Mathematics for Finance and Actuarial Studies 2

Overview

Contents:
Integrals of trig functions and reduction formulae - Integration by trig substitution and partial fractions - Integration + Partial Fractions - Integration via substitutions - Separable Differential Equations - Linear and Exact Differential Equations - Homogeneous first order ordinary differential equation - Mixing problems and differential equations - How to solve 2nd order differential equations - Solution to a 2nd order, linear homogeneous ODE with repeated roots - How to solve second order differential equations - Integration and differential equations - Sequences and their limits - What is a Taylor polynomial?-Limit of a sequence - Limit of a sequence: L'Hopital's rule applied to $(ln n)/n$ - Limit of a sequence: $n - $th root of $n^2$

Intro to series + the integral test-Series, comparison + ratio tests - Alternating series and absolute convergence - What is a Taylor series? - What is a power series? - How to calculate power series: a tutorial - Partial derivatives and error estimation - Gradient and directional derivative - Gradient & directional derivative tutorial - Tangent plane approximation and error estimation - Tutorial on gradient and tangent plane -Multivariable Taylor Polynomials - Critical points of functions - How to find critical points of functions - Second derivative test: two variables - Critical points + 2nd derivative test: Multivariable calculus - How to find and classify critical points of functions - Max / min on closed, bounded sets - Lagrange multipliers - Intro to double integrals - Double integrals over general regions - Double integral tutorial - Double integrals and area - Double integrals in polar co-ordinates - Reversing order in double integrals