MATH 21300: Calculus III with Planar Vector Analysis
Career: Undergraduate
Category: Regular
Term Offered: Fall, Spring, Summer
Pre-requisites: C or better in Math 21200 or
placement
Hours/Credits: 4 HR/WK; 4 CR
Date Effective: Fall 2024
Course Supervisor: Sergiy Merenkov
Catalog Description
Vectors, multivariate functions, partial differentiation, multiple integrals, vector fields, line integrals, and Green's theorem.
Text: Calculus Early Transcendentals (9th ed.), Stewart, Clegg, Watson.
Topics and Allotted Times
| Section | Topics | Suggested Periods |
|---|---|---|
| 12.2 | Vectors (omit applications) | 1.5 |
| 12.3 | The Dot Product (omit direction angles and cosines, work) | 1.5 |
| 12.4 | The Cross Product (omit torque) | 1.5 |
| 12.5 | Equations of Lines and Planes | 2.5 |
| 12.6 | Cylinders and Quadric Surfaces (review) | 0.5 |
| 14.1 | Functions of Several Variables | 1 |
| 14.2 | Limits and Continuity (omit computing - , only cover - definition) | 2 |
| 14.3 | Partial Derivatives (omit PDEs) | 1.5 |
| 14.4 | Tangent Planes and Linear Approximations | 2 |
| 14.5 | The Chain Rule | 2 |
| 14.6 | Directional Derivatives and the Gradient Vector | 2 |
| 14.7 | Maximum and Minimum Values | 2 |
| 15.1 | Double Integrals over Rectangles | 1.5 |
| 15.2 | Double Integrals over General Regions | 2.5 |
| 15.3 | Double Integrals in Polar Coordinates | 2 |
| 15.4 | Applications of Double Integrals (omit radius of gyration and probability) | 1 |
| 15.6 | Triple Integrals | 3 |
| 15.7 | Triple Integrals in Cylindrical Coordinates | 1 |
| 15.8 | Triple Integrals in Spherical Coordinates | 1 |
| 10.1 | Curves Defined by Parametric Equations (omit graphing with technology) | 2 |
| 13.1 | Vector Functions and Space Curves (omit using technology) | 2 |
| 13.2 | Derivatives and Integrals of Vector Functions (omit integrals) | 0.5 |
| 13.3 | Arc Length and Curvature (omit curvature, normal and binormal vectors, torsion) | 1.5 |
| 16.1 | Vector Fields | 2.5 |
| 16.2 | Line Integrals | 2.5 |
| 16.3 | The Fundamental Theorem for Line Integrals | 2.5 |
| 16.4 | Green's Theorem | 2.5 |
| 16.5 | Curl and Divergence | 2 |
| 50 |
Course Learning Outcomes
After taking this course, the student should be able to:
- Model spatial problems with vectors, lines, planes, curves, and surfaces in space. a, b, c
- Differentiate multivariate functions. a, b
- Use differentiation of vector-valued functions to compute tangent lines. a, b, c
- Use differentiation of multivariate functions to find extrema and rates of change. a, b, c
- Set-up and evaluate multiple integrals for regions in the plane and in space. a, b
- Use iterated integrals to measure areas, compute volumes, and find centers of mass. a, b, c
- Compute work and mass integrals on curves and solids, respectively. a, b, c
- State and apply Green's theorem. a, b, e1, e2
- Find and use potential functions to compute work integrals along curves. a, b, c
Course Assessment Tools
- Term average, based mostly on in-class examinations: 60% of grade.
- Comprehensive written final exam: 40% of grade.
Departmental Learning Outcomes
The mathematics department, in its varied courses, aims to teach students to:
a. Perform numeric and symbolic
computations.
b. Construct and apply symbolic and graphical
representations of functions.
c. Model real-life problems mathematically.
d. Use technology appropriately to analyze mathematical
problems.
e. State (e1) and apply (e2) mathematical definitions and
theorems.
f. Prove fundamental theorems.
g. Construct and present (generally in writing, but
occasionally orally) a rigorous mathematical argument.
