MATH 251 - Engineering Mathematics III

MATH 251 - Engineering Mathematics III teaser image

Vector algebra, calculus of functions of several variables, partial derivatives, directional derivatives, gradient, multiple integration, line and surface integrals, Green's and Stokes' theorems.

The sections below have practice problems with solutions and videos covering the material. Also, the Quantitative Finance workshop has videos covering Chapter 14. See Lectures 1-8 of the Multivariable Calculus portion of the workshop.

Math for Quantitative Finance

Summary

This course covers the content in Texas Common Course MATH 2315.

Sections

Module 1

Section 12.1 - Three-Dimensional Coordinate System Section 12.2 - Vectors Section 12.3 - The Dot Product Section 12.4 - The Cross Product

Module 2

Section 12.5 - Equations of Lines and Planes Section 12.6 - Cylinders and Quadratic Surfaces Section 13.1 - Vector Functions and Space Curves

Module 3

Section 13.2 - Derivatives and Integrals of Vector Functions Section 13.3 - Arc Length and Curvature Section 13.4 - Motion in Space: Velocity and Acceleration

Module 4

Section 14.1 - Functions of Several Variables Section 14.1 - Amy Austin's Workshop Section 14.2 - Amy Austin's Workshop Section 14.3 - Partial Derivatives Section 14.3 - Amy Austin's Workshop

Module 5

Section 14.4 - Tangent Planes and Linear Approximations Section 14.4 - Amy Austin's Workshop Section 14.5 - The Chain Rule Section 14.5 - Amy Austin's Workshop Section 14.6 - Directional Derivatives and the Gradient Vector Section 14.6 - Amy Austin's Workshop

Module 6

Section 14.7 - Maximum and Minimum Values Section 14.7 - Amy Austin's Workshop Section 14.8 - Lagrange Multipliers Section 14.8 - Amy Austin's Workshop

Module 7

Section 15.1 - Double Integrals over Rectangles

Module 8

Section 15.2 - Double Integrals over General Regions Section 15.3 - Double Integrals in Polar Coordinates

Module 9

Section 15.6 - Triple Integrals Section 15.7 - Triple Integrals in Cylindrical Coordinates Section 15.8 - Triple Integrals in Spherical Coordinates

Module 10

Section 15.9 - Change of Variables in Multiple Integrals

Module 12

Section 16.2 - Line Integrals Section 16.3 - The Fundamental Theorem for Line Integrals Section 16.4 - Green's Theorem

Module 13

Section 16.5 - Curl and Divergence Section 16.6 - Parametric Surfaces and Their Areas Section 16.7 - Surface Integrals

Module 14

Section 16.8 - Stokes' Theorem Section 16.9 - The Divergence Theorem