness of solution of linear first order ODE.

Week 2    (Sections :  (2.4, 2.6, 2.8)  Bernoulli equation. Exact differential equations and integrating factors. The existence and uniqueness theorem of the initial value problem for first order  ODE’s.

Week 3   (Sections :  (2.8, 3.1, 3.2)   The existence and uniqueness theorem (Picard’s iterations). Second order linear ODE’s with  constant coefficients. Existence and uniqueness of solutions to the Cauchy problem. Abel’s theorem.

Week 4   (Sections :  (3.2, 3.3, 3.4)

Applications of Abel’s theorem. Complex roots of characteristic equation. Reduction of order of second order linear ODE’s

Week 5  (Sections :  (3.6, 3.8, 5.1) Non-homogeneous second order ODE’s: method of variation of parameters. Forced periodic vibrations. Review of power series.

Week 6  (Sections :  (5.2, 5.3, 6.1) Series solutions of ODEs. Laplace transform and its properties. 

Week 7  (Sections :  (6.2, 6.3, 6.4, 6.6. )  Solution of initial value problems by using the Laplace transform. Step functions,. ODEs  with discontinuous forcing functions. The convolution integral.

Week 8  (Sections :  ( 7.1, 7.2, 7.3) Systems of of first-order linear ODE’s. Matrices . Systems of linear algebraic equations. Eigenvalues and eigenvectors of matrices.

Week 9  (Sections :  (7.4, 7.5, 7.6) Basic theory of systems of first-order linear ODE’s, Abel’s Theorem. Homogeneous linear systems with constant coefficients. Complex valued eigenvalues.

Week 10  (Sections :  (7.7, 7.8,  7.9)  Fundamental Matrices. Repeated eigenvalues, Non-homogeneous systems.

Week 11  (Sections :  (10.1, 10.2, 10.3, 10.4) ,Two-point boundary value problems. Fourier series, The Fourier convergence Theorem.  Even and odd functions (Fourier cosine and sine series).

 

MATH 204: DIFFERENTIAL EQUATIONS, SPRING 2023

 

Problems from W.E. Boyce, R.C. Diprima, D.B. Meade :

Homework 6

Section 5.1  p. 202, Problems : 2(a,b), 7 (a,b),  9(a,b)

Section 6.1   p. 245, Problems: 4, 7, 16, 20

Section 6.2  p. 253, Problems: 4, 10, 13, 20, 24

Section 6. 3  p. 253, Problems:  7, 10, 18

Homework 5

Section 3. 6 p. 144, Problems : 6, 9, 12, 16, 17

Section 3. 8 p. 165, Problems : 9, 13(a,b), 15(a)

Section 5.1  p. 193, Problems : 4, 10,   13, 17 

Homework 4 

Section 3.2 p. 117, Problems : 9, 12, 18, 27, 29

Section 3.3 p. 123, Problems : 11, 13, 16, 18 (a,b),

Section 3. 4 p. 130, Problems : 5, 15.

Homework 3.

Problems from W.E. Boyce, R.C. Diprima, D.B. Meade :

 Section 2.8 p. 89, Problems: 2, 5, 7, 11, 14 .

 Section 3.1 p. 107, Problems : 4, 5, 13, 15, 16, 20

and the following problem 

Problem A.  Show that if w(t) is continuous, non-negative on some interval [0, ∞)and satisfies the inequality

w(t)≤  ∫^t0  s² w(s)ds ,    for all t ∈ [0, ∞)

and w(0)=0, for all t ∈ [0, ∞).

 

Homework 1.

Problems from W.E. Boyce, R.C. Diprima, D.B. Meade :

Section 2.1   p. 31: Problems 6, 10, 24, 26 .

 Section 2.2  p. 38 : Problems 6, 9, 17, 20, 23.