Mathematical Methods For Engineers I (AM 10)

 

Course Description: AM 10 provides an introduction to linear algebra and its applications. In addition, students will learn to use computational software (MATLAB/OCTAVE) and the basics of numerical linear algebra.

Instructor: Prof. Daniele Venturi (venturi@ucsc.edu)

Teaching Assistants: Lia Gianfortone (lgianfor@ucsc.edu), Yuanran Zhu (yzhu22@ucsc.edu), Long Lu (lklu@ucsc.edu)   

Main Lectures: Tu/Th 3:20PM-4:55PM, Earth & Marine Sciences B206 

Sections: Tu/Th 7:10PM-8:45PM BE-152 (Webcast Link user: am-10-1 password: AM10_section)

CANVAS COURSE WEBPAGE: AM10

LECTURE NOTES: PDF

Group tutoring sections: MWF 12PM-1PM, Social Sciences 1, room 153.

Office Hours: 

  • Prof. Venturi, Monday 10AM-12PM  BE-361C
  • Yuanran Zhu, Wedensday 4-6PM BE 153 A
  • Lia Gianfortone, Tuesday 11AM-1PM BE-312
  • Long Lu, Friday 10AM-12PM BE118

Homework Assignments: Homework assignments will not be collected or graded. The quiz problems and the final exam problems will be very similar to homework problems.

Quizzes and Exams: There will be in-class quizzes, and a comprehensive final exam.

Quizzes (tenative dates): Oct. 15, Oct. 29, Nov 12, Nov 26.

Final Exam: Monday Dec 9th, 4-7PM Earth & Marine Sciences B206. 

Grading Policy: 70% in-class quizzes, 30% comprehensive final exam.

 


Course Syllabus:  

  • Week 1: Real numbers and introduction to complex numbers
  • Week 2: Complex numbers, algebraic and polar form, De Moivre formula, complex exponential function, nth root of a complex number, quadratic quations and polynomial equations in the complex plane.
  • Week 3:  Homogeneous linear equations, matrices, row operations and Gauss elimination, linear combination.
  • Week 4:  Matrix algebra, multiplication and addition, matrices associated with linear systems, LU factorization acorresponding to Gauss elimination.
  • Week 5: Vector spaces, linear combinations, convex sets, linear independendence, dimension, matrix rank.
  • Week 6: Linear Maps, kernel and image of a linear map, matrix associated with a linear map, change of bases.
  • Week 7: Scalar products, orthogonal bases, bilinear maps and matrices.
  • Week 8: Determinants, Cramer's rule, inverse of a matrix.
  • Week 9: Eigenvalues and eigenvectors, characteristic polynomial, geometric and algebraic multiplicity of eigenvalues.
  • Week 10: Similarity transformations, diagonalization.

 

Textbooks:

  • Serge Lang, ``Introduction to linear algebra'', Springer 

https://link.springer.com/book/10.1007/978-1-4612-1070-2  (free download from campus network) 

 

  • Thomas Shores, ``Applied Linear Algebra and Matrix Analysis'', Springer 

https://link.springer.com/book/10.1007/978-3-319-74748-4 (free download from campus network)

 

  • Serge Lang, ``Llinear algebra'', Springer 

https://link.springer.com/book/10.1007/978-1-4757-1949-9 (free download from campus network)