## 2017 — 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:

LEC01 | Monday | 08-09:00 | AA 112 |

Friday | 08-10:00 | AA 112 |

**High level overview:**

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

**Weekly overview:**

- Week 1
**readings:**7.1, 7.2**concepts:**- Linear inequalities in two variables
- Linear programming terminology
- Linear programming method.

- Week 2
**readings:**7.2, 7.3**concepts:**- Multiple optimal solutions
- Linear programming applications

- Week 3
**readings:**6.1, 6.2, 6.3**concepts:**- Matrix notation
- Matrix terminology
- Matrix operations
- Systems of equations
- Applications

- Week 4
**readings:**6.4, 6.5**concepts:**- Row operations
- Solving systems of equations by matrix reduction
- Parametrized solutions
- Applications

- Week 5
**readings:**6.6**concepts:**- Inverse of a matrix
- Calculating the inverse of a matrix
- Solving systems of equations using matrix inverses

- Week 6
**readings:**notes**concepts:**- Determinants
- Calculating 2×2 and 3×3 determinants
- General determinants by co-factor expansion
- Cramer’s Rule
- General properties of determinants
- Row operations and determinants
- Applications

- Week 7
**readings:**2.8, 7.1**concepts:**- Coordinates
- Level curves
- Partial derivatives
- Applications

- Week 8
**readings:**17.1, 17.2, 17.3**concepts:**- Partial derivatives
- Implicit partial differentiation
- Applications

- Week 9
**readings:**17.4, 17.5**concepts:**- Higher-order partial differentiation
- Chain rule for partial derivatives

- Week 10
**readings:**17.6, notes**concepts:**- Extrema for functions of two variables
- Second derivative test
- Hessian matrix

- Week 11
**readings:**17.7**concepts:**- Lagrange multipliers
- Multiple constraints on Lagrange multipliers

- Week 12
**readings:**17.9**concepts:**- Repeated integration
- Double and triple integrals
- Order of integration

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