Course Discipline and



GAVILAN COLLEGE

CURRICULUM DEVELOPMENT

|form C |

|Modify or Inactivate an Existing Course |

|Date: |May 2, 2012 |Prepared & Submitted by: |Ken Wagman |

|Department: |Nat. Sci. |Course Discipline and Number: |Math 1C |

|1. |What is the effective term? |

| |Fall Spring Summer Year: 2012 |

|2. | Inactivate Course(s): (Inactivating a course will remove it from the course catalog. Courses may be re-activated by updating the course |

| |and bringing it back to the Curriculum Committee for approval. Transferable courses will need to be re-articulated, should you decide to |

| |reactivate the course.) |

| |Reason for inactivation:       |

|3. | Modification of the following: (Attach existing course outline, note changes as appropriate. Update Prerequisite/Advisory Form, if |

| |appropriate ) |

| Number | Hours | Prerequisite/Advisory | Discipline |

| Title | Units | Description | Content |

| Grading | GE Applicability | Repeatability | Transferability |

| General Update | Reinstate Course | Cross list course with       |

| Update Textbook | Other (please describe.)       |

|FROM: |      |      |      |      |      |

| |Discipline & Number |Course Title |Units |Lec |Lab |

| | | | |Hours per |Hours per |

| | | | |week |week |

|TO: |      |      |      |      |      |

| |Discipline & Number |Course Title |Units |Lec |Lab |

| | | | |Hours per |Hours per |

| | | | |week |week |

|Reason for modification:       |

|4. |Will this course be offered via distance education? Yes No |

| |If yes, fill out Form D – Distance Education form. |

5. Routing/Recommendation for Approval

Signatures Approval

Dept. Approval (Chair Sign) __________________________________ Date ______________ Yes___ No___

Area Dean __________________________________ Date ______________ Yes___ No___

Curriculum Committee Chair __________________________________ Date ______________ Yes___ No___

VP of Instruction __________________________________ Date ______________ Yes___ No___

Superintendent/President

For District Board __________________________________ Date ______________ Yes___ No___

GAVILAN COLLEGE

CURRICULUM DEVELOPMENT

|COURSE OUTLINE | |

|DISCIPLINE: |      |DEPARTMENT: |      |

| |(Discipline and Number) | | |

|COURSE TITLE: |Multivariable Calculus |

(Maximum of 58 spaces)

|ABBREVIATED TITLE: |MULTIVARI CALCULUS |

(Maximum of 28 spaces)

|SEMESTER UNITS:       |LEC HOURS PER WEEK:       |LAB HOURS PER WEEK:       |

|Classification: |Non Credit Category: |Occupational Code (SAM): |

|TOP Code: 0000.00 |LEH Factor:       |FTE Load:       |

CATALOG DESCRIPTION:

No Change Change

     

COURSE REQUISITES:

List all prerequisites separated by AND/OR, as needed. Also fill out and submit the Prerequisite/Advisory form.

No Change

Replaces existing Advisory/Prerequisite

In addition to existing Advisory/Prerequisite

Prerequisite:      

Co-requisite:      

Advisory:      

GRADING SYSTEM:

No Change

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REPEATABLE FOR CREDIT:

(Note: Course Outline must include additional skills that will be acquired by repeating this course.)

No Change

Credit Course Yes No If yes, how many times? 1 2 3

Non Credit Course Yes No If yes, how many times? 1 2 3 Unlimited

(Noncredit only)

STAND ALONE:

No Change

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[pic]

METHODS OF INSTRUCTION:

No Change

     

RECOMMENDED OR REQUIRED TEXT/S:

(The following information must be provided: Author, Title, Publisher, Year of Publication, Reading level and Reading level verification)

Required: Recommended: n/a

Author: Stewart Title: Calculus, Early Transcendentals, 7th edition Publisher: Brooks/Cole Year of Publication: 2012, or other appropriate college level text.

ISBN:       (if available)

Reading level of text, Grade: 14 Verified by: Ken Wagman

Other textbooks or materials to be purchased by the student: Graphing calculator

CULTURAL DIVERSITY:

Does this course meet the cultural diversity requirement? Yes No

If Yes, please indicate which criteria apply. At least two criteria must be selected and evidenced in the course content section and at least one Student Learning Outcome must apply to cultural diversity.

This course promotes understanding of:

Cultures and subcultures

Cultural awareness

Cultural inclusiveness

Mutual respect among diverse peoples

Familiarity with cultural developments and their complexities

SLO #      

PROGRAM LEARNING OUTCOMES:

Is this course part of a program (degree or certificate)? If yes, copy and paste the appropriate Program Learning Outcomes and number them. Enter the PLOs by number in the Student Learning Outcomes below.

