Teaching

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) 

CANVAS COURSE WEBPAGE: CANVAS

LECTURE NOTES: 

  • Lecture note 1: real numbers (PDF)
  • Lecture note 2: complex numbers (PDF) 
  • Lecture note 3: roots of complex polynomials (PDF) 
  • Lecture note 4: matrices (PDF) 
  • Lecture note 5: linear equations (PDF) 
  • Lecture note 6: vector spaces (PDF) 
  • Lecture note 7: linear transformations (PDF) 
  • Lecture note 8: scalar products, norms and orthogonality (PDF) 
  • Lecture note 9: determinants (PDF)
  • Lecture note 10: eigenvalues and eigenvectors (PDF)

 

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.
  • 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 and orthogonality.
  • 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)