ANALYTICAL GEOMETRY AND CALCULUS II 0031 ( Official )
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ANALYTICAL GEOMETRY AND CALCULUS II 0031 ( Official )
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ANALYTICAL GEOMETRY AND CALCULUS II 0031 ( Official )

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SECTION A

 

1. Division:

  Sciences & Mathematics

2. Course Discipline:

  MATH

3. Course Number:

  0031

4. Course Title:

  ANALYTICAL GEOMETRY AND CALCULUS II

5. First semester this new version/new course will be offered: Fall 2015



 

 

SECTION B

General Course Information

 

1. Units: 4.0                 Variable units N/A

2. This Course is:

Degree-Applicable Credit - Transferable

 

3A.  Cross-List: 

  

3B.  Formerly:

  

 

 

Course Format and Duration

 

4. Standard Term Hrs per Wk

      

5. Standard Term Total Semester Hrs

Lecture/Discussion:  

               4

 

Lecture/Discussion:  

              72

Laboratory:

                 

 

Laboratory:

                 

Activity:

                 

 

Activity:

                 

By Arrangement:

                 

 

By Arrangement:

                 

Total Hrs per Wk

               4

 

Total Hrs

              72

 

6. Minimum hours per week of independent work done outside of class:    8

 

Course Preparation – (Supplemental form B required)

 

7a. Prerequisite(s): (Course and/or other preparation/experience that is REQUIRED to be completed previous to enrollment in this course.)

Completion of MATH 30 with grade of "C" or better

    

7b. Co-requisite(s):  (Courses and/or other preparation that is REQUIRED to be taken concurrently with this course.)


    

7c. Advisory: (Minimum preparation RECOMMENDED in order to be successful in this course.  Also known as “Course Advisory”.)


    

 

 

Catalog Description And Other Catalog Information

 

8. Repeatability:

Not Repeatable

Please Note: 8. (Repeatability) does not refer to repeating courses because of substandard grades or a lapse of time since the student took the course. A course may be repeated only if the course content differs each time it is offered and the student who repeats it is gaining an expanded educational experience as stipulated in Title 5.

 

Skills or proficiencies are enhanced by supervised repetition and practice within class periods.

Active participatory experience in individual study or group assignments is the basic means by which course objectives are attained.

Course content differs each time it is offered.

 

Explanation for above repeatability selection:


    

9a. Grading Option:

Standard Grade

9b. Catalog Description:

Continuation of MATH 30. Content includes techniques of integration, improper integrals, applications of integration, infinite series, parametric equations and polar coordinates.

    

 

 

Course Outline Information

 

10. Course Objectives: (Course objectives for all credit courses must indicate that students will learn critical thinking and will be able to apply concepts at college level.  Course objectives must be related to items listed in Section 11.)

1. Evaluate definite and indefinite integrals using a variety of integration formulas and techniques;
2. Apply integration to areas and volumes, and other applications such as work or length of a curve;
3. Evaluate improper integrals;
4. Apply convergence tests to sequences and series;
5. Represent functions as power series; and
6. Graph, differentiate and integrate functions in polar and parametric form.

    

11. Course Content Outline: (Provides a comprehensive, sequential outline of the course content, including all major subject matter and the specific body of knowledge covered.)

1. Areas between curves;
2. Volume, volume of a solid of revolution;
3. Additional techniques of integration including integration by parts and trigonometric substitution;
4. Numerical integration; trapezoidal and Simpson's rule;
5. Improper integrals;
6. Applications of integration to areas and volumes;
7. Additional applications such as work, arc length, area of a surface of revolution, moments and centers of mass, separable differential equations, growth and decay;
8. Introduction to sequences and series;
9. Multiple tests for convergence of sequences and series;
10. Power series, radius of convergence, interval of convergence;
11. Differentiation and integration of power series;
12. Taylor series expansion of functions;
13. Parametric equations and calculus with parametric curves; and
14. Polar curves and calculus in polar coordinates.

    

12. Typical Out-of-Class Assignments: Credit courses require two hours of independent work outside of class per unit of credit for each lecture hour, less for lab/activity classes.  List types of assignments, including library assignments.)

    

a. Reading Assignments: (Submit at least 2 examples)

Example 1: Read in your textbook about 2 methods for calculating the volume of a solid of revolution.

Example 2: Research online the history of Newton's discovery of the Binomial Series.

    

b. Writing, Problem Solving or Performance: (Submit at least 2 examples)

1. Students will write a 3 - 5 paragraph report on Newton's discovery of the binomial series.
2. Calculate areas bounded by polar graphs. Example: Find the area enclosed inside the cardiod r = 5cos(t) and outside the rose r = 2sin(3t).

    

c. Other (Term projects, research papers, portfolios, etc.)


    

13. Required Materials:

a. All Textbooks, resources and other materials used in this course are College Level?

  Yes

  No

 

b. Representative college-level textbooks (for degree-applicable courses) or other print materials.

