DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA 0033 ( Official )
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DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA 0033 ( Official )
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DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA 0033 ( Official )

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SECTION A

 

1. Division:

  Sciences & Mathematics

2. Course Discipline:

  MATH

3. Course Number:

  0033

4. Course Title:

  DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA

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



 

 

SECTION B

General Course Information

 

1. Units: 6.0                 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:  

               6

 

Lecture/Discussion:  

            108

Laboratory:

                 

 

Laboratory:

                 

Activity:

                 

 

Activity:

                 

By Arrangement:

                 

 

By Arrangement:

                 

Total Hrs per Wk

               6

 

Total Hrs

            108

 

6. Minimum hours per week of independent work done outside of class:    12

 

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 31 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”.)

Completion of MATH 32 with grade of "C" or better strongly recommended

    

 

 

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:

First and second order ordinary differential equations, linear differential equations, numerical methods and series solutions, Laplace transforms, modeling and stability theory, systems of linear differential equations, matrices, determinants, vector spaces, linear transformations, orthogonality, eigenvalues and eigenvectors.

    

 

 

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. Create and analyze mathematical models using ordinary differential equations;
2. Verify solutions of differential equations;
3. Identify the type of a given differential equation and select and apply the appropriate analytical technique for finding the solution of first order and selected higher order ordinary differential equations;
4. Apply the existence and uniqueness theorems for ordinary differential equations;
5. Find power series solutions to ordinary differential equations including Frobenius solutions;
6. Determine the Laplace Transform and inverse Laplace Transform of functions and use to solve differential equations with initial value conditions;
7. Solve Linear Systems of ordinary differential equations;
8. Find solutions of systems of equations using various methods appropriate to lower division linear algebra;
9. Use bases and orthonormal bases to solve problems in linear algebra;
10. Find the dimension of spaces such as those associated with matrices and linear transformations;
11. Find eigenvalues and eigenvectors and use them in applications;
12. Prove basic results in linear algebra using appropriate proof-writing techniques such as linear independence of vectors; properties of subspaces; linearity, injectivity and surjectivity of functions; and properties of eigenvectors and eigenvalues;
13. Verify that the axioms of a vector space, subspace, and inner product are satisfied for a variety of sets including: n-dimensional space, polynomials, matrices, continuous and differentiable functions;
14. Examine Legendre and Bessel differential equations and their solutions;
15. Examine the phase plane for generating a qualitative representation of the solution to a system of nonlinear differential equations.

    

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. First order differential equations including separable, homogeneous, exact, and linear;
2. Existence and uniqueness of solutions;
3. Applications of first order differential equations such as circuits, mixture problems, population modeling, orthogonal trajectories, and slope fields;
4. Second order and higher order linear differential equations;
5. Fundamental solutions, independence, Wronskian;
6. Nonhomogeneous equations;
7. Applications of higher order differential equations such as the harmonic oscillator and circuits;
8. Methods of solving differential equations including variation of parameters, Laplace transforms, and series solutions;
9. Systems of ordinary differential equations;
10. Techniques for solving systems of linear equations including Gaussian and Gauss-Jordan elimination and inverse matrices;
11. Matrix algebra, invertibility, and the transpose;
12. Relationship between coefficient matrix invertibility and solutions to a system of linear equations and the inverse matrices;
13. Special matrices: diagonal, triangular, and symmetric;
14. Determinants and their properties;
15. Vector algebra for Rn;
16. Real vector spaces and subspaces, linear independence, and basis and dimension of a vector space;
17. Matrix-generated spaces: row space, column space, null space, rank, nullity;
18. Change of basis;
19. Linear transformations, kernel and range, and inverse linear transformations;
20. Matrices of general linear transformations;
21. Eigenvalues, eigenvectors, eigenspace;
22. Diagonalization including orthogonal diagonalization of symmetric matrices;
23. Dot product, norm of a vector, angle between vectors, orthogonality of two vectors in Rn;
24. Orthogonal and orthonormal bases: Gram-Schmidt process;
25. Matrix exponential function for a system of differential equations;
26. Convolution integral;
27. Green's theorem;
28. Differential equations with forcing functions involving the unit step function and forcing functions involving the Dirac delta function;
29. Assess the need for the appropriate shifting theorems and apply when appropriate to solve a differential equation;
30. Cramer's rule;
31. Slope Fields including equilibrium solutions, Isoclines and concavity changes;
32. Inner Product Spaces including the norm of a vector and Cauchy-Schwarz Inequality;
33. Isomorphisms;
34. Quadratic and Jordan Canonical Forms;
35. Method of Undetermined Coefficients; and
36. LU Factorization.

    

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 the textbook about the axioms of a vector space. Come to class prepared to discuss the subtle nature of these axioms.

Example 2: Read in your textbook (and research online) slope fields of the form D(y)=f(x,y) including isoclines, equilibrium solutions, and concavity.

    

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

Example 1: Sketch the slope field and some representative solution curves for the differential equation D(y)=y(y-1).

Example 2: Use technology to graph the slope field and connect the solution with the algebraic calculations of isoclines, equilibrium solutions, and concavity.

    

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:

  Gilbert Strang

Title:

  Differential Equations and Linear Algebra

Publisher:

  Wellesley-Cambridge

Date of Publication:

  2014

Edition:

  First

Book 2:

Author:

  Stephen W. Goode

Title:

  Differential Equations and Linear Algebra

Publisher:

  Prentice Hall

Date of Publication:

  2007

Edition:

  Third

Book 3:

Author:

  Edwards & Penney

Title:

  Differential Equations and Linear Algebra

Publisher:

  Prentice Hall

Date of Publication:

  2010

Edition:

  Third

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: The students and instructor will engage in interactive discussion concerning whether P3 with certain restrictions constitutes a vector space. This will be accomplished by measuring P3 with restrictions against the axioms that constitute a vector space.

Example 2: The instructor will direct the student to review power series representations of functions from the previous calculus course. The instructor will then guide the student to synthesize this background material to the power solution technique of solving differential equations.

 

 

 

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.

 

 

 

Example 1 - Write the linear first order differential equation dy/dx + p(x)y = q(x) in the form Mdx + Ndy = 0 and use the techniques of solving an exact differential equation to find the proper integrating factor. What does this tell you about all linear first order differential equations?


Example 2: Prove that P3 is a vector space by verifying that the set P3 satisfies each of the axioms for a vector space. This problem is graded for completeness and accuracy. Students need to verify each of the ten vector space axioms.

 

 

 

 

 

 

 

 

 

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 910S Differential Equations and Linear Algebra

 

 

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.

 

Allan Hancock College: MATH 184 Linear Algebra and Differential Equations
Cal Poly Pomona: MAT 224 Elementary Linear Algebra and Differential Equations
San Jose State University: MATH 123 Differential Equations and Linear Algebra
UC Berkeley: Math 54 Linear Algebra and Differential Equations

 

 

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 course.
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: