• Mathematics Department Course Syllabus
    Course: Introduction to Differential Equations

    Great Oak High School has the unique opportunity to offer its students math courses with the option of dual enrollment with the California State University at San Marcos. Students enrolled in Introduction to Differential Equations here at Great Oak High School may also register with the California State University at San Marcos and receive college credit for the course from CSUSM. Students register directly with CSUSM and will receive a transcript from CSUSM. Course Description: CSUSM: MATH 262 (3 Units): Introduction to Differential Equations. Models involving first-order equations, higher-order linear equations, systems of equations, numerical methods, and applications.


    Students must successfully complete AP Calculus AB, AP Calculus BC and Calculus D. In addition to this, all students must pass the AP Calculus BC exam with a 3 or higher.

    Student Expectations:

    This course is a college level course. The course will be approached as a college level course and students are expected to do college level work. Students will be expected to adhere to all TVUSD behavior policies. Preparation includes being on time with required material including notebook, pencil/eraser, graphing calculator and any other materials designated by the teacher. The Schools tardy policy will be strictly enforced. Be Engaged. Please leave all distracting items out of the classroom (i.e. food, drinks, iPods, video games, graphing calculator games, etc.). Cell phones must be turned off during class time and may not be used as calculators.


    Grades will be based on a combination of tests, quizzes, in class assignments, homework, and a final. Grades will be calculated using weighted categories:
    Tests: 50%
    Final: 20%
    Quizzes: 15%
    Homework: 15%

    The following grading scale will be used to determine letter grades:
    A 90-100%
    B 80-89%
    C 70-79%
    F 00-69%

    Office Hours:

    I will be available on a regular basis. I will be available everyday from 6:30 – 7:30. I will also be available upon request. I am here to help, so if you need help, PLEASE let me know!!!!


    I am a firm believer in homework. In math, you learn through practice. Homework will be assigned on a weekly basis and students are expected to turn in that homework assignment on the Friday of the week it was assigned. No credit will be given for late work.


    Quizzes will usually be given midway between units. Tests will be given at the end of each unit. Make-up tests and quizzes will not be given.


    I expect you to look at the notes from when you are absent and come in with them complete. USE THE WEBSITE.

    Academic Integrity:

    Academic dishonest will not be tolerated. If you are found to have committed academic dishonesty, a zero will be awarded for that grade and you will not be given the opportunity to make this grade up. Disciplinary action will be taken. If I find anyone copying the work of anyone else all guilty parties will receive zeroes and disciplinary action will be taken. You will not be given the opportunity to make up this grade.

    Textbook for Introduction to Differential Equations:

    The text we will be using is A First Course in Differential Equations by Dennis G. Zill, ninth edition, published by Brooks/Cole.

    Teacher Contact:

    The school’s phone number is 294-6450 and my extension is3603. If it is an emergency during the school day, please contact the school
    operator. To contact me via e-mail use: smaxey@tvusd.k12.ca.us


    Introduction to Differential Equations Course Outline:
    I. Introduction to Differential Equations
       A. Definitions and Terminology
       B. Initial Value Problems
       C. Differential Equations as Mathematical Models

    II. First Order Differential Equations
       A. Solution Curves Without a Solution
       B. Separable Variables
       C. Linear Equations
       D. Exact Equations
       E. Solutions by Substitution
       F. Numerical Methods

    III. Modeling with First Order Differential Equations
       A. Linear Models
       B. Modeling With Systems of Differential Equations

    IV. Higher Order Differential Equations
       A. Linear Differential Equations
       B. Reduction of Order
       C. Homogeneous Linear Equations with Constant Coefficients
       D. Undetermined Coefficients
       E. Variation of Parameter
       F. Cauchy-Euler Equation
       G. Solving Systems of Linear Equations by Elimination
       V. Modeling with Higher Order Differential Equations
       A. Linear Models – Initial-Value Problems
       B. Linear Models – Boundary-Value Problems

    VI. Series Solution of Linear Equations
       A. Solutions About Ordinary Points
       B. Solutions About Singular Points
       C. Bessel’s Equation
       D. Legendre’s Equation


    VII. The Laplace Transform
       A. Definition
       B. Inverse Transforms and Transforms of Derivatives
       C. Operational Properties
       D. The Dirac Delta Function
       E. Systems of Linear Differential Equations

    VIII. Systems of Linear First Order Equations
       A. Preliminary Theory
       B. Homogeneous Linear Systems
       C. Nonhomogeneous Linear Systems
       D. Matrix Exponential

    IX. Numerical Solutions of Ordinary Differential Equations
       A. Euler Methods
       B. Runge-Kutta Methods
       C. Multistep Methods
       D. Higher Order Equations and Systems
       E. Second Order Boundary-Value Problems