No change

STUDENT LEARNING OUTCOMES:

1. Complete this section in a manner that demonstrates student’s use of critical thinking and reasoning skills. These include the ability to formulate and analyze problems and to employ rational processes to achieve increased understanding. Reference Bloom's Taxonomy of action verbs.

2. List the Type of Measures that will be used to measure the student learning outcomes, such as written exam, oral exam, oral report, role playing, project, performance, demonstration, etc.

3. Identify which Program Learning Outcomes (PLO) are aligned with this course. List them by number in order of emphasis.

4. Identify which Institutional Learning Outcomes (ILO) are aligned with this course. List them, by number in order of emphasis. For example: "2, 1" would indicate Cognition and Communication.

(1) Communication, (2) Cognition, (3) Information Competency, (4) Social Interaction, (5) Aesthetic Responsiveness, (6) Personal Development & Responsibility, (7) Content Specific.

5. For GE courses, enter the GE Learning Outcomes for this course. For example "A1, A2". GE Learning Outcomes are listed below.

6. Indicate when the course was last assessed.

Indicate by number which Program Learning Outcomes, Institutional Learning Outcomes and GE Learning Outcomes are supported by each of the Student Learning Outcomes.

|1. |Identify, describe, and illustrate lines, planes, solids, cylinders, and quadric surfaces using three-dimensional coordinate systems. |

|Measure: Homework, Quiz, Project,|PLO: 1, 2, 3, 4 |ILO: 2, 3, 1 |GE-LO: B3 |Year Assessed: 2012 |

|Exam | | | | |

|2. |Formulate, analyze, and solve problems containing vectors and use parametric equations and vector functions to describe space curves. |

|Measure: Homework, Quiz, Project,|PLO: 1, 2, 3, 4 |ILO: 2, 3, 1 |GE-LO: B3 |Year Assessed: 2012 |

|Exam | | | | |

|3. |Apply differentiation and integration of vector functions to real world problems including arc length, curvature, velocity, and acceleration. |

|Measure: Homework, Quiz, Project,|PLO: 1, 2, 3, 4 |ILO: 2, 3, 1 |GE-LO: B3 |Year Assessed: 2012 |

|Exam | | | | |

|4. |Apply the concepts of domain, range, evaluation, limits, and continuity to functions of more than one variable |

|Measure: Homework, Quiz, Project,|PLO: 1, 2, 3, 4 |ILO: 2, 3, 1 |GE-LO: B3 |Year Assessed: 2012 |

|Exam | | | | |

|5. |Formulate, analyze, and solve problems using partial derivatives including directional derivatives, gradient, and optimizations |

|Measure: Homework, Quiz, Project,|PLO: 1, 2, 3, 4 |ILO: 2, 3, 1 |GE-LO: B3 |Year Assessed: 2012 |

|Exam | | | | |

|6. |Calculate double and triple integrals utilizing various three-dimensional coordinate systems and Jacobian transformations. |

|Measure: Homework, Quiz, Project,|PLO: 1, 2, 3, 4 |ILO: 2, 3, 1 |GE-LO: B3 |Year Assessed: 2012 |

|Exam | | | | |

|7. |Apply integration of mutilvariable functions to real-world problems including mass, moments, center of mass, surface area, and volume. |

|Measure: Homework, Quiz, Project,|PLO: 1, 2, 3, 4 |ILO: 2, 3, 1 |GE-LO: B3 |Year Assessed: 2012 |

|Exam | | | | |

|8. |Identify and sketch vector fields; find and sketch gradient fields. |

|Measure: Homework, Quiz, Project,|PLO: 1, 2, 3, 4 |ILO: 2, 3, 1 |GE-LO: B3 |Year Assessed: 2012 |

|Exam | | | | |

|9. |Calculate line integrals and apply the Fundamental Theorem of Line Integrals and Green's Theorem. |

|Measure: Homework, Quiz, Project,|PLO: 1, 2, 3, 4 |ILO: 2, 3, 1 |GE-LO: B3 |Year Assessed: 2012 |

|Exam | | | | |

|10. |Identify parametric surfaces; calculate surface integrals, and apply Stokes' Theorem and the Divergence Theorem. |

|Measure: Homework, Quiz, Project,|PLO: 1, 2, 3, 4 |ILO: 2, 3, 1 |GE-LO: B3 |Year Assessed: 2012 |

|Exam | | | | |

GENERAL EDUCATION LEARNING OUTCOMES

AREA A Communications in the English Language

After completing courses in Area A, students will be able to do the following:

1. Receive, analyze, and effectively respond to verbal communication.

2. Formulate, organize and logically present verbal information.

3. Write clear and effective prose using forms, methods, modes and conventions of English grammar that best achieve the writing’s purpose.

