MAT 232 Calculus of Several Variables

Π2018-11-09-5 at 19h

- Syllabus
- Week 1
- Dylan
- Cartestian coordinates
- Polar coordinates
- Graphing in polar coordinates
- Converting between polar and cartesian
- Slop in polar coordinates

- Week 2
- Dylan
- Area in polar coordinates
- sin(k theta) for k even and odd
- parametric equations
- parametric curves
- the cycloid
- calculus with parametric curves
- area with parametric curves

- Week 3
- Dylan
- parametric curves
- orientation of parametric curves
- arclength
- the coordinate system on R^3
- the dot product
- lines and planes
- normal to a plane
- parametric equations for lines in space
- functions of several variables
- domain of functions of several variables
- cross sections
- level sets

- Week 4
- Dylan
- limits and continuity
- continuity at a point
- partial differentiation
- partial derivatives
- tangent planes
- the multivariate chain rule
- implicit partial differentiation

- Week 5
- directional derivatives
- unit vectors
- gradient vector
- higher order partial derivatives
- Clairaut's theorem
- maxima and minima
- critical points
- Hessian matrix
- multivariable second derivative test
- reducing number of variables in optimization

- Week 6
- Lagrange multipliers
- test review

- Week 7
- Week 8
- integration
- order of integration
- Fubini's theorem
- changing order of integration
- sketching regions of integration
- first octant
- volume in polar coordinates

- Week 9
- integration in polar coordinates
- area as volume of prism
- surface area
- line integrals
- force fields

MAT B41 Techniques in Multivariate Calculus

Π2018-10-30-2 at 14h

- Week 1
- Kostya
- Shrijan
- vectors
- lengths
- angles
- standard basis
- i,j,k basis
- parametric equation of lines
- dot product
- orthogonal
- parallel
- parametrix equation of a plane
- normal form of a plane

- Week 2
- Shrijan
- Eric
- Kostya
- matrix multiplication
- transpose
- inverse of a matrix
- determinants
- volume of parallelpipeds
- co-factor expansion
- determinant and row operations
- det(AB) = det(A)det(B)
- the cross product

- Week 3
- Kostya
- vector geometry
- geometry and dot products
- limits
- delta-epsilon limits
- contour plots
- continuity
- the circle-box argument
- open sets
- open disks
- partial derivatives

- Week 4
- directional derivative
- differentiability
- gradient vector
- paths in space
- total derivatives
- the chain rule for R^n --> R
- the chain rule for R^n --> R^n

- Week 5
- Week 8
- Tabeeb
- critical points
- the Hessian matrix
- Clairaut's theorem
- relative minima and maxima
- cup, cap, and saddle
- multivariable second derivative test
- optimization

- Week 9
- Shrijan
- Tabeeb
- constrained optimization
- open sets
- closed sets
- bounded sets
- extreme value theorem
- Lagrange multipliers

- Week 10
- Shrijan
- Tabeeb
- integration
- fundamental theorem of calculus
- Cavalieri's principle
- Archimede's theorem: cone + semi-sphere = cylinder
- double integrals
- x-simple regions
- y-simple regions
- simple regions
- area and integrals
- Fubini's theorem

- Week 11
- Tabeeb
- changing order of integration
- upper and lower bound inequalities
- triple integrals
- applications of integrals
- averages
- mass and density

- Week 12
- change of variables
- onto functions
- one-to-one functions
- domain and range
- linear transformations
- fundamental theorem of linear algebra
- Jacobian matrix
- polar coordinates
- polar to cartesian
- "r dr dtheta"
- integrating in polar coordinates

MAT 133 Calculus and Linear Algebra for Commerce

Π2018-10-30-2 at 14h

MAT A29 Calculus I for the Life Sciences

Π2018-10-25-4 at 23h

- Week 1
- quadratic functions
- parabolas
- factoring
- quadratic formula

- Week 2
- angles
- radians and degrees
- visual angles
- special triangles
- Pythagorean identity
- unit circle

- Week 3
- limits
- continuity
- sin(x)/x
- existence of limits
- limit principles
- continuity principles
- piecewise functions

- Week 4
- average rate of change
- instant rate of change
- derivatives

- scaling
- the power rule
- quotient rule

- Week 5
- increasing
- decreasing
- critical points
- relative maxima and maxima
- first derivative test
- curve sketching table
- concave up and down
- second derivative test
- point of inflection
- limits of rational functions
- vertical asymptotes
- horizontal asymptotes
- oblique asymptotes

- Week 6
- Week 7
- optimization
- end points
- implicit differentiation
- related rates
- the sliding ladder problem

- Week 8
- exponential functions
- population growth
- logarithms
- properties of logarithms
- Ebbinghaus learning model

- Week 9
- solving logarithmic equations
- exponential decay
- radioactive decay
- radio carbon dating
- semi-log graphing
- log-log graphing

- Week 10
- integration
- anti-derivatives
- integrating polynomials
- summation notation

- Week 11
- Riemann sums
- definite integrals
- indefinite integrals
- fundamental theorem of calculus
- integration by substitution

- Week 12
- integration by parts
- iterated integration by parts
- partial fractions
- cross-sectional area
- volume

MAT A31 Calculus for the Mathematical Sciences

Π2018-10-25-4 at 20h

- Week 1:
- functions
- one-to-one
- onto
- graphs
- transformations
- function composition
- inverses
- intervals
- inequalities
- absolute values
- distances

- Week 2:
- Exponential functions
- logarithms
- the unit circle
- radians
- degrees
- trigonometric identities
- quantifiers
- implication
- logic
- counter-examples
- proofs with quantifiers
- proofs with inequalities
- proofs as essays

- Week 3:
- limits
- limits to infinity
- existence of limits
- uniqueness of limits
- vertical asymptotes
- horizontal asymptotes

- Week 4:
- Week 5:
- Bounds
- upper bound
- lower bound
- least upper bound (lub)
- greatest lower bound (glb)
- completeness of the reals
- continuitty
- continuity of linear functions
- continuity of f(x) = x^2
- intermediate value theorem

- Week 6:
- Uniqueness of limits
- squeeze theorem
- continuity of polynomials

- Week 7:
- Slope
- the slope function
- secant lines
- tangent line
- left derivative
- right derivative
- derivative
- physics of falling objects

- Week 8:
- Scaling
- adding
- power rule
- product rule
- quotient rule
- composition
- chain rule
- higher order derivatives
- anti-derivatives

- Week 9:
- Logarithms
- exponentials
- logarithmic differentiation
- differentiation of piecewise functions
- power series for e^x
- derivatives of inverse functions

- Week 10:
- maxima and minima
- curve sketching
- local extrema
- global extrema
- critical points
- Fermat's theorem (extrema are critical)
- Rolle's theorem
- closed interval method
- mean value theorem
- equivalence of mean value theorem and Rolle
- first derivative test

- Week 11:
- curve sketching algorithm
- concavity

- Week 12:
- l'Hopital's rule
- logarithms and limits
- anti-derivatives
- anti-differentiation
- integration by substitution

MAT 246 Concepts in Abstract Mathematics

Π2018-10-25-4 at 15h