MATA23 (Linear Algebra 1)
The following topics cover systems of linear equations, matrices, Gaussian elimination; basis, dimension; dot products; geometry to Rn; linear transformations; determinants, Cramer's rule; eigenvalues and eigenvectors, diagonalization.
The following is a list of online reference websites which cover all the material in MATA23.
Notes:
- (type in any linear algebra phrase into the search bar e.g. Hermitian matrix).
Tools:
Free online tools that can be used to perform many different Linear Algebra Operations:
- (includes inverses, determinants, characteristic equations, eigenvalue, and eigenfunction)
- (includes addition, scalar/matrix multiplication, exponents)
Videos:
Videos that demonstrate several techniques of Linear Algebra
- How to
- How to
- How to
- Definition and example of a
- How to
Lectures:
Linear Algebra lectures by professors from other universities
- Lecture, Spring Semester 2005 (by Gilbert Strang)
Complete Courseware:
Complete online courses (including lecture notes, assignments, and exams) of universities
- , Spring Semester 2010 (by Gilbert Strang)
MATA30/31/32 (Calculus I)
An introduction to the basic techniques of Calculus. Elementary functions: rational, trigonometric, root, exponential and logarithmic functions and their graphs. Basic calculus: limits, continuity, derivatives, derivatives of higher order, analysis of graphs, use of derivatives; integrals and their applications, techniques of integration.
Notes:
Reference websites which cover all the material in MATA30
- Online by Ken Kuniyuki
- Online by Dr. Sean F. Ellermeyer
Tools:
Free online tools that can be used to solve many different single-variable calculus operations:
Videos:
Videos that explain important concepts and demonstrate the different techniques of introductory calculus.
Lectures:
Complete series of lecture videos from other institutions
- , Fall Semester 2007 (by David Jerison)
- , Summer Semester 2006 (by Marilyn McCollum)
- (by Richard Delaware)
- (by Chris Tisdell)
Complete Courseware:
Complete online Calculus course content (including lecture notes, assignments, and exams) of universities.
- , Fall Semester 2010 (by David Jerison)
MATA35/36/37 (Calculus II)
Topics to be covered include: Newton's method, approximation of functions by Taylor polynomials, numerical methods of integration, complex numbers, sequences, series, Taylor series, differential equations.
Notes:
Reference websites which cover all the material in MATA36
- (University of Singapore)
Tools:
Free online tools that can be used to solve many different single-variable calculus operations:
Videos:
Videos that explain important concepts and demonstrate the different techniques of introductory Calculus II.
Lectures:
Complete series of lecture videos from other institutions:
- (by Chris Tisdell)
Complete Courseware:
Complete online calculus course content (including lecture notes, assignments, and exams) of universities
- , Fall Semester 2005 (by Jason Starr)
- , Fall Semester 2011 (by D. Joyce, M. Satz, and G. Maschler)
Socratic by Google
This is a helpful free app that offers help on a variety of biological related concepts. Socratic also has the function to take pictures of problems and offers possible help to solve them or connect to resources to help. The app includes videos, step-by-step explanations and external resources.
UTSC Research Guides
Research advice, useful tools, and the best resources for your subject needs by U of T librarians. Search the guides written specifically for your course at UofT.