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FINAL EXAM: 11:30-2:30 ON MONDAY, MARCH 15, MANDEVILLE AUD.
How to study mathematics offers advice for studying Mathematics.
Lecture 1: Introduction. Probablity density function.
Lecture 2: Probability density function. Interpretation. Cumulative distribution function. Examples.
Lecture 3: Median. Mean. Examples.
Lecture 4: Geometric series: infinite and finite. Examples.
Lecture 5: Taylor polynomials.
Lecture 6: 3D space. Distance in 3D. Functions of 2 variables and their graphs.
Lecture 7: Spheres, cylinders, paraboloids and cross sections.
Lecture 8: Level curves and contour diagrams. Contour diagrams need to have the level curves labeled by the level.
Lecture 9: Linear functions and planes. We need two slopes to write down the equation of the plane. We can see the two slopes as slopes of cross sections. Planes through 3 points.
Lecture 10: Midterm review. Started vectors, showed how to add vectors and multiply them by scalars.
Lecture 11: More on vectors. Length. Vectors of several components.
Lecture 12: Dot product. Perpendicular vectors have zero dot product. Angle between vectors can be computed by dot product. Vectors normal to a plane.
Lecture 13: Cross product. Cross product is perpendicular to two vectors. Cross product has length given by the area of the parallelogram spanned by the two vectors. Plane through 3 points.
Lecture 14: More on cross product. Derivatives.
Lecture 15: Computing partial derivatives.
Lecture 16: Tangent plane. Linear approximation. Differential.
Lecture 17: Directional derivative and gradient. Gradient is the direction of steepest increase. Gradient is normal to the level curves.
Lecture 18: Chain rule in several variables and examples.
Lecture 19: Second order derivatives. Order of differentiaton is not important. Taylor polynomials.
Lecture 20: Critical points. Local min and local max. Second derivative test. Saddle points.
Lecture 21: Compact sets. Functions defined on compact sets have a gloabl min and a global max.
Lecture 22: Functions on compact sets continued. Example of a function maximized/minimized over a rectangular boundary.
Lecture 23: Lagrange multipliers: gradient vectors are parallel at the min/max. Examples.