# SRJC Course Outlines

 8/7/2024 7:00:56 PM MATH 2 Course Outline as of Fall 2021 Changed Course CATALOG INFORMATION Discipline and Nbr:  MATH 2 Title:  CALCULUS 4 Full Title:  Calculus, Fourth Course-Differential Equations Last Reviewed:11/28/2022

 Units Course Hours per Week Nbr of Weeks Course Hours Total Maximum 3.00 Lecture Scheduled 3.00 17.5 max. Lecture Scheduled 52.50 Minimum 3.00 Lab Scheduled 0 8 min. Lab Scheduled 0 Contact DHR 0 Contact DHR 0 Contact Total 3.00 Contact Total 52.50 Non-contact DHR 0 Non-contact DHR Total 0

 Total Out of Class Hours:  105.00 Total Student Learning Hours: 157.50

Title 5 Category:  AA Degree Applicable
Repeatability:  00 - Two Repeats if Grade was D, F, NC, or NP
Also Listed As:
Formerly:  MATH 2B

Catalog Description:
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First and second order differential equations with applications, series solutions, numerical methods, introduction to Laplace transforms, systems of differential equations with applications.

Prerequisites/Corequisites:
Course Completion of MATH 1C

Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description: Untitled document
First and second order differential equations with applications, series solutions, numerical methods, introduction to Laplace transforms, systems of differential equations with applications.

Prerequisites:Course Completion of MATH 1C
Recommended:
Limits on Enrollment:
Transfer Credit:CSU;UC.
Repeatability:00 - Two Repeats if Grade was D, F, NC, or NP

ARTICULATION, MAJOR, and CERTIFICATION INFORMATION

 Associate Degree: Effective: Fall 1981 Inactive: Area: BMC Communication and Analytical ThinkingMath Competency CSU GE: Transfer Area Effective: Inactive: IGETC: Transfer Area Effective: Inactive: CSU Transfer: Transferable Effective: Fall 1981 Inactive: UC Transfer: Transferable Effective: Fall 1981 Inactive: C-ID: CID Descriptor: MATH 240 Ordinary Differential Equations SRJC Equivalent Course(s): MATH2

Certificate/Major Applicable: Major Applicable Course

COURSE CONTENT

Student Learning Outcomes:
At the conclusion of this course, the student should be able to:
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1. Identify and solve ordinary differential equations and initial value problems using analytical and numerical methods.
2. Identify and solve systems of differential equations.
3. Model and solve applied problems using differential equations and systems of differential equations.

Objectives: Untitled document
Students will be able to:
1.   Classify differential equations as to order, type, and kind.
2.   Use slope fields to provide a qualitative analysis of the solutions to a differential equation.
3.   Solve homogeneous and exact first-order linear differential equations, including initial value problems.
4.   Solve separable first-order differential equations, including initial value problems.
5.   Apply the existence and uniqueness theorems for ordinary differential equations.
6.   Use the Wronskian to identify sets of fundamental solutions to higher order linear differential equations.
7.   Solve homogeneous and non-homogeneous linear differential equations of second and higher order using various techniques such as variation of parameters, undetermined coefficients and the annihilator method.
8.   Solve ordinary differential equations using numerical methods such as Euler's method and the method of Runge-Kutta.
9.   Apply techniques of solving differential equations and initial value problems to at least three out of the five following applications.
a) mixture problems
b) electrical circuits
c) population modeling
d) inductance, resistance and capacitance, LRC circuits
e) forced oscillations
10. Solve initial value problems using the methods of Laplace transforms.
11. Solve systems of differential equations.
12. Solve differential equations using power series methods.

Topics and Scope
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I. Ordinary Differential Equations
A. Linear differential equations with applications
B. Separable differential equations
C. Slope fields
D. Existence and uniqueness of solutions
E. Use of Wronskian
F. Numerical methods including 4th order Runge-Kutta

II. Introduction to Laplace Transforms
A. Laplace transform and inverse
B. Use of tables
C. Application to linear differential equations

III. Series Solutions to Differential Equations
A. Power series solutions
B. Taylor series solutions

IV. Systems of Differential Equations
A. Analysis of phase portraits
B. Solution by matrices
C. The operator method or Laplace transforms
D. Use of systems to solve higher order linear ordinary differential equations
E. Applications
1. Coupled spring-mass systems
2. Compartment analysis
3. Other applications

Assignments:
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1. Daily reading outside of class (20-50 pages per week)
2. Problem set assignments from required text(s) or supplementary materials chosen by the instructor (1-6 per week)
3. Quizzes (0-4 per week)
4. Exams (2-7 per term)
5. Final Exam
6. Projects (for example, computer explorations or modeling activities, 0-10 per term)