4. Advocate effectively for a position using persuasive strategies, argumentative support, and logical reasoning.

5. Employ the methods of research to find information, analyze its content, and appropriately incorporate it into written work.

6. Read college course texts and summarize the information presented.

7. Analyze the ideas presented in college course materials and be able to discuss them or present them in writing.

8. Communicate conclusions based on sound inferences drawn from unambiguous statements of knowledge and belief.

9. Explain and apply elementary inductive and deductive processes, describe formal and informal fallacies of language and thought, and compare effectively matters of fact and issues of judgment and opinion.

AREA B Physical Universe and its Life Forms

After completing courses in Area B, students will be able to do the following:

1. Explain concepts and theories related to physical and biological phenomena.

2. Identify structures of selected living organisms and relate structure to biological function.

3. Recognize and utilize appropriate mathematical techniques to solve both abstract and practical problems.

4. Utilize safe and effectives laboratory techniques to investigate scientific problems.

5. Discuss the use and limitations of the scientific process in the solution of problems.

6. Make critical judgments about the validity of scientific evidence and the applicability of scientific theories.

7. Utilize appropriate technology for scientific and mathematical investigations and recognize the advantages and disadvantages of that technology.

8. Work collaboratively with others on labs, projects, and presentations.

9. Describe the influence of scientific knowledge on the development of world’s civilizations as recorded in the past as well as in present times.

AREA C Arts, Foreign Language, Literature and Philosophy

After completing courses in Area C, students will be able to do the following:

1. Demonstrate knowledge of the language and content of one or more artistic forms: visual arts, music, theater, film/television, writing, digital arts.

2. Analyze an artistic work on both its emotional and intellectual levels.

3. Demonstrate awareness of the thinking, practices and unique perspectives offered by a culture or cultures other than one’s own.

4. Recognize the universality of the human experience in its various manifestations across cultures.

5. Express objective and subjective responses to experiences and describe the integrity of emotional and intellectual response.

6. Analyze and explain the interrelationship between self, the creative arts, and the humanities, and be exposed to both non-Western and Western cultures.

7. Contextually describe the contributions and perspectives of women and of ethnic and other minorities.

AREA D Social, Political, and Economic Institutions

After completing courses in Area D, students will be able to do the following:

1. Identify and analyze key concepts and theories about human and/or societal development.

2. Critique generalizations and popular opinion about human behavior and society, distinguishing opinion and values from scientific observation and study.

3. Demonstrate an understanding of the use of research and scientific methodologies in the study of human behavior and societal change.

4. Analyze different cultures and their influence on human development or society, including how issues relate to race, class and gender.

5. Describe and analyze cultural and social organizations, including similarities and differences between various societies.

AREA E Lifelong Understanding and Self-Development

After completing courses in Area E, students will be able to do the following:

1. Demonstrate an awareness of the importance of personal development.

2. Examine the integration of one’s self as a psychological, social, and physiological being.

3. Analyze human behavior, perception, and physiology and their interrelationships including sexuality, nutrition, health, stress, the social and physical environment, and the implications of death and dying.

AREA F Cultural Diversity

After completing courses in Area F, students will be able to do the following:

1. Connect knowledge of self and society to larger cultural contexts.

2. Articulate the differences and similarities between and within cultures.

|CONTENT, STUDENT PEFORMANCE OBJECTIVES and OUT-OF CLASS ASSIGNMENTS. |

|No Change |

|Copy and paste the existing content from the official course outline of record. Edit the content as needed. |

|WEEK 1 4 HOURS CONTENT |

|Course introduction. Three-dimensional coordinate systems; distance formula; Vectors. |

|HOMEWORK |

|Read sections covered in textbook and complete homework assignments. |

|PERFORMANCE OBJECTIVES |

|The students will be able to: Represent points, lines, planes and regions in three dimensional coordinates; Perform basic vector operations. |

|WEEK 2 4 HOURS CONTENT |

|Dot product; direction angles and direction cosines; projections. Cross product. |

|HOMEWORK |

|Read sections covered in textbook and complete homework assignments. |

|PERFORMANCE OBJECTIVES |

|The students will be able to: Perform dot product, cross product, and triple product calculations; Apply the concepts to direction angles and cosines, |

