MATH A285H: Introduction to Linear Algebra and Differential Equations Honors
| Item | Value |
|---|---|
| Eff Term | Fall 2026 |
| Curriculum Committee Approval Date | 11/12/2025 |
| Top Code | 170100 - Mathematics, General |
| Units | 6 Total Units (Lecture Units 6) |
| Hours | 108 Total Hours (Lecture Hours 108) |
| Total Outside of Class Hours | 216 |
| Total Student Learning Hours | 324 |
| Course Credit Status | Credit: Degree Applicable (D) |
| Material Fee | No |
| Basic Skills | Not Basic Skills (N) |
| Repeatable | No |
| Open Entry/Open Exit | No |
| Grading Policy | Standard Letter (S) |
| Associate Arts Local General Education (GE) |
|
| Associate Science 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; Topics include matrices, determinants, vector spaces, linear systems of equations, linear product spaces, first and second order differential equations, systems of differential equations, and Laplace transforms; Additional honors topics include Jacobian matrices, properties of R3 and simple abstract topological spaces, and some exterior algebra Enrollment Limitation: MATH A285; students who complete MATH A285H may not enroll in or receive credit for MATH A285. PREREQUISITE: MATH A185, MATH A185H, MATH A280, or MATH A280H. Transfer Credit: CSU; UC.
Course Level Student Learning Outcome(s)
- Use matrix algebra and row-reduction methods to solve linear systems.
- Solve linear systems, including under- and over-determined systems.
- Prove lemmas and corollaries in linear algebra.
- Relate linear transformations to their matrices with respect to given bases.
- Describe linear transformations as functions mapping an n-dimensional space to an m-dimensional space.
Course Objectives
- 1. Use matrix algebra and row reduction methods to solve linear systems.
- 2. Prove basic properties of linear spaces and linear maps, including spans, independence and basic dimension theorems.
- 3. Compute null spaces and images of linear functions, and apply this to superposition of solutions in applications.
- 4. Compute change of bases.
- 5. Explore consequences of the Rank Nullity Theorem.
- 6. Work with inner product and orthogonality, including abstract Fourier coefficients, and the Gramm Schmidt processes.
- 7. Define n?n determinants and explore their elementary properties.
- 8. Use linear theory to solve first and second order ordinary differential equations and linear systems of ordinary differential equations.
- 9. Compute eigenvalues and eigenvectors.
- 10. Use appropriate technology to enhance understanding of differential equations and linear algebra.
Lecture Content
- Row-reduction methods, including elementary row operations, Gauss-Jordan elimination, and echelon matrices
- Matrix algebra including matrix addition, scalar multiplication, multiplication of matrices, identities, inverses, and proofs of some of the properties of these operations
- Using the inverse of a matrix and transpose of a matrix to solve systems of linear equations
- Linear spaces with focus on subspaces, spans, independence, bases, and dimension theory
- Linear functions with emphasis on null spaces, images, fundamental theorems including the Rank-Nullity Theorem, and change of basis
- Introduction to Inner Product Spaces including definitions, examples, norms, orthogonality, Fourier coefficients and the Gramm-Schmidt processes
- Determinants with emphasis on multilinear functions, elementary properties of determinants, adjoints, and Cramer’s rule
- First Order Differential Equations
- Separable
- Linear
- Exact
- Homogeneous
- Second Order and Higher Order Differential Equations
- Homogeneous linear
- Non-homogeneous linear
- Eigenvalues and eigenvectors: definitions, computation, and eigenbases
- Introduction to systems of ordinary differential equations using elimination, eigen methods, and the exponential matrix
- Introduction to Laplace transforms and their use in the solution of linear and non-linear differential equations
- Numerical methods for solution of ordinary differential equations such as Euler’s method, an improved Euler’s method, or the Runge-Kutta method
- Series solutions to differential equations
- Introduction to Fourier series
- Introduction to Jacobian matrices in the discussion of differentiability of mappings from Euclidean n-space to m-space with extension to a general analysis of the chain rule, implicit function theorem and the inverse function theorem
Method(s) of Instruction
- Lecture (02)
Instructional Techniques
Lecture, discussion
Reading Assignments
Students will spend approximately 1 hour per week reading from assigned text.
Writing Assignments
Students will spend approximately 1 hour per week on writing assignments, including written definitions, theorems, proofs, and justifications.
Out-of-class Assignments
Students will spend approximately 10 hours per week on out-of-class assignments, including reading, written defintions, justifications, and test preparation.
Study Non-Contact Hours Recommended
216
Methods of Student Evaluation
- Midterm Exam
- Final Exam
- Short Quizzes
- Written Assignments
- Projects (Individual/Group)
- Problem Solving Exercises
Demonstration of Critical Thinking
Students write definitions, theorems, proofs, and justifications.
Required Writing, Problem Solving, Skills Demonstration
Several written tests and a comprehensive final
Textbooks Resources
1. Required Goode, Stephen . Differential Equations and Linear Algebra, 4th ed. Pearson, 2017 Rationale: -
Resources Subscreen
- Textbook: Goode, Stephen. Differential Equations and Linear Algebra. Pearson (2017).
Eligible Discipline(s)
- Mathematics: Master’s degree in mathematics or applied mathematics OR bachelor’s degree in either of the above AND master’s degree in statistics, physics, or mathematics education OR the equivalent. Master's degree required.