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AMATH 351 A: Introduction to Differential Equations and Applications

Meeting Time: 
MWF 10:30am - 11:20am
CMU 120
Saumya Sinha
Saumya Sinha

Syllabus Description:

LecturesMWF 10:30-11:20 am, CMU 120.

InstructorSaumya Sinha (Email:

Office Hours: Monday & Thursday, 1:30-2:30 pm, LEW 129; or by appointment.

Teaching Assistant: Henry Kavle (Email:

Office Hours - Tuesday 11:30-12:30 & Wednesday 12:30 to 1:30, LEW 128.

Lecture Schedule: The planned schedule of lectures/topics is given below. 

Date Class Topic
03/26/18 Lecture 1 Course overview, Introduction to ODEs and motivation.
03/28/18 Lecture 2 Direction fields; 1st order ODEs - separation.
03/30/18 Lecture 3 Separable ODEs, 1st order linear ODEs - integrating factors.
04/02/18 Lecture 4 Applications - mixture problems, equations of motion, radioactive decay.
04/04/18 Lecture 5 Applications - population model; 1st order nonlinear - stability and phase-line analysis.
04/06/18 Lecture 6 1st order nonlinear - exact ODEs.
04/09/18 Lecture 7 Exact ODEs, substitution methods.
04/11/18 Lecture 8 Substitution methods; applications - linear electrical circuit, streamlines in planar fluid flow.
04/13/18 Lecture 9 Second order ODEs with constant coefficients.
04/16/18 Lecture 10 Linear independence for linear (variable coefficient) 2nd order ODEs.
04/18/18 Lecture 11 Euler Equations, Method of undetermined coefficients.
04/20/18 Lecture 12 Method of undetermined coefficients; midterm review.
04/23/18 Exam 1 In-class.
04/25/18 Lecture 13 Variation of parameters.
04/27/18 Lecture 14 Applications of 2nd order ODEs.
04/30/18 Lecture 15 Applications of 2nd order ODEs.
05/02/18 Lecture 16 Laplace transform (notes will be uploaded).
05/04/18 Lecture 17 Laplace transform, heaviside function.
05/07/18 Lecture 18 Laplace transforms, Dirac delta, example in spring-mass system.
05/09/18 Lecture 19 Overview/recap of Laplace transforms and 2nd order ODEs.
05/11/18 Lecture 20 Midterm review. Introduction to systems of ODEs
05/14/18 Exam 2 In-class.
05/16/18 Lecture 21 Linear algebra basics.
05/18/18 Lecture 22 Linear algebra basics
05/21/18 Lecture 23 Linear independence of solutions, the Wronskian, homogeneous vs. particular solutions.
05/23/18 Lecture 24 Constant-coefficient homogeneous first-order systems of ODEs.
05/25/18 Lecture 25 Constant-coefficient homogeneous first-order systems of ODEs.
05/28/18 No class. Memorial Day Holiday 
05/30/18 Lecture 26 Nonhomogeneous ODEs - variation of parameters.
06/01/18 Lecture 27 Variation of parameters, numerical methods, nonlinear differential equations.
06/04/18 Final Exam  CMU 120, 8:30 - 9:30 am

Prerequisites: Proficiency in manipulation of algebraic equations and methods of differentiation and integration at the level of MATH 124 & 125 is assumed.

Course description: Introductory survey of ordinary differential equations; linear and nonlinear equations; Taylor series; and Laplace transforms. Emphasizes on formulation, solution, and interpretation of results. Examples drawn from physical and biological sciences and engineering.

Course Materials:

Textbook: W.E. Boyce & R.C. DiPrima: Elementary Differential Equations and Boundary Value Problems, 10th edition.

The text is not required, but obtaining some edition of it to use as a reference is strongly recommended. The course material will otherwise be self-contained. Prof. Bernard Deconinck’s lecture notes, and additional material as needed, will be posted on Canvas.

Grading: Homeworks - 25%; Exams: 25% each × 3. Grades for this class will not be curved. All four scores (out of 100) will be added and scaled down to a 0-4 scale.


There will be a total of seven graded homeworks, due every Friday (except midterm weeks) at the beginning of class. (Homework 0 will not be graded.) Each homework will typically contain five to seven problems. A subset of these will be randomly selected and graded for credit, while the remaining will be graded for completeness.

You are encouraged to type up your homework using LATEX or another typesetting software. Each reaonably legible typed homework is worth ∼6% bonus points. Typed homework may be submitted through Canvas, while handwritten ones must be submitted in person.

Late policy: No late assignments will be accepted for any reason. In the rare event of an emergency, with sufficient documentation, a homework will be dropped and other homeworks re-weighted.

Discussion and collaboration is encouraged, but solutions must be written up individually and not shared with others. Questions may be brought to class, office hours and the Canvas discussion board. Please note that homework-related questions will not be answered via email.

Exams: There will be two in-class midterm exams, tentatively scheduled for Monday, 04/23/18 and Monday, 05/14/18, and a final exam on Monday, 06/04/18. Each of the exams is equally weighted, and they are not intentionally cumulative. However, topics build on each other, so familiarity with previously covered material is necessary.

You are allowed one handwritten, double-sided reminder sheet (8.5”×11” max.) No calculators, computers, or collaboration allowed.

Extra Credit: You may complete an extra-credit assignment worth approximately 5% of the total grade, in the form of a project. The project must focus on an application of ODEs in your major/field of interest. More details will be given in due time.

Catalog Description: 
Introductory survey of ordinary differential equations; linear and nonlinear equations; Taylor series; and. Laplace transforms. Emphasizes on formulation, solution, and interpretation of results. Examples drawn from physical and biological sciences and engineering. Prerequisite: MATH 125 or MATH 135. Offered: AWSpS.
GE Requirements: 
Natural World (NW)
Last updated: 
October 17, 2018 - 9:00pm