|work, projections, torque, areas and volumes. |

|WEEK 3 4 HOURS CONTENT |

|Vector and parametric equations of lines and planes. |

|Cylinders and quadric surfaces. |

|HOMEWORK |

|Read sections covered in textbook and complete homework assignments. Complete a project that applies vectors to a three-dimensional coordinate system. |

|PERFORMANCE OBJECTIVES |

|The students will be able to: Represent lines and planes using vector, parametric, symmetric, and linear forms; Identify and sketch cylinders and |

|quadric surfaces. |

|WEEK 4 4 HOURS CONTENT |

|Cylindrical and spherical coordinates. Vector functions and space curves. |

|HOMEWORK |

|Read sections covered in textbook and complete homework assignments. |

|PERFORMANCE OBJECTIVES |

|The students will be able to: Convert between rectangular, cylindrical, and spherical coordinates; Identify surfaces and solids using cylindrical and |

|spherical coordinates; Find domains and limits of vector functions; Sketch space curves by hand and illustrate them with computer software. |

|WEEK 5 4 HOURS CONTENT |

|Derivatives and integrals of vector functions. Arc length and curvature; normal and binormal vectors. |

|HOMEWORK |

|Read sections covered in textbook and complete homework assignments. |

|PERFORMANCE OBJECTIVES |

|The students will be able to: Find derivatives of vector functions; Evaluate integrals of vector functions; Find arc length, curvature; find unit |

|tangent, normal, and binormal vectors. |

|WEEK 6 4 HOURS CONTENT |

|Velocity and acceleration; Kepler's Laws of planetary motion. Functions of two or more variables. |

|HOMEWORK |

|Read sections covered in textbook and complete homework assignments. Complete a project that explores Kepler's Laws. |

|PERFORMANCE OBJECTIVES |

|The students will be able to: Calculate velocity, acceleration, speed, and position of a particle; Find the tangential and normal components of |

|acceleration vectors; Derive and apply Kepler's Laws. Find the domain, range, and values of functions of two or more variables; Describe and |

|sketch functions of two or more variables. |

|WEEK 7 4 HOURS CONTENT |

|Limits and continuity. Partial derivatives and higher derivatives; partial differential equations. |

|HOMEWORK |

|Read sections covered in textbook and complete homework assignments. |

|PERFORMANCE OBJECTIVES |

|The students will be able to: Calculate limits and determine continuity; Find first partial and higher derivatives; Verify solutions to partial |

|differential equations. |

|WEEK 8 4 HOURS CONTENT |

|Tangent planes; linear approximations; differentials. The Chain Rule; implicit differentiation. |

|HOMEWORK |

|Read sections covered in textbook and complete homework assignments. |

|PERFORMANCE OBJECTIVES |

|The students will be able to: Find the equation of the tangent plane to a surface at a point; Find linear approximations and differentials of a |

|function; Apply the Chain Rule to find partial derivatives; Differentiate functions of two or more variables using implicit differentiation. |

|WEEK 9 4 HOURS CONTENT |

|Directional derivatives and the gradient vector; maximizing the directional derivative; tangent planes to level surfaces. Maximum and minimum values. |

|HOMEWORK |

|Read sections covered in textbook and complete homework assignments. Complete a project that determines a maximum or minimum value. |

|PERFORMANCE OBJECTIVES |

|The students will be able to: Find directional derivatives and gradient vectors; Find the equations of tangent planes and normal lines to surfaces; Find|

|local maximum and minimum values using the Second Derivatives Test; Find absolute maximum and minimum values. |

|WEEK 10 4 HOURS CONTENT |

|Lagrange multipliers. Volumes and double integrals; the midpoint rule; average value. |

|HOMEWORK |

|Read sections covered in textbook and complete homework assignments. |

|PERFORMANCE OBJECTIVES |

|The students will be able to: Find maximum and minimum values using Lagrange multipliers; Evaluate double integrals over rectangles. |

|WEEK 11 4 HOURS CONTENT |

|Iterated integrals. Double integrals over general regions; properties of double integrals. |

|Double integrals in polar coordinates. |

|HOMEWORK |

|Read sections covered in textbook and complete homework assignments. |

|PERFORMANCE OBJECTIVES |

|The students will be able to: Calculate iterated integrals; Sketch solids related to iterated integrals; Set up and evaluate double integrals over |

|general regions; Set up and evaluate double integrals using polar coordinates. |

|WEEK 12 4 HOURS CONTENT |

|Applications of double integrals. Surface area. Triple integrals. |

|HOMEWORK |

|Read sections covered in textbook and complete homework assignments. Complete a project that involves mass, center of mass, moments of inertia, etc. |

