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