Mathematical Methods for Engineers I

**AMS 10** – Mathematical Methods for Engineers I. This is an applications-oriented course on complex numbers and linear algebra integrating Matlab as a computational support tool. The topics include introduction to complex algebra, system of linear equations, vectors, matrix algebra, eigenvalue and eigenvector, vector space, orthogonality, etc.

**Instructor**: Qi Gong, Associate Professor, BE 361A, email: qigong at soe.ucsc.edu

**Teaching Assistants:**

Kenneth Caluya, Email: kcaluya at ucsc.edu

Skylar Trigueiro, Email: striguei at ucsc.edu

Youngjun Lee, Email: ylee109 at ucsc.edu

**Lectures:** TuTh 7:10PM - 8:45PM, Jack Baskin Auditorium 101

**Sections: **There are five mandatory lab/discussion sections. Students are required to attend one of these five sections. Lab/discussion sections will be used to teach MATLAB programming needed for the course, review lectures, take quizzes, and solve practice problems.

Section 01A: Monday, 11:00AM-1:00PM, BE 109 (TA: Skylar Trigueiro)

Section 01B: Monday, 1:00PM-3:00PM, BE 109 (TA: Skylar Trigueiro)

Section 01C: Monday, 3:00PM-5:00PM, BE 109 (TA: Youngjun Lee)

Section 01D: Wednesday, 11:00AM-1:00PM, BE 109 (TA: Kenneth Caluya)

Section 01E: Wednesday, 1:00PM-3:00PM, BE 109 (TA: Kenneth Caluya)

**Office Hours:**

Qi Gong: Tuesday and Thursday, 10:30AM to 12:00PM, BE 361A

Kenneth Caluya: Monday 1:00pm to 3:00pm, BE 121

Skylar Trigueiro, Tuesday 1:00pm to 2:30pm, BE 121

Youngjun Lee, Thursday 2:00pm to 3:00pm, BE 119

**Textbook:** Linear Algebra and Its Applications, David C. Lay, Addison-Wesley, 4th Edition.

**Homework: **Homework will be due weekly at the beginning of class. Homework will be posted online. Late homework is NEVER accepted. For each homework, a selected set of problems will be graded. The graded homework will be returned to you in lab sections. Please print your name, lab section number, and Student ID clearly on the first page of your homework.

**Quizzes: **We will have fours quizzes, all in Lab sections.

**Grading: **

Option 1: Homework: 15%, Quizzes: 15%, Midterm: 30%, Final: 40%

Option 2: Final: 100%

**Tentative Schedule: **

Week 1 (lecture 1 & 2): Introduction to complex numbers.

Week 2 (lecture 3 & 4): System of linear equations, elementary row operations, and echelon form.

Week 3 (lecture 5 & 6): Vector equations, matrix equations.

Week 4 (lecture 7 & 8): Solution set of homogeneous and nonhomogeneous equations, linear dependency, and matrix operations (addition and scalar multiplication).

Week 5 (lecture 9 & 10): Matrix operations (multiplication, power, transpose), properties of matrix multiplication, the inverse of a matrix, characterizations of invertible matrices.

**Midterm exam:** Thursday 11/02/2017, in class

Week 6 (lecture 11 & 12): Subspaces, column spaces and null spaces of a matrix.

Week 7 (lecture 13 & 14): Basis for a subspace, dimension, rank, and coordinate systems.

Week 8 (lecture 15 & 16): Determinant and its properties.

Week 9 (lecture 17 & 18): Eigenvalues and eigenvectors.

Week 10 (lecture 19 & 20): Norm, inner product, orthogonality, orthogonal set, orthogonal projection, The Orthogonal Decomposition Theorem, The Best Approximation Theorem, and least-square problems.

**Final Exam: **Tuesday,12/12/2017, 7:30pm - 10:30pm

**Disability Resource Center:** UC Santa Cruz is committed to creating an academic environment that supports its diverse student body. If you are a student with a disability who requires accommodations to achieve equal access in this course, please submit your Accommodation Authorization Letter from the Disability Resource Center (DRC) to me privately during my office hours or by appointment, preferably within the first two weeks of the quarter. At this time, I would also like us to discuss ways we can ensure your full participation in the course. I encourage all students who may benefit from learning more about DRC services to contact DRC by phone at 831-459-2089, or by email at drc@ucsc.edu.