MA 255 - Calculus with Analytic Geometry III

2. Work with vectors as mathematical objects and as tools for solving practical problems.

3. Examine the relationship between vector-valued functions and space curves, using calculus to study their properties and applications.

4. Demonstrate the ability to compute, interpret and apply partial derivatives, directional derivatives, and gradient.

5. Demonstrate the ability to compute, interpret and apply multiple integrals in various coordinate systems.

6. Synthesize vector and calculus concepts to develop key ideas of vector calculus, and apply these to the physical world.
Course Outline:
I. Three-Dimensional Analytic Geometry and Vectors

A. Three-dimensional rectangular coordinate system

B. Vectors

C. Dot and cross products

D. Equations of lines and planes

E. Quadric surfaces

F. Vector-valued function

G. Space curves, arc length, and curvature

H. Velocity and acceleration in three-dimensional space

I. Other coordinate systems

II. Multivariable Differential Calculus

A. Functions of several variables

B. Limits and continuity

C. Partial derivatives

D. Differentials and tangent planes

E. Chain rule

F. Directional derivatives and the gradient vector

G. Maximums and minimums

H. Lagrange multipliers

III. Multivariable Integral Calculus

A. Double integrals in rectangular coordinates

B. Double integrals in polar coordinates

C. Triple integrals in rectangular coordinates

D. Triple integrals in cylindrical and spherical coordinates

E. Applications of double and triple integrals

IV. Vector Calculus

A. Vector fields

B. Line integrals

C. Fundamental theorem of line integrals

D. Green’s theorem

E. Curl and divergence

F. Surface integrals

G. Stokes theorem

H. Divergence theorem

Facilitated discussion: 10-80%

Group work: 5-30%
Mandatory Course Components:
None
Equivalent Courses:
None