Calculus III
Instructors: Dr. Daria Bugajewska
(Lecture)
Consultant: NCSU faculty member Dr. Leslie Kurtz
This course is based on the NCSU course MA242
(4 credits).
The corresponding ISU course is MATH265.
"Calculus for Engineers
and Scientists ", 1st Edition, by J. Franke, J. Griggs, and L. Norris.
Third
of three semesters in a calculus sequence for science and engineering majors.
Vectors, vector algebra, and vector functions. Functions of several variables,
partial derivatives, gradients, directional derivatives, maxima and mimima. Multiple integration. Line and surface integrals,
Green's Theorem, Divergence Theorems, Stokes' Theorem, and applications. Use of
computational tools.
Lecture |
Section |
Topics |
1 |
1.1 1.2 1.3 |
3-D Coordinate Systems
Vectors Begin: The Dot Product |
2 |
1.3 1.4 |
Continue with: The Dot
Product The Cross Product Maple Lab #0: Review Maple Lab #1: Vectors |
3 |
1.5 |
Equations of Lines and
Planes |
4 |
2.1 2.2 |
Vector Functions &
Space Curves Derivative and Integrals of Vector functions; parameterized
Curves; Applications to Physics and Engineering; Projectile motion; |
5 |
2.3 2.4 2.5 |
Fundamental quantities for
curves: Tangent vector, Arc Length & Curvature Intrinsic geometry of
curves. |
6 |
|
Test 1 |
7 |
3.1 3.2 |
Multivariable Functions
Limits and Continuity |
8 |
3.3 3.4 |
Directional Derivative;
Partial Derivatives, higher derivatives Tangent Planes and Linear
approximations Differentiability of multivariable functions |
9 |
3.4 3.5 |
Finish Differentiability of
multivariable functions The Directional Derivative and the Gradient Chain
Rules Maple Lab #2: Applications of the Gradient |
10 |
3.6 3.7 |
Optimization Lagrange
multipliers (optional, time permitting) |
11 |
|
Test 2 |
12 |
4.1 |
Double Integrals Over
Rectangles; Iterated integrals Double Integrals Over General Regions Maple
Lab #3: Regions in the Plane |
13 |
4.2 4.3 |
Applications of Double
Integrals Begin Triple Integrals; applications of triple integrals |
14 |
5.1 5.2 |
Double Integrals in Polar
Coordinates Begin Triple integrals; applications of triple integral |
15 |
5.2 5.3 |
Triple Integrals in
Cylindrical Coordinates; Triple Integrals in Spherical Coordinates |
16 |
|
Test 3 |
17 |
6.1 6.2 6.3 |
Vector Fields Line
Integrals of functions – First review parametrized curves from Section 2.2
Begin line integrals of vector fields |
18 |
6.3 6.4 |
Line integrals of vector
fields; The Fundamental Theorem for Line Integrals Conservative vector fields
and potential functions Parametric surfaces Maple Lab #4: Parameterized
Surfaces |
19 |
6.5 |
Surface Area of parameterized
surfaces Surface integral of a Function Surface Integral of Vector Fields
Maple Lab #5: Surface, surface area and flux integrals |
20 |
7.1 7.2 |
Integral Curves of Vector
Fields Divergence and Curl of a Vector Field; Differential Identities |
21 |
7.3 |
Green’s Theorems for
Circulation and Flux |
22 |
|
Test 4 |
23 |
7.4 7.5 |
Stokes’ Theorem The
Divergence Theorem |
24 |
7.6 |
Integration on Manifolds |
|
|
Final Exam |