ANALYTICAL GEOMETRY AND CALCULUS I 0030 ( Official )
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ANALYTICAL GEOMETRY AND CALCULUS I 0030 ( Official )
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ANALYTICAL GEOMETRY AND CALCULUS I 0030 ( Official )

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SECTION A

 

1. Division:

  Sciences & Mathematics

2. Course Discipline:

  MATH

3. Course Number:

  0030

4. Course Title:

  ANALYTICAL GEOMETRY AND CALCULUS I

5. First semester this new version/new course will be offered: Fall 2018



 

 

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 27 and either MATH 12 or 29 with grades of "C" or better, or placement by matriculation assessment process

    

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:

Introduction to differential and integral calculus. Content includes limits, continuity, differentiation and integration of algebraic, trigonometric, exponential, logarithmic, hyperbolic and other transcendental functions; as well as application problems.

    

 

 

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. Compute the limit of a function at a real number.
2. Determine if a function is continuous at a real number.
3. Find the derivative of a function as a limit.
4. Find the equation of a tangent line to a function.
5. Compute derivatives using differentiation formulas.
6. Use differentiation to solve applications such as related rate problems and optimization problems.
7. Use implicit differentiation.
8. Graph functions using methods of calculus.
9. Evaluate a definite integral as a limit.
10. Evaluate integrals using the Fundamental Theorem of Calculus.
11. Apply integration to find area.

    

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.)

I. Definition and computation of limits using numerical, graphical, and algebraic approaches
II. Continuity and differentiability of functions
III. Derivative as a limit
IV. Interpretation of the derivative as: slope of tangent line, a rate of change
V. Differentiation formulas: constants, power rule, product rule, quotient rule and chain rule
VI. Derivatives of transcendental functions such as trigonometric, hyperbolic, exponential or logarithmic
VII. Implicit differentiation with applications, and differentiation of inverse functions
VIII. Higher-order derivatives
IX. Graphing functions using first and second derivatives, concavity and asymptotes
X. Maximum and minimum values, and optimization
XI. Mean Value Theorem
XII. Antiderivatives and indefinite integrals
XIII. Area under a curve
XIV. Definite integral; Riemann sum
XV. Properties of the integral
XVI. Fundamental Theorem of Calculus
XVII. Integration by substitution
XVIII. Derivatives and integrals of inverse functions and transcendental functions such as trigonometric, exponential or logarithmic
XIX. Indeterminate forms and L'Hopital's Rule

    

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)

1. Read in your textbook how the first and second derivative of a function influence the graph of the function and be prepared to discuss in class.

2. Research online the history of the development of calculus, including Newton and Leibniz and be prepared to discuss in class.

    

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

1. Write a report on the historical and mathematical origins of l'Hospital's rule.

2. After reading about Newton's and Leibniz's development of calculus, write a 3 - 5 paragraph essay comparing and contrasting each approach.

    

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 & 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 what a derivative represents, given a variety of functions (e.g., rational, polynomial, trigonometric, exponential, logarithmic). To help students see the commonalities and differences between the derivatives of each type of function, the instructor will incorporate algebraic analysis through equations 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 applied physics problems involving derivatives. These will include analysis of velocity, acceleration, and other instantaneous rates of change. Students will practice reading problems, interpreting problems, 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. A particle moves on a vertical line so that its coordinate at time t is y = t^3 - 12t + 3, for t > 0. Find the velocity and acceleration functions. When is the particle moving upwards and when is it moving downwards? Find the distance the particle moves in the time interval t = 1 to t = 3. This problem is graded for correct method and accuracy.

2. Find an equation of the line through the point (3, 5) that cuts off the least area from the first quadrant. 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
Physical Sciences

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 210 Single Variable Calculus I Early Transcendentals; and, with MATH 31, 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 400 Calculus I
CSU Sacramento: MATH 30 Calculus I
UC Davis: MATH 21A 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: