Course description: This course includes most of the standard material for differential equations: first-order differential equations and analytic methods of their solution, mathematical modeling using differential equations, numerical methods for solving differential equations, linear equations of higher order, systems of linear and nonlinear equations, stability of equilibrium solutions, Laplace transform methods. In addition some related material from linear algebra is included. We use a computer algebra system Maple in this course for some computer projects.
Textbook: C.H.Edwards,Jr. and D.E.Penney , Differential Equations and Linear Algebra , (Third and Fourth Editions) Prentice Hall.
It is expected that you will work most of the basic exercises at the end of each section. A list of additional problems to work will be placed at the course webpage (see homework problems). It is recommended to write down solutions of these problems and keep your homework to use in preparation for quizzes, mid-term and final exams. Every week we'll have a quiz containing two or three problems analogous to ones solved in class and from homework. If you have any questions about problems, please ask them in class or during office hours.
Complementary useful reading for problems and solutions manual is available on the Web via WMU Library page in the electronic form: Bronson, R. Schaum’s outline of theory and problems of differential equations [electronic resource]
Office Hours: Monday,Tuesday, Thursday and Friday: 2 pm - 2:50 pm.
Week 15: April 16 - April 20
Topics for study and reading :
- Section 9.2 Nonlinear Systems - their critical points and equilibrium solutions. Stability of equilibrium solutions. Linearization of systems near equilibrium solutions.
- Section 10.1 Laplace transforms and inverse transforms
- Review of the course
Quiz on Thursday includes problems from Section 9.2.
Week 14: April 09 - April 13
Topics for study and reading :
Quiz on Friday: problems from Section 8.1, 8.2 and 9.1.
- Section 8.2 Non-homogeneous linear system and method of variation of parameters. Cauchy's formula.
- Section 9.1 Phase portraits. Stability and asymptotic stability of solutions of linear systems. Equilibrium solutions.
Week 13 April 02 - April 06
Topics for study and reading :
Quiz on Tuesday: Section 7.3.
- Section 8.1 Matrix exponential and linear systems : fundamental matrix solution and exponential matrix.
- Section 8.2 Nonhomogeneous linear system and method of variation of parameters. Cauchy's formula.
Week 12: March 26 - March 30
Topics for study and reading :
2nd Midterm exam on Thursday includes topics from Chapter 5 (Sections 5.1-5.6) and Chapter 7 (Sections 7.1-7.3): sample exam
- Section 7.3 Eigenvalue method for linear systems ( including complex eigenvalues).
- Section 7.5 Multiple eigenvalue solutions.
- Section 8.1 Matrix exponential and linear systems : fundamental matrix solution and exponential matrix.
Week 11: March 19 - March 23
Topics for study and reading :
- Section 5.6 Forced oscillations and resonance
- Section 7.1 First-order systems of differential equations. Transformation of higher-order differential equation to first-order system. Simple two-dimensional systems.
- Section 7.2.Matrices and linear systems.
- Section 7.3 Eigenvalue method for linear systems ( including complex eigenvalues).
Quiz on Friday : problems from Sections 5.6, 7.1 and 7.2.
Week 10: March 12 - March 16
Topics for study and reading :
Quiz on Friday: Sections 5.3, 5.4, 5.5.
- Section 5.4 Mechanical vibrations: simple pendulum, spring-dashpot mechanical system. Free undamped motion: amplitude, circular frequency and phase angle. Free damped motion.
- Section 5.5 Non-homogeneous equations and the method of undetermined coefficients.
- Section 5.6 Forced oscillations and resonance
Week 8: February 26 - March 02
Topics for study and reading
Quiz on Monday, February 26: problems from Section 5.1.
- Section 5.3 Linear n-th order linear differential equations with constant coefficients. Characteristic equation. Cases of distinct and repeated roots. Complex numbers, Euler formula..
- Section 5.4 Mechanical vibrations: simple pendulum, spring-dashpot mechanical system. Free undamped motion: amplitude, circular frequency and phase angle. Free damped motion.
- Section 5.5 Non-homogeneous equations and the method of undetermined coefficients.
Week 7: February 19 - February 23
Topics for study and reading :
Quiz on Monday, February 19: problems from Sections 3.4,3.5 and 3.6,(matrix products, determinants, inverse matrices.).
- Section 4.3: Linear combinations, linear dependence and independence of vectors.
- Section 5.1 Linear second-order differential equations and their general solutions
- Sections 5.2 Linear n-th order differential equations.Existence and uniqueness of solutions. Superposition principle. Linear dependence of solutions, wronskians. General solutions homogeneous linear differential equations.
Quiz on Friday contains problems from Sections 5.1 and 5.2.
Week 6: February 12 - February 16
Topics for study and reading :
First mid-term exam on Thursday, February 15 (sample exam) will cover Chapters 1 and 2 (sections 2.1-2.3) and Chapter 3 (Sections 3.1-3.3).
- Chapter 3: Elements of linear algebra: vector and matrix operations, matrix product, determinants, inverse matrices.
- Chapter 3: Determinants, inverse matrices, homogeneous linear systems of equations.
- Section 4.3: Linear combinations, linear dependence and independence of vectors.
Maple computer project. Maple Computer Project #2 is due to Tuesday, February 13.
Week 5: February 05 - February 09
Topics for study and reading :
Quiz on Friday: problems from Sections 2.2, 2.3 and 3.1.
- Computer algebra system Maple: Introduction ( basic capabilities, plotting, programming, Differential Equations packages)
- Sections 2.4, 25 Numerical approximation of solutions: Euler's method, improved Euler method, Runge-Kutta method.
- Sections 3.1-3.3: Linear system of algebraic equations and their general solutions. Gauss-Jordan elimination method.
- Chapter 3: Elements of linear algebra: vector and matrix operations, matrix product, determinants, inverse matrices.
Quiz on Friday: Sections 2.2, 2.3 , 3.1. Maple Computer Project #1 is due to Tuesday, February 6.
Second Maple Computer project is due to Tuesday, February 13. Download Maple worksheets:
- Numerical methods for first-order differential equations (Euler and Improved Euler methods)
- Maple worksheet with a task for the Computer project #2
Week 4: January 29 - February 02
Topics for study and reading
We'll meet at Computer Lab (Rood 3396 ) on Friday at 3 pm to work on Maple computer project. Maple Computer Project #1 is due to Tuesday, February 6.
- Section 2.1 Mathematical models: population models. Logistic equation and its applications.
- Section 2.2 Equilibrium solutions and their stability.
- Section 2.3 Acceleration-velocity models. Motion under resistance forces.
- Computer algebra system Maple: Introduction ( basic capabilities, plotting, programming, Differential Equations packages)
Quiz on Thursday (Sections 2.1 and 2.2) .
Week 3: January 22 - January 26
Topics for study and reading
Quiz on Friday : problems from Sections 1.5, 1.6 .
- Section 1.6 Substitution (or, change of variables) method, homogeneous equations,Bernoulli equations.
Exact differential equations and criterion for exactness.- Section 2.1 Mathematical models: population models. Logistic equation and its applications.
- Section 2.2 Equilibrium solutions and their stability.
Quiz on Friday problems from Sections 1.3, 1.4, 1.5 ,theorem on existence and uniqueness of solutions
Quiz on Friday: problems from Sections 1.1, 1.2 , similar to homework problems for 4th edition, homework problems for 3rd edition.
Note that problems
marked with * are extra.
Section 2.2 (page 92) 1, 3, 6, 9, 11, 14, 15, 21
Section 2.3 (page 101) 2, 4, 7, 10, 11, 20, 28
Section 2.4 (page 114) 1, 3, 4, 9, 12, 14
Section 2.6 (page
133) 2, 4, 14, 15
Section 3.1 (page 145) 1, 5, 7, 11, 17, 23, 31
Section 3.2 (page 154) 1, 5, 11, 19, 24*,
Section 3.3 (page 162) 1, 3, 17
Section 3.4 (page 173) 1, 3, 5, 7, 14, 17, 27*
Section 3.5 (page 185) 1, 3, 25, 30, 32
Section 3.6 (page 201) 1, 2, 47, 48, 52
Section 4.3 (page 234) 17, 18, 19
Section 5.1 (page 276) 1, 5, 8, 11, 12, 13, 14, 16, 20, 23, 26, 27, 33, 34, 36. , 41, 43, 46, 48,
Section 5.2 (page 288) 1, 4, 7, 9, 11, 13, 14, 18, 21, 24
Section 5.3 (page
300) 1,4,5,6, 11,13, 20, 21, 24, 25, 27, 30, 33, 39, 43
Section 5.4 (page 311) 1, 3, 4, 5, 8, , 10, 13, 15, 24, 27
Section 5.5 (page 325) 1, 4, 7, 11, 12, 17, 21, 26, 36, 41, 44, 47, 58
Section 5.6 (page 335) 2, 5, 10, 15, 20, 22, 26, 28, 30
Section 7.1 (page 371) 1, 2, 5, 8, , 9, 11, 15, 21, 28
Section 7.2 (page 384) 1, 3 , 5, 15, 24, 28, 37
Section 7.3 (page 395) 1, 3, 7, 9, 17, 19, 25, 38
Section 7.6 (page
451) 1, 3, 6, 7
Section 8.1 (page 479) 1, 3, 5, 9, 11, 13
Section 8.2 (page 489) 1, 3, 5, 7
Section 9.1 (page 511) 9, 11, 13, 14, 15, 20
Section 9.2 (page 522) 1,3, 5, 7. 9. 19. 21. 27. 29
Note that problems marked with * are extra.
Section 2.2 (page 96) 1, 3, 6, 9, 11, 14, 15, 21
Section 2.3 (page 106) 2, 4, 7, 10, 11, 20, 28
Section 2.4 (page 119) 1, 3, 4, 9, 12, 14
Section 2.6 (page 141) 2, 4, 14, 15
Section 3.1 (page 152) 1, 5, 7, 11, 17, 23, 31
Section 3.2 (page 162) 1, 5, 11, 19, 24*,
Section 3.3 (page 170) 1, 3, 17
Section 3.4 (page 182) 1, 3, 5, 7, 14, 17, 27*
Section 3.5 (page 194) 1, 3, 25, 30, 32
Section 3.6 (page 212) 1, 2, 47, 48, 52
Section 4.3 (page 248) 17, 18, 19
Section 5.1 (page 294) 1, 5, 8, 11, 12, 13, 14, 16, 20, 23, 26, 27, 33, 34, 36. , 41, 43, 46, 48,
Section 5.2 (page 306) 1, 4, 7, 9, 11, 13, 14, 18, 21, 24
Section 5.3 (page 319) 1,4,5,6, 11,13, 20, 21, 24, 25, 27, 30, 33, 39, 43,
Section 5.4 (page 331) 1, 3, 4, 5, 8, , 10, 13, 15, 24, 27
Section 5.5 (page 346) 1, 4, 7, 11, 12, 17, 21, 26, 36, 41, 44, 47, 58
Section 5.6 (page 357) 2, 5, 10, 15, 20, 22, 26, 28, 30
Section 7.1 (page 400) 1, 2, 5, 8, , 9, 11, 15, 21, 28
Section 7.2 (page 413) 1, 3 , 5, 15, 24, 28, 37
Section 7.3 (page 426) 1, 3, 7, 9, 17, 19, 25, 38
Section 7.5 (page 457) 1, 3, 6, 7
Section 8.1 (page 487) 1, 3, 5, 9, 11, 13
Section 8.2 (page 496) 1, 3, 5, 7
Section 9.1 (page 519) 9, 11, 13, 14, 15, 20
Section 9.2 (page
532) 1,3, 5, 7. 9. 19. 21. 27. 29
In general, there
will be NO makeups for exams. If you miss an exam for a valid
well-documented reason then arrangements may be made on an
individual basis.
Last modified : April
13, 2018