# Math 2110 Outline (Fall 2023)

 Week Sections Covered Topic Additional Practice Worksheets 1 12.1 12.2 12.3 12.4 Three-Dimensional Coordinate Systems Vectors The Dot Product The Cross Product Calculus I and II Review 2 12.5 12.6 Equations of Lines & Planes Cylinders and Quadric Surfaces Understanding Surfaces 3 14.1 14.3 14.4 14.5 Functions of Several Variables Partial Derivatives Tangent Planes and Linear Approximation The Chain Rule Lines and Planes 4 14.6 14.7 14.8 Directional Derivatives & the Gradient Vector Maximum and Minimum Values Lagrange Multipliers Tangent Planes and Directional Derivatives Classifying Critical Points 5 EXAM 1 15.1 15.2 Covers Ch 12 and 14, (during discussion) Double Integrals over Rectangles Double Integrals over General Regions Double Integrals and Volume 6 15.3 15.6 Double Integrals in Polar Coordinates Triple Integrals in Cartesian Coordinates Double Integrals in Polar Coordinates (solutions) Cartesian Triple Integrals 7 15.7 15.8 Triple Integrals in Cylindrical Coordinates Triple Integrals in Spherical Coordinates Cylindrical Triple Integrals Spherical Triple Integrals 8 15.9 Change of Variables in Multiple Integrals 15.9 Change of Variables Notes (15.9 solutions) 9 EXAM 2 13.1 13.2 13.3 Covers Ch 14 and 15 (during discussion) Vector Functions Derivatives & Integrals of Vector Functions Arc Length Vector Functions and Parameterized Curves 10 16.2 16.1 16.2 Line Integrals (Scalar Functions) Vector Fields Line Integrals (Vector Fields) Line Integrals 11 16.3 16.4 The Fundamental Thm for Line Integrals Green’s Theorem Line Integral Theorems 12 16.5 16.6 Curl and Divergence Parametric Surfaces and Their Areas Curl and Divergence Common Parametric Surfaces — THANKSGIVING BREAK, NO CLASSES 13 EXAM 3 16.7 16.8 Covers Ch 15, 13 and 16.1-6 (during discussion) Surface Integrals (Scalar and Vector Functions) Stokes’ Theorem Line Integrals vs. Surface Integrals.pdf 14 16.9 Divergence Theorem Using the Divergence Theorem Finals Week Final Portfolio Due Monday 12/11