MATH 119

Pre midterm

• Taylor Series
• Taylor polynomials and Taylor's Inequality
• Big O suste,
• Basic Series
• sinx = sum((-1)^k * x^(2k+1)) / (2k+1)!
• cosx = sum((-1)^k * x^(2k)) / (2k)!
• e^x = sum (x^k/k!)
• 1/(1-x)
• Convergence of infinite series
• Power series
• Radius and Interval of Convergence (when the power series converges to the exact value of the function)
• Manipulation of power series (integrate, differentiate, divide by x)
• Multiplying power series is messy without Big O

Post Midterm

• Graphing scalar fields
• Partial derivatives (fx, fy, fxx, fxy, fyy)
• Two-variable Taylor Series with linear approximation (tangent plane)
• Differentials
• Parametric Equations (vector fields, vector functions)
• vector function r(t) = (x(t), y(t))
• velocity vector r'(t) = (x'(t), y'(t)), acceleration vector r"(t) = (x"(t), y"(t))
• Chain Rule with trees
• Gradiant vector ∇f = (fx, fy) ( think of it as the derrivative of a field )
• can find greatest slope is in the direction of ∇f(a,b)
• greatest slope is ||∇f(a,b)||
• can be used to find critical points
• Unconstrained optimization (critical points and classification, know the formula)
• Constrained optimization ( optimization in a closed region ) ∇f = λ∇g
• Double/Triple integration
• Change of variable, coordinate systems