|PERFORMANCE OBJECTIVES |

|The students will be able to: Apply double integrals to mass, center of mass, moments of inertia, etc.; Calculate surface area; Evaluate triple |

|integrals. |

|WEEK 13 4 HOURS CONTENT |

|Triple integrals in cylindrical and spherical coordinates. Change of variables in multiple integrals. |

|HOMEWORK |

|Read sections covered in textbook and complete homework assignments. Complete a project that investigates the intersection of solids. |

|PERFORMANCE OBJECTIVES |

|The students will be able to: Set up and evaluate triple integrals using cylindrical and spherical coordinates; Find the Jacobian of a transformation; |

|Use a given transformation to evaluate an integral; Evaluate an integral by making an appropriate change of variables. |

|WEEK 14 4 HOURS CONTENT |

|Vector fields.Line integrals. |

|HOMEWORK |

|Read sections covered in textbook and complete homework assignments. |

|PERFORMANCE OBJECTIVES |

|The students will be able to: Recognize and sketch vector fields; Evaluate line integrals in the plane, in space, and in vector fields. |

|WEEK 15 4 HOURS CONTENT |

|Fundamental Theorem for Line Integrals; independence of path; conservation of energy. Green's Theorem. |

|HOMEWORK |

|Read sections covered in textbook and complete homework assignments. |

|PERFORMANCE OBJECTIVES |

|The students will be able to: Determine whether a given vector field is conservative; Find a potential function for a conservative vector field; Show |

|independence of path and evaluate line integrals; Evaluate line integrals using Green's Theorem. |

|WEEK 16 4 HOURS CONTENT |

|Curl and divergence. Parametric surfaces and their areas. Surface integrals. |

|HOMEWORK |

|Read sections covered in textbook and complete homework assignments. |

|PERFORMANCE OBJECTIVES |

|The students will be able to: Find the curl and divergence of a vector field; Identify and represent parametric surfaces; Evaluate surface integrals. |

|WEEK 17 4 HOURS CONTENT |

|Stokes' Theorem. The Divergence Theorem. Final Review. |

|HOMEWORK |

|Read sections covered in textbook and complete homework assignments. Complete a project investigating the work of mathematicians Green, Stokes, and |

|Thompson. |

|PERFORMANCE OBJECTIVES |

|The students will be able to: Use Stokes' Theorem to evaluate integrals; Use the Divergence Theorem to calculate flux; Discuss the development of |

|mathematical ideas through conjecture and proof. |

|WEEK 18 2 HOURS |

|Final Exam Included in content section of course outline. |

|METHODS OF INSTRUCTION: |

|Instruction will follow a standard lecture/discussion format. Extensive homework will be assigned in order to assure mastery of the concepts and |

|techniques of multivariable calculus. Students will also be required required to utilize technology, both calculators and computer software, to |

|enhance their understanding of the material. |

| |

| |

|The content should include: |

|Hours it will take to cover each topic - Hours are based on an 18 week term, even though the instruction is compressed into a 16 week calendar. For |

|example, a 3 unit course should have 54 hours (3 hours per week times 18 weeks = 54 Total Contact Hours). 2 hours should be set aside for the final. |

|Topic |

|Student Performance Objectives |

|Out of Class Assignments - Out of Class Assignments: essays, library research, problems, projects required outside of class on a 2 to 1 basis for |

|Lecture units granted. Include specific examples of reading and writing assignments. |

METHODS OF EVALUATION:

No Change

|METHODS OF EVALUATION: |

|CATEGORY 1 - The types of writing assignments required: |

|Percent range of total grade: 5 % to 15 % |

| Written Homework |

| Reading Reports |

| Lab Reports |

| Essay Exams |

| Term or Other Papers |

| Other:       |

|If this is a degree applicable course, but substantial writing assignments are not appropriate, indicate reason: |

| Course is primarily computational |

| Course primarily involves skill demonstration or problem solving |

|CATEGORY 2 -The problem-solving assignments required: |

|Percent range of total grade: 85 % to 95 % |

| Homework Problems |

| Field Work |

| Lab Reports |

| Quizzes |

| Exams |

| Other:       |

|CATEGORY 3 -The types of skill demonstrations required: |

|Percent range of total grade:       % to       % |

| Class Performance/s |

| Field Work |

| Performance Exams |

|CATEGORY 4 - The types of objective examinations used in the course: |

|Percent range of total grade:       % to       % |

| Multiple Choice |

| True/False |

| Matching Items |

| Completion |

| Other:       |

|CATEGORY 5 - Any other methods of evaluation: |

|Percent range of total grade:       % to       % |

|      |

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