Math 2110 Outline (Spring 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

12.2 Vectors Notes (12.2 solutions)

Practice with Vectors (solutions)

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

14.5 The Chain Rule Notes (14.5 solutions)

 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

14.8 Lagrange Multipliers Notes (14.8 Solutions)

5 EXAM 1

15.1

15.2

Covers Ch 12 and 14, Wednesday 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)
  SPRING BREAK, NO CLASSES
9 EXAM 2

13.1

13.2

13.3

Covers Ch 14 and 15

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

13 EXAM 3

16.7

16.8

Covers Ch 15, 13 and 16.1-6

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 5/1