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# Mathematics for Finance and Actuarial Studies 2

Other, , Prof. Chris Tisdell

Updated On 02 Feb, 19

##### 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

## Lecture 27: Gradient and directional derivative

4.1 ( 11 )

###### Lecture Details

Free ebook httptinyurl.comEngMathYTA lecture on the gradient and directional derivative of functions of two (or more) variables. Plenty of examples are discussed. The ideas find uses in applied mathematics, science and engineering.

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