Math 342: Differential Equations with Linear Algebra IITime: TR 8:00 am – 9:15 am

Place: Purnell Hall Room 228

Instructor Jingmei QiuOffice: Ewing 307E-mail: jingqiu@udel.edu

Office Hours: TR 9:30 am – 10:30 am or by appointment

Textbook • Linear Algebra, a modern introduction, 4th ed., by David Poole.

• Advanced Engineering Mathematics, 5th ed., D. G. Zill, W.S. Wright.

Topics(subjectto change)

1. Zill, Chap 10

(a) 10.2 Homogeneous linear system (review)

(b) 11.2 Stability of linear systems (review)

(c) 10.3 Solution by diagonalization (review)

(d) 10.5 Matrix exponential (review)

(e) 10.4 Nonhomogeneous linear system

2. Poole, Chap 6

(a) 6.4 Linear transformation

(b) 6.5 The kernel and range of a linear transformation

(c) 6.6. The matrix of a linear transformation

3. Zill, Chap 4

(a) 4.1 Definition of Laplace transform

(b) 4.2 The inverse Transform and transforms of derivatives

(c) 4.3 Translation Theorems

(d) 4.4 Additional operational properties (skip 4.4.3)

(e) 4.5 The Dirac Delta function

4. Poole, Chap 5

(a) 5.1 Orthogonality in Rn

(b) 5.2 Orthogonal complements and orthogonal projections

(c) 5.3 The Gram-Schmidt process and QR factorization

5. Poole, Chap 7

(a) 7.1 Inner product spaces

(b) 7.2 Norms and distance functions

(c) 7.3 Least square approximation

(d) 7.4 The singular value decomposition

(e) 7.5 Applications (Fourier series only)

6. Zill, Chap 12

(a) 12.2 Fourier series

(b) 12.3 Fourier Cosine and Sine series

HomeworkPolicy

There will be weekly homework assignment. You are responsible for knowing how tosolve all posted homework problems to better prepare for quizzes and exams. Homeworkproblems will be selected as problems in weekly quizzes.

Grading 10% − Weekly quizzes.

25% − Midterm exam 1: Thursday, Oct. 12th, 2017.

25% − Midterm exam 2: Thursday, Nov. 9th, 2017.

40% − Final exam: check university exam schedule. Final exam is mandatory.

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