MATH-2415 Calculus III
Ahmad Kamalvand
Credit Summer 2024
Section(s)
MATH-2415-005 (99154)
LEC TuTh 4:30pm - 7:10pm DIL DLS DIL
Course Subjects
|
Week |
Sections |
Material |
|
1 |
13.1, 13.2 |
Vectors in the Plane, Vectors in Three Dimensions |
|
|
13.3, 13.4 |
Dot Products, Cross Product |
|
2 |
13.5, 13.6 |
Lines and Planes in Space, Cylinders and Quadric Surfaces |
|
|
14.1, 14.2 |
Vector-Valued Functions, Calculus of Vector-Valued Functions |
|
3 |
14.3 |
Motion in Space, Test 1 |
|
|
14.4, 14.5 |
Length of Curves, Curvature and Normal Vectors |
|
4 |
15.1, 15.2 |
Graphs and Level Curves, Limits and Continuity |
|
|
15.3, 15.4 |
Partial Derivatives, The Chain Rule |
|
5 |
15.5, 15.6 |
Directional Derivatives and the Gradient, Tangent Planes and Linear Approximation |
|
|
15.7 |
Maximum/Minimum Problems, Test 2 |
|
6 |
15.8, 16.1 |
Lagrange Multipliers, Double Integrals over Rectangular Regions |
|
|
16.2, 16.3 |
Double Integrals over General Regions, Double Integrals in Polar Coordinates |
|
7 |
16.4, 16.5 |
Triple Integrals, Triple Integrals in Cylindrical and Spherical Coordinates |
|
|
16.7 |
Change of Variables in Multiple Integrals, Test 3 |
|
8 |
17.1, 17.2 |
Vector Fields, Line Integrals |
|
|
17.3, 17.5 |
Conservative Vector Fields, 17.4 Green’s Theorem, Divergence and Curl |
|
9 |
17.6, 17.7 |
Surface Integrals, Stokes’ Theorem |
|
|
17.8 |
Divergence Theorem |
|
10 |
Review |
|
|
|
|
Final Exam |
Student Learning Outcomes/Learning Objectives
- Demonstrate the ability to analyze and visualize curves, surfaces, and regions in 2 and 3 dimensions, in Cartesian, polar, cylindrical, and spherical coordinate systems.
- Perform calculus operations on vector‐valued functions including limits, derivatives, integrals, curvature, and the description of motion in space.
- Perform calculus operations on functions of several variables including limits, partial derivatives, directional derivatives, and multiple integrals.
- Find and classify extrema and tangent planes of functions of two variables.
- Apply some of the theorems of vector calculus, such as the Fundamental Theorem of Line Integrals, Green’s Theorem, the Divergence Theorem, and Stokes' Theorem, to simplify integration problems.
- Apply the computational and conceptual principles of calculus to the solutions of various scientific and business applications.
Office Hours
T Th 12:10 PM - 12:40 PM Online
NOTEM W 2:20 PM - 2:50 PM online
NOTET Th 4:00 PM - 4:30 PM Online
NOTEPublished: 05/27/2024 11:23:09