Discipline: Mathematics Degree Credit  [X]
Non Credit  [ ]
Nondegree Credit  [ ]
Comm Service  [ ]
 

Riverside Community College District
Integrated Course Outline of Record

Mathematics 1C


COURSE DESCRIPTION
1C Calculus III Units: 4.00
 
Prerequisite(s): MAT 1B: Calculus II
Vectors in a plane and in space, vector valued functions, partial derivatives, multiple integrals, line and surface integrals, indeterminate forms, and elementary applications to the physical sciences. 72 hours lecture.
 
SHORT DESCRIPTION FOR CLASS SCHEDULE
Vectors, partial differentiation, and multiple integrals with applications.
 
ADVISORY ENTRY SKILLS
None.

STUDENT LEARNING OUTCOMES
 Upon successful completion of the course, students should be able to:

1.  Write vector dot and cross products and apply dot and dross product to writing equations for lines and planes and surfaces in space.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

2.  Write Cartesion equations, in Spherical and cylindrical coordinates.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Integrate knowledge across a range of contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

3.  Differentiate and integrate vector valued functions.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

4.  Apply integration and differentiation to finding velocity and acceleration of bodies in space.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

5.  Find unit tangent and unit normal vectors and their application to velocity, acceleration and curvature.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

6.  Compute partial derivatives, differentials, directional derivatives and gradients.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  3. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

7.  Apply partial derivatives and language multipliers to solve the Optimization Problems

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

8.  Compute double and triple integrals and apply double and triple integration to the solution of center of mass, area, and volume problems.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

9.  Use the Jacobian and transformation of coordinates to solve multiple integration problems

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

10.  Graph vector fields

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Integrate knowledge across a range of contexts
  3. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

11.  Compute line and surface integrals

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  3. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

12.  Use Green’s Divergence and Stoke’s Theorems to solve various types of physical applications.
   

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace
 
COURSE CONTENT
  TOPICS
 

1.   Vectors and the geometry of space
      a.   Dot and cross products, lines, planes, and surfaces in space,
            cylindrical and spherical coordinates
2.   Vector-valued functions
      a.   Differentiation and integration, velocity and acceleration,
            tangent and normal vectors
3.   Functions of several variables
      a.   Limits and continuity, partial derivatives, differentials, 
           directional derivatives and gradients, extrema application, 
           Lagrange multipliers.
4.   Multiple integration
      a.   Double integrals, center of mass and centroids, first and 
            second moments, triple integrals, applications of double and
            triple integrals, change of variables; Jacobians
5.   Vector analysis
      a.   Vector fields, line integrals, surface integrals, Green’s 
            divergence and Stokes Theorems
 
METHODS OF INSTRUCTION
 Methods of instruction used to achieve student learning outcomes may include, but are not limited to:

  • Class lectures/discussions/demonstrations
  • Drills and pattern practices
  • Videos/films/slides/audio tapes
  • Pair and small group activities/discussion
  • Class exercises
  • Reports and papers
  • Handouts
  • Cooperative learning tasks
  • Online/distance education and technology based
 
METHODS OF EVALUATION
 Students will be evaluated for progress in and/or mastery of learning outcomes by methods of evaluation which may include, but are not limited to:

  • Oral reports/presentations/performance
  • Written reports/presentations
  • Quizzes/examinations
  • Written assignments
  • Class and individual projects
  • Final examination
ASSIGNMENTS

Required Reading Assignments


Required Writing Assignments


Other Outside-of-Class Assignments
 
COURSE MATERIALS
 All materials used in this course will be periodically reviewed to ensure that they are appropriate for college level instruction. Possible texts include:

  • Steward. Calculus, Multivariable. 4th ed. Brooks/Cole, 1999.
  • Larson Hostetler, Edwards. Multivariable Calculus. 6th ed. Houghton Mifflin Company, 1998.
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