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Status: Historical
 
PALOMAR COLLEGE
 COURSE OUTLINE FOR CREDIT COURSE
 
  • Courses numbered 1 - 49 are remedial or college preparatory courses which do not apply toward an A. A. Degree and are not intended for transfer.
  • Courses numbered 50-99 apply toward an AA Degree, but are not intended for transfer.
  • Courses numbered 100 and higher apply toward an AA Degree and/or are intended for transfer to a four-year college or university.
 
Course Number and Title: MATH 205 Calculus with Analytic Geometry, Third Course
 

Unit Value: 4  

Lecture Hours Per Week: 4  

Lab Hours Per Week:  

Lecture/Lab Hours Per Week:  

 

Grading Basis: Grade/Pass/No Pass
 
Basic Skills Requirements: Appropriate Language and/or Computational Skills.
 
Requisite(s)
To satisfy a prerequisite, the student must have earned a letter grade of A, B, C or P(Pass) in the prerequisite course, unless otherwise stated.
Prerequisite:
A minimum grade of 'C' in MATH 141
Corequisite:
None
Prerequisite: Completion of, or concurrent enrollment in
None
Recommended Preparation:
None
Limitation on Enrollment:
None
Catalog Description:
Vectors in the plane and space, three-dimensional coordinate system and graphing, vector-valued functions and differential geometry, partial differentiation, multiple integration, and vector calculus.
 
Specific Course Objectives:
Upon successful completion of the course the student will be able to:
  1. Do computations with vectors in the plane and space, including dot and cross products, and solve application problems with vectors.
  2. Find the equations of lines and planes in space
  3. Solve problems and graph in rectangular coordinates, cylindrical coordinates, and spherical coordinates.
  4. Know the graphs of surfaces in space
  5. Calculate limits, derivatives, and integrals of vector-valued functions, and solve application problems with vector-valued functions.
  6. Calculate arc length, curvature, tangential and normal components of acceleration, and velocity of vector-valued functions.
  7. Calculate partial derivatives of functions of several variables.
  8. Calculate differentials, directional derivatives, equations of tangent planes and normal lines.
  9. Solve application problems of functions of several variables, using the 2nd-Derivatives test and Lagrange Multipliers.
  10. Set up and calculate double and triple integrals using rectangular, cylindrical, spherical, and polar coordinates.
  11. Change variables in multiple integration.
  12. Use multiple integration to solve application problems, including finding area and volume.
  13. Set up and calculate line integrals and surface integrals.
  14. Understand and apply Green's Theorem, the Divergence Theorem, Stokes Theorem, and the Fundamental Theorem of Line Integrals.
 
Methods of Instruction:
Methods of Instruction may include, but are not limited to, the following:
  1. Lecture
 
Content in Terms of Specific Body of Knowledge:

At least the following topics will be covered:

  1. Vectors
    1. Dot product
    2. Cross product
    3. Vector projections
    4. Unit vectors
    5. Lines in space
    6. Planes
    7. Applications
  2. 3-Dimensional Coordinate Systems
    1. Graphing Surfaces
    2. Change of coordinate systems
    3. Midpoint and distance formulas
  3. Vector-Valued Functions
    1. Definition of limits, derivatives, and integrals
    2. Evaluation of limits, derivatives, and integrals
    3. Tangent and Normal Vectors
    4. Applications
  4. Differential Geometry
    1. Velocity
    2. Acceleration
    3. Arc length
    4. Curvature
  5. Partial Differentiation
    1. Limits and Continuity of Functions of Several Variables
    2. Definition of partial derivatives
    3. Computation of partial derivatives
    4. Chain Rule
    5. Differentials
    6. Directional derivatives
    7. Gradients
    8. Tangent planes and Normal Lines
    9. 2nd-partials test
    10. Lagrange Multipliers
    11. Functions of several variables
    12. Level curves and level surfaces
    13. Applications
  6. Multiple Integration
    1. Iterated integrals
    2. Definition of double and triple integrals
    3. Double and triple integrals using rectangular coordinates, polar coordinates, cylindrical coordinates, and spherical coordinates.
    4. Area and volume
    5. Center of Mass and Moments of Inertia
    6. Applications
  7. Vector Calculus
    1. Vector fields
    2. Divergence
    3. Curl
    4. Line integrals
    5. Surface Integrals
    6. Green's Theorem
    7. Stoke's Theorem
    8. Divergence Theorem
    9. Fundamental Theorem of Line Integrals
    10. Applications
  8. Additional topics may be included at instructor's discretion.
Textbooks/Resources:
May Include Textbooks, Manuals, Periodicals, Software, and Other Resources
  1. Stewart, James. Multivariable Calculus: Early Transcendentals, 5th Edition, pp 792-1139. Belmont: Brooks/Cole-Thomson Learning, Inc. 2003. OR
  2. Equivalent pages from other multivariable texts.
Required Reading:
Instructors will require reading in a textbook on Multivariable Calculus
 
Suggested Reading:
Additional reading may be included at instructor's discretion.
 
Critical Thinking:
Students are expected to apply critical thinking and quantitative reasoning skills to mathematical problem solving and related areas of endeavor.
 
Required Writing:
Problem-solving exercises on homework assignments and written tests are more appropriate. Homework assignments may require the students to write out detailed solutions at least one paragraph in length. Some essay questions may be assigned when appropriate. These essays will be of 1 to 3 pages in length. Examinations may also require the students to write solutions to problems. These will be 1 to 10 pages in length. All writing assignments will require the use of correct grammar and punctuation. In addition, students may be required to write reports from one paragraph to several pages explaining concepts or explaining and interpreting solutions to non-routine or applied problems.
 
Outside Assignments:
Students are expected to spend a minimum of three hours per unit per week in class and on outside assignments, prorated for short-term classes.

Instructors may require students work exercise in the textbook.
 
Methods of Assessment:
Methods of Assessment may include, but are not limited to, the following:
  • Exams/Tests
  • Homework
  • Quizzes
  • Class Participation
  • Class Work
 
Open Entry/Open Exit:
No, course is not offered as open entry/open exit.
 
Is Course Repeatable for Reason(s) Other Than Deficient Grade? No
 
Contact Person: Jay R. Wiestling