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: 

  • Long Lu,  lklu@ucsc.edu
  • Joseph Moore, jonimoor@ucsc.edu
  • Poonam Deshpande, podeshpa@ucsc.edu
  • Shashank Gandhi, shgandhi@ucsc.edu

Main Lectures: Tu/Th 9:50AM-11:25AM, (Remote instruction)  

Section: Wednesday 5:20PM-6:55PM Jack Baskin Auditorium (BE-101)

CANVAS COURSE WEBPAGE: CANVAS

LECTURE NOTES: PDF

Group tutoring section: Friday 4:00PM-5:05PM (Remote instruction) held by Long Lu

Office Hours: 

  • Daniele Venturi (remote), Wednesday 11AM-12PM
  • Joseph Moore BE 312 C/D (in person), Friday 2PM-4PM
  • Poonam Deshpande, BE 312 C/D (in person), Thursday 3:30PM-5:30PM
  • Shashank Gandhi BE 312 C/D (in person), Monday 11:30AM-1:30PM

Homework Assignments, Grading Policy and Exams: See CANVAS course webpage. 

 


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.
  • Week 5: Vector spaces, linear combinations, 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)