Math Resources

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:

• Wolfram Mathworld (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:

• Linear equation solver
• Matrix calculator (includes inverses, determinants, characteristic equations, eigenvalue, and eigenfunction)
• Matrix multiplier (includes addition, scalar/matrix multiplication, exponents)

Videos:

Videos that demonstrate several techniques of Linear Algebra

• How to reduce a matrix to Row Reduced Echelon Form
• How to calculate the determinant of a 3x3 matrix
• How to calculate the determinant of an nxn matrix
• Definition and example of a sample space
• Hermitian, unitary, and normal matrices
• How to Diagonalize a matrix

Lectures:

Linear Algebra lectures by professors from other universities

• Massachusetts Institute of Technology Lecture, Spring Semester 2005 (by Gilbert Strang)

Complete Courseware:

Complete online courses (including lecture notes, assignments, and exams) of universities

• Massachusetts Institute of Technology, 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 lectures notes and tests by Ken Kuniyuki
• Online lecture notes by Dr. Sean F. Ellermeyer

Tools:

Free online tools that can be used to solve many different single-variable calculus operations:

• Indefinite integral solver
• Tool for plotting single variable functions

Videos:

Videos that explain important concepts and demonstrate the different techniques of introductory calculus.

• The “big picture” of calculus
• The limit concept
• Finding the limit of a function

Lectures:

Complete series of lecture videos from other institutions

• Massachusetts Institute of Technology, Fall Semester 2007 (by David Jerison)
• North Carolina State University, Summer Semester 2006 (by Marilyn McCollum)
• University of Missouri Kansas (by Richard Delaware)
• University of New South Wales (by Chris Tisdell)

Complete Courseware:

Complete online Calculus course content (including lecture notes, assignments, and exams) of universities.

• Massachusetts Institute of Technology, 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

• Online lecture notes by Jie Wu (University of Singapore)

Tools:

Free online tools that can be used to solve many different single-variable calculus operations:

• Indefinite integral solver
• Tool for plotting single variable functions

Videos:

Videos that explain important concepts and demonstrate the different techniques of introductory Calculus II.

• The basic concept of a sequence
• Examples of convergence and divergence of a sequence
• Geometric series Test
• The basic concept of a series
• An example of a telescoping series
• Ratio test of for converging series
• Absolute convergence test for series
• Limit comparison test for converging series
• Root test for converging series
• An introduction to Taylor series
• The intuition behind Taylor and Maclaurin series
• An introduction to power series, finding the radius of convergence
• An introduction to differential equations
• Seperable differential equations
• First order linear differential equations

Lectures:

Complete series of lecture videos from other institutions:

• University of New South Wales (by Chris Tisdell)

Complete Courseware:

Complete online calculus course content (including lecture notes, assignments, and exams) of universities

• MIT, Fall Semester 2005 (by Jason Starr)
• Clark University, 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.  
https://socratic.org/

UTSC Research Guides