MATH C285: Introduction to Linear Algebra and Differential Equations
| Item | Value |
|---|---|
| Curriculum Committee Approval Date | 09/25/2017 |
| Top Code | 170100 - Mathematics, General |
| Units | 5 Total Units |
| Hours | 90 Total Hours (Lecture Hours 90) |
| Total Outside of Class Hours | 0 |
| Course Credit Status | Credit: Degree Applicable (D) |
| Material Fee | No |
| Basic Skills | Not Basic Skills (N) |
| Repeatable | No |
| Grading Policy | Standard Letter (S),
|
| Local General Education (GE) |
|
| California General Education Transfer Curriculum (Cal-GETC) |
|
| Intersegmental General Education Transfer Curriculum (IGETC) |
|
| California State University General Education Breadth (CSU GE-Breadth) |
|
Course Description
Introduction to linear algebra and differential equations, matrices, determinants, eigenvectors and eigenvalues, inverse and implicit function theorems, linear methods and numerical methods, and Laplace transforms. PREREQUISITE: MATH C185. Transfer Credit: CSU; UC. C-ID: MATH 910 S.C-ID: MATH 910 S.
Course Level Student Learning Outcome(s)
- Solve ordinary differential equations using elementary techniques including Laplace transformations.
- Find eigenvalues and eigenvectors and use them in applications.
- Prove basic results in linear algebra using appropriate proof-writing techniques such as linear independence of vectors; properties of subspaces; linearity of transforms and operators; and properties of eigenvectors and eigenvalues.
Course Objectives
- 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;
- 6. Determine the Laplace Transform and inverse Laplace Transform of functions;
- 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; and
- 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.
Lecture Content
First order differential equations including separable, homogeneous, exact, and linear Existence and uniqueness of solutions Applications of first order differential equations such as circuits, mixture problems, population modeling, orthogonal trajectories, and slope fields Second order and higher order linear differential equations Fundamental solutions, independence, Wronskian Nonhomogeneous equations Applications of higher order differential equations such as the harmonic oscillator and circuits Methods of solving differential equations including variation of parameters, Laplace transforms, and series solutions Systems of ordinary differential equations Techniques for solving systems of linear equations including Gaussian and Gauss-Jordan elimination and inverse matrices Matrix algebra, invertibility, and the transpose Relationship between coefficient matrix invertibility and solutions to a system of linear equations and the inverse matrices Special matrices: diagonal, triangular, and symmetric Determinants and their properties Vector algebra for Rn Real vector spaces and subspaces, linear independence, and basis and dimension of a vector space Matrix-generated spaces: row space, column space, null space, rank, nullity Change of basis Linear transformations, kernel and range, and inverse linear transformations Matrices of general linear transformations Eigenvalues, eigenvectors, eigenspace Diagonalization including orthogonal diagonalization of symmetric matrices Dot product, norm of a vector, angle between vectors, orthogonality of two vectors in Rn Orthogonal and orthonormal bases: Gram-Schmidt process
Method(s) of Instruction
- Lecture (02)
- DE Online Lecture (02X)
Instructional Techniques
1. Deliver lectures of course content. 2. Assign homework and quizzes. 3. Relate material in the course to real life and the outside world. 4. Require participation including student-to-student and student-to-instructor interaction through the use of small-group activities and whole-class discussion. 5. Apply technologies to increase learner motivation such as Scientific and/or Graphing Calculator and computer software such as Wolfram
Reading Assignments
Alpha. 6. Objective Examinations 7. Midterm Exam (comprehensive) 8. Final Exam (comprehensive)
Writing Assignments
MyMathLab online homework assignments
Out-of-class Assignments
Textbook on ordinary differential equations and their applications
Demonstration of Critical Thinking
Final Exam Midterm Exam Objective Examinations Problem Solving Exercises Projects (ind/group) Report Short Quizzes Skills Demonstration Written Assignments
Required Writing, Problem Solving, Skills Demonstration
Critical thinking and problem solving skills are required in solving homework assignments, quizzes, and exams.
Eligible Disciplines
Mathematics: Masters degree in mathematics or applied mathematics OR bachelors degree in either of the above AND masters degree in statistics, physics, or mathematics education OR the equivalent. Masters degree required.
Manuals Resources
1. Required Lay, D. Linear Algebra and Its Applications, 5th ed. Pearson/Prentice-Hall, 2016 Rationale: - 2. Required Nagle, Saff. Fundamentals of Differential Equations, 9th ed. Pearson Education, 2018