## 2016 — MAT A33

**This page is not an official syllabus.** The official MAT A33 syllabus and course information documents are available here. The information provided below is to help you with the course. I’ve posted my lecture notes online so that you can have easy access to them. Please come to lecture and take your own notes as well.

My sections of lecture are:

LEC30 | Tuesday | 17-19:00 | SY 110 |

Thursday | 13-14:00 | SY 110 |

**High level overview:**

- Weeks 1-2: Linear programming
- Weeks 3-6: Matrix algebra and determinants
- Weeks 7-12: Multivariate calculus

**Week-by-week overview:**

**Week 1 (Jan 4-8)***Notes and references are available here*.- Introduction to MATA33: course policies and overview
- Linear inequalities in two variables
- Linear programming terminology and method

**Week 2 (Jan 11-15)***Notes and references are available here*.- Linear programming terminology and method
- Multiple optimal solutions

**Week 3 (Jan 18-22)***Notes and references are available here*.- Matrices, basic matrix operations, terminology
- Systems of equations

**Week 4 (Jan 25-29)***Notes and references are available here*.- Solving systems of equations by matrix reduction
- Row operations
- Parameterized solutions

**Week 5 (Feb 1-5)***Notes and references are available here*.- Matrix inverse
- Solving systems of equations using matrix inversion

**Week 6 (Feb 8-12)***Notes and references are available here*.- Determinants (2 × 2 and 3 × 3)
- Determinants of general square matrices via co-factor expansion
- Cramer’s rule
- General properties, row operations and the determinant

**Week 7 (Feb 22-26)***Notes and references are available here*.- Introduction to functions of several variables
- Level curves
- Partial derivatives

**Week 8 (Feb 29 – Mar 4)***Notes and references are available here*.- Applications of partial derivatives
- Implicit partial differentiation

**Week 9 (Mar 7-11)***Notes and references are available here*.- Higher-order partial differentiation
- Chain rule for partial derivatives

**Week 10 (Mar 14-18)***Notes and references are available here*.- Extrema for functions of two variables
- Terminology and overview, second derivative test
- Hessian matrix for optimization

**Week 11 (Mar 21-24)***Notes and references are available here*.- Lagrange multipliers overview
- Optimization techniques for functions of 2 and 3 variables