TRI-COUNTY TECHNICAL COLLEGE

COURSE SYLLABUS

Course Prefix & Number:    MAT 240

Course Title:                          Analytic Geometry and Calculus III

Class  Hours                        Lab Hours                     Credits

Per week:    4.0                   Per Week:  0                  Awarded:  4

Catalog  Description:           

This course includes the following topics:  multivariable calculus including vectors, partial derivatives and their application to maximum and minimum problems with and without constraints; line integrals; multiple integrals in rectangular and other coordinates; and Stokes’ and Green’s theorems. 

Entry Level Skills:  Two semesters of calculus

Pre-requisites:  MAT 141, Analytic Geometry and Calculus II

Co-requisites: None

Text(s)/Required Materials: Calculus Early Transcendental function, Fourth Edition, by Ron Larson, Robert Hostetler, Bruce H. Edwards, published by Houghton Mifflin Company, 2007

Equipment: A graphing calculator is required.  A model with a computer algebra  system (such as the TI-89 or TI-92 Plus) is recommended

Course Competencies and Objectives / Major Course Topics:      

Unit 1: Vectors and Geometry of Space

Upon completion of this unit (Chapter 11) the successful student should be able to:

1.        Sketch vectors as arrow in coordinate plane.

2.        Express the vectors in terms of their lengths and directions.

3.        Add or subtract vectors and their scalar multiples.

4.        Find the distance between two points in space and write the equation of sphere.

5.        Expressing any vector in terms of the standard basic vectors i, j, k.

6.        Find the unit vector in any direction.

7.        Perform the dot product of two vectors.

8.        Find the angle between two vectors.

9.        Write a vector as sum of orthogonal vectors.

10.    Find the vector product of two vectors in space.

11.    Perform the test for parallelism.

12.    Find the volume of a box by the triple scalar or box product.

13.    Write the parametric equations for the line segments joining the points in space

14.    Find the point in which the line meets the plane.

15.    Sketch cylinders, ellipsoids, paraboloid, cones, hyperboloid, and hyperbolic paraboloid surfaces.

16.    Converting rectangular, cylindrical, and spherical coordinate to each other.

17.    Describe and sketch the surfaces in space represented by equations or inequalities.

Unit 2: Vector-Valued Functions

Upon completion of this unit (Chapter 12) the successful student should be able to:

1.      Find the domain and limit of a vector-valued function.

2.      Describe and sketch the curve defined by a vector-valued function

3.      Find the derivative, differential, and integral of a vector-valued function.

4.      Find the velocity, acceleration, and speed of particle in space.

5.      Describe the velocity and acceleration associated with a vector-valued function.

6.      Use a vector-valued function to analyze projectile motion.

7.      Find unit tangent and unit normal vectors.

8.      Find the length of a given curve.

9.      Find the curvature of a plane curve, and curvature of a curve in space.

10.  Evaluate the tangential and normal scalar components of acceleration.

Unit 3: Functions of  Several Variables

Upon completion of this unit (Chapter 13) the successful student should be able to:

1.      Find the domain and the range of a function of two or more variables.

2.      Evaluate the value of a function at a point.

3.      Describe the level curve and find the equation for the level curve of a function.

4.      Sketch the graph of functions and their level curves

5.      Evaluate the limit of a multivariable function.

6.      Discuss the limit and continuity of a function with two variables.

7.      Find first, second, and mixed partial derivatives of a function

8.      Find equations for the tangent plane and normal line of the surface.

9.      Find the linear approximation of a function at a given point.

10.  Find the differential of a function.

11.  Use the differential to estimate the maximum error in a calculation.

12.  Apply the chain rule for multivariable functions.

13.  Apply the chain rule to find partial derivatives.

14.  Calculate the directional derivatives and gradient of a function.

15.  Find the direction of maximum rate of change.

16.  Find maximum, minimum, and saddle point of a function.

17.  Apply the first derivative test for local extreme values.

18.  Use the second partial derivatives test to find relative extrema of a function of two variables.

19.  Use the Method of LaGrange Multipliers to find the greatest and smallest values of a function subjected to a given constraint.

Unit 4: Multiple Integration

Upon completion of this unit (Chapter 14) the successful student should be able to:

1.      Evaluate and interpret a given double integral.

2.      Estimate the volume of the solid that lies above a region.

3.      Sketch the region of integration and reverse the order of integration.

4.      Find the area of a region by double integral.

5.      Find the volume of a given solid by using double integral.

6.      Change Cartesian integral into equivalent polar integral and evaluate the polar integral.

7.      Use double integral to find the area of a region for polar equations.

8.      Find the center of mass and moments by using double integrals.

9.      Find the area of a surface lies above a region.

10.  Find the volume of irregular three-dimensional shapes by triple integrals.

11.  Find the mass, center of mass and moments of three-dimensional object.

12.  Evaluate triple integrals in cylindrical and spherical coordinates.

13.  Find the Jacobian of a transformation.

14.  Evaluate multiple integrals by substitution.

 Upon completion of this unit (Chapter 15) the student should be able to:

 1.      Describe and sketch a given vector field.

 2.      Determine whether a vector field is conservative or not.

 3.      Find the curl, and divergence of a vector field.

 4.      Integrate a function along a given path.

 5.      Find the mass and the center of mass for wires, springs, and thin rods by using line integrals.

 6.      Evaluate the work done by a vector field over a curve.

 7.      Find a potential function for a conservative vector field.

 8.      Apply Green’s theorem to evaluate the line integral of a region enclosed by a piecewise smooth, simple, closed curve.

 9.      Find the parametric representation for a surface.

 10.  Integrate a function over a curved surface.

 11.  Find the center of mass and moment for thin shells.

 12.  Find the flux of a vector field by using the divergence theorem.

 13.  Use Stokes’ Theorem to evaluate a surface integral.

  Grade Calculation Method:                          Unit 1    = 16%

                                                                         Unit 2    = 16%                                 

                                                                         Unit 3    = 16%

                                                                         Unit 4    = 16%

 Unit 5    = 16%

                                                                Final Exam     = 20%                  

                                                                                     ________

                                                                                         100%

Prepared by: Mohammad Ghobadi              Date written or revised: April 4, 2007