MAT 133 Calculus and Linear Algebra for CommerceΠ

2019-04-05-5 at 18h

- Week 3
- financial math
- present value
- future value
- principal
- effective continuous rate
- effective annual rate
- annuities

- Week 4
- bonds
- perpetuities
- linear systems
- types of linear systems
- input/output models

- Week 5
- solving linear systems with matrices
- parameters
- row echelon form
- reduced row echelon form
- Gaussian algorithm

- Week 6
- matrix operations
- algebra with matrices
- linear combinations
- matrix products
- strange phenomena with matrix multiplication
- inverse matrices
- matrix inversion algorithm

- Week 7
- linear algebra
- geometry of matrix multiplication
- eigenvalues and eigenvectors

- Week 8
- probability and counting
- basic counting principle |A x B| = |A||B|
- permutations
- power sets
- factorial
- permutations with repeated elements
- combinations
- Poker

- Week 9
- independence
- inclusion/exclusion
- total probability
- conditional probability

- Week 10
- conditional probability
- conditional total probability
- Bayes' law
- expected value
- expectation
- limits
- one sided limits
- existence of limits

- Week 11
- limits and asymptotes
- limit laws
- continuity

- Week 12 (doc cam)
- slope and tangent lines
- secant lines
- tangent lines
- derivatives
- product rule
- quotient rule
- one-sided continuity
- toolbox of continuous functions
- types of discontinuities

- Week 13
- derivatives
- examples of derivative calculations
- differentiability
- natural exponentials
- cusps, vertical tangent lines, and jumps
- types of non-differentiability

- Week 14
- the chain rule
- asymptotes
- "designer" functions
- derivatives of inverses
- logarithmic differentiation
- implicit differentiation

- Week 15
- shape and derivatives
- strictly increasing/decreasing
- sign charts
- critical points
- concavity and the second derivative
- points of inflection

- Week 16
- optimization
- extreme value algorithm
- first derivative test
- second derivative test
- applied optimization

- Week 17
- approximation
- linear approximation
- approximating area
- power series for exp(x)
- Riemann sum setup

- Week 18
- Riemann sums
- Fundamental Theorem of Calculus
- anti-derivatives
- total area
- signed area
- substitution

- Week 19
- substitution
- integration and the product rule
- integration by parts
- iteratred integration by parts
- bounds and parts

- Week 20
- vertical slices
- horizontal slices
- dividing a region in to two parts of equal area
- area between curves
- differential equations warm-up

- Week 21
- differential equation
- simple differential equations
- seperable equations
- linear equations
- integrating factors

- Week 22
- differential equations
- growth/decay model
- second order constant coefficients
- second order constand coefficients with repeated roots
- multivariate functions
- partial derivatives
- tangent planes
- contour plots

- Week 23
- hessian matrices
- second derivative test
- unconstrained optimization

- Week 24
- optimization over regions
- volume calculations
- dxdy and dydx