Book 1:

Author:

  William Briggs and Lyle Cochran

Title:

  Calculus for Scientists and Engineers: Early Transcendentals

Publisher:

  Addison-Wesley

Date of Publication:

  2014

Edition:

  2nd

Book 2:

Author:

  

Title:

  

Publisher:

  

Date of Publication:

  

Edition:

  

Book 3:

Author:

  

Title:

  

Publisher:

  

Date of Publication:

  

Edition:

  

Book 4:

Author:

  

Title:

  

Publisher:

  

Date of Publication:

  

Edition:

  

Book 5:

Author:

  

Title:

  

Publisher:

  

Date of Publication:

  

Edition:

  

c. Other materials and/or supplies required of students:


 

Methods of Instruction

 

14a. Check all instructional methods used to present course content.

Lecture/Discussion

Laboratory and/or Activity

Distance Learning (requires supplemental form)

Other:

   

 

14b. Provide specific examples for each method of instruction checked above; include a minimum of two examples total. Reference the course objective(s) addressed by instructional method(s). Explain both what the instructor and students are expected to be doing and experiencing.

Example 1- Interactive lecture format to develop the concept of finding a power series representation of a variety of functions. For each type of function, the instructor will incorporate algebraic derivation and visual analysis through graphing. Students will participate verbally and will work several examples.

Example 2: In class, small group collaborative learning activities will focus on determining which methods of integration to use for a variety of problems. Students will practice recognizing which method to try, testing their conjectures, and developing solutions with peers.

 

 

 

15. Methods of Assessing Student Learning  

 

15a.  Methods of Evaluation:

 

Essay Examinations

Objective Examinations

Problem Solving Examinations

Skill Demonstrations

Projects

 

Classroom Discussions

 

Reports

 

Other (explain below)

 

 

 

 

 

 

15b. Based upon course objectives, give examples of how student performance will be evaluated. Provide examples for each method checked above; include a minimum of two examples total.

 

 

 

1. Find the volume generated when the region bounded by the curves y = cos x and y = (cos x)^2 for values of x between x = 0 and x = pi, is revolved about the y axis. This problem is graded for correct method and accuracy.

2. Use Taylor's Inequality to determine the number of terms of the Maclaurin series for e^x that should be used to estimate e^0.1 to within 0.00001. This problem is graded for method and accuracy.

 

 

 

 

 

 

 

 

 

SECTION C

 

1. Program Information:  

In an approved program.  

Part of a new program.

Not part of an approved program.  

2. Course TOP Code:

   Program title - TOP Code:  

Mathematics, General- 170100

 

3. Course SAM Code:

 A  Apprenticeship

 B  Advanced Occupational

 C  Clearly Occupational

 D  Possibly Occupational

 E  Non-Occupational

 

4. Faculty Discipline Assignment(s):

 

Mathematics

 

Comments:


 

     

 

SECTION D

 

General Education Information:  

1.  College Associate Degree GE Applicability:    


Communication & Analytic Thinking
Math Competency

2.  CSU GE Applicability (Recommended-requires CSU approval):


B-4 Mathematics/Quantitative Reasoning

3.  IGETC Applicability (Recommended-requires CSU/UC approval):  


2: Mathematical Concepts & Quantitative Reasoning

4. C-ID:  

  MATH 220 Single Variable Calculus II Early Transcendentals; and, with MATH 30, MATH 900S Single Variable Calculus Sequence

 

 

SECTION E

 

Articulation Information:  (Required for Transferable courses only)

 1.  

 

CSU Transferable.  

UC Transferable.

CSU/UC major requirement.  

  

If CSU/UC major requirement, list campus and major. (Note: Must be lower division)

 

 


 2.

List at least one community college and its comparable course.  If requesting CSU and/or UC transferability also list a CSU/UC campus and comparable lower division course.

 

American River College: MATH 401 Calculus II
CSU Sacramento: MATH 31 Calculus II
UC Davis: MATH 21B Calculus

 

 

SECTION F

 

Planning and Resources - Please address the areas below:  

1. Evidence of Planning: connection to existing or planned degrees/certificates, place in general education; relationship to mission (basic skills, transfer, career technical education, lifelong learning); transfer university requirements; advisory/regional/national needs; or other planning considerations.

Required for all math, physics, and engineering majors.
Transfer-level math class.
Meets GE applicability for Math Competency and Communication and Analytical Thinking. Course includes all four math program SLO's. (Equations and Expressions, Visual Models, Applied Problems, Communication)

 
2. Potential Impact on Resources: faculty, facilities, computer support/lab, library, transportation, equipment, or other needs.
All math faculty members meet the minimum qualifications to teach this course. No special training would be required.
No additional resources are needed since we have the classroom space and technology already available.

 

 

 

SECTION G

1.  Maximum Class Size (recommended):              35

2.  If recommended class size is not standard, then provide rationale: