MATH 204: DIFFERENTIAL EQUATIONS, SPRING 2023

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

Homework 1

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.

home]     [course outline]     [homework]

Instructors and Office Hours

• Arda Demirhan,     Office:              , Office Hours: TBA.
• Varga Kalantarov, Office: SCI 162, Office Hours: TBA.

Teaching Asistants and Office Hours

• TBA ,e-mail: TBA, Office Hours: TB
• Syllabus  

Homework 1

D. C. Lay, S. Lay, J.J. McDonald Linear Algebra and Its Applications 

SIXTH EDITION

Week 1: Systems of Linear equations.  Row reduction and Echelon Form.  ( Section1.1, Section 1.2)

Week 2: Vector Equations.  The Matrix equation Ax=b ( Section1.3, Section 1.4)

Week 3: Solution Sets of Linear Systems.  Linear Independence.  ( Section1.5, Section 1.7)

Week 4 : Introduction to Linear Transformations.  The Matrix of Linear Transformation  (Section1.8, Section 1.9)

Week 5 :  Matrix operations. The Inverse of a Matrix  (Section 2.1, Section 2.2)

Week 5 :  Characterisation of Invertible Matrices.  ( Section 2.2, Section 2.3)

Week :  Vector Spaces and Subspaces.  (Section 4.1)

Problems from Adams and Essex (10th Ed.) : 

Week 1 :

Section 10.1,  Page 574: 13, 18, 37;

 Section 10.2, Page 583: 3, 13, 20, 23;

 Section 10.3,  Page 592: 4, 15, 17, 26;

Week 2 :

Problems from the textbook.\\

{\bf Section 10.4} Page 599: 4, 8, 10, 16, 19, 22, 26

{\bf Section 12.1} Page 653: 10, 21, 24, 26

Week 3 :

Problems from the textbook.

 Section 13.1 Page 702, Problems : 4, 6, 15, 20

 Section 13.2  Page 707, Problems  4, 7, 12, 14, 20

Week 4 :

Problems from the textbook.

 Section 13.3,  Page 714, Problems : 7, 17, 19, 20, 28, 30

 Section 13.4, Page 720,  Problems : 4, 11, 13, 15

Week 5 :

Problems from the textbook.

 Section 13.5,  Page 729, Problems : 2, 6, 11, 15, 19, 22

 Section 13.6, Page 740,  Problems : 2, 5, 21, 22

Section 13.7, Page 751,  Problems : 5, 7, 12, 17, 19, 24, 31

Week  6:

Problems from the textbook.

Section 4.10 p. 283: Problems 3, 23, 34
Section 14.1 p. 777 : Problems 3, 4, 13, 22, 25
Section 14.2 p. 783: Problems 5, 9, 13

Week 1 :  Sections 10.1 -10.4: Trangle inequality.  Distance between points on plane and in space. Open and closed sets. Vectors , dot product and cross product of vectors.  Equations of plane and line in space.

Week 2 :  Sections 10.3 -10.4:  Scalar triple product: volume of a parallelepiped. Equation of plane. Equation of line. Distancew from a point to a plane. Distance from a point to a line. Intersections of planes and lines. 

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).