Feb 24, 2020  
2019 - 2020 Cowley College Academic Catalog 
2019 - 2020 Cowley College Academic Catalog



3 Credit Hours

Student Level:

This course is open to students on the college level in the sophomore year. 

Catalog Description:

MTH4465 ‐ Differential Equations (3 hrs.)  

Techniques for solving ordinary first and second order differential equations, Laplace transforms, Eigen values, and approximation techniques. This course requires that the students furnish their TI‐89 or TI‐

92 graphing calculator. Prerequisite: Minimum grade of C in MTH4455 Calculus III.

Course Classification:



Minimum grade of C in Math 4440 CALCULUS II 

Controlling Purpose:

To equip science and pre‐engineering students with a knowledge of advanced methods in solving differential equations and systems of differential equations.  

Learner Outcomes:

Students will learn to solve ordinary linear differential equations by various methods, including simple approximation techniques and Laplace transforms, and be introduced to solving systems of these equations using Laplace transforms and matrix techniques.  Technology will be used to a modest extent. 

Units Outcomes and Criterion Based Evaluation Key for Core Content: 

The following defines the minimum core content not including the final examination period. Instructors may add other content as time allows. 

UNIT I: Introduction to Differential Equations ‐ 8 hours

(Chapters 2.1‐2.6 & 4.1‐4.4) 

Outcomes: Upon completing this unit, the student will be able to solve ordinary linear first‐order differential equations. 

  • Become familiar with the terminology and classification of differential equations.
  • Verify solutions for differential equations. 
  • Solve ordinary linear first‐order differential equations by separation of variables and by using integrating factors. 
  • Set up and solve interesting application problems requiring these techniques. 

UNIT 2:  Numerical Methods ‐ 8 hours             (Chapter 3) 

Outcomes: Upon completing this unit, the student will be able to approximate ordinary linear first‐order differential equations.

  • Investigate direction fields. 
  • Approximate solutions using Euler’s method, the Runge‐Kutta method, and two‐ and three term Taylor approximations.
  • Write programs for approximation technique. 

UNIT 3: Homogeneous Linear Differential Equation ‐ 8 hours

(Chapter 6.1‐6.9 & 7.1‐7.5) 

Outcomes: Upon completing this unit the student will be able to solve higher order homogeneous differential equations. 

  • Test for the existence of a solution.
  • Solve homogeneous equations with constant coefficients and various kinds of roots.
  • Solve application problems in undamped and damped vibrations requiring these techniques. 

UNIT 4: Nonhomogeneous Linear Differential Equations ‐ 8 hours

(Ch 8.1‐8.4, 9.3‐9.4 & 10.1‐10.5) 

Outcomes: Upon completing this unit, the student will be able to solve ordinary linear differential equations. 

  • Solve nonhomogeneous linear differential equations using the method of undetermined coefficients and variation of parameters.
  • Solve application problems in mechanical systems, damped forced vibrations, and electrical circuits. 

UNIT 5:  Linear Systems of Differential Equations ‐ 8 hours

(Chapter 11.1‐11.7 & 12.1‐4) 

Outcomes: Students will use the fundamental theorem of calculus to find areas between plane curves, explore techniques of integration and approximation of integrals, and make applications to surplus and continuous income streams. 

  • Solve simple systems of differential equations by algebraic elimination. 
  • Solve systems of differential equations using Laplace transforms. 
  • Use matrices to solve systems of differential equations.
  • Solve homogeneous and nonhomogeneous systems with distinct, complex, and repeated eigenvalues.

UNIT 6:  The Laplace Transform Method ‐ 8 hours

(Chapter 14.1 ‐ 14.8 & 15.1 ‐ 3; 15.9) 

Outcomes: Upon completing this unit, the student will be able to solve initial value problems using the Laplace transform method. 

  • Become familiar with the notation of transforms and the conditions under which the Laplace transform method can be applied. 
  • Find Laplace transforms using tables.
  • Find inverse Laplace transforms. 
  • Use shifting theorems to extend the use of tables. 
  • Solve initial‐value problems using derivatives of Laplace transforms. 
  • Set up and solve interesting application problems requiring these  techniques. 

Projects Required:  None 

Text Book:

Contact the Bookstore for current textbook. 


Computers will be available to the student in the Computer Lab.  Students should provide their own graphics calculators such as a TI‐89 or TI‐92 especially. 

Attendance Policy: 

Students should adhere to the attendance policy outlined by the instructor in the course syllabus. 

Grading Policy: 

The grading policy will be outlined by the instructor in the course syllabus. 

Maximum class size: 

Based on classroom occupancy 

Course Timeframe:

The U.S. Department of Education, Higher Learning Commission and the Kansas Board of Regents define credit hour and have specific regulations that the college must follow when developing, teaching and assessing the educational aspects of the college. A credit hour is an amount of work represented in intended learning outcomes and verified by evidence of student achievement that is an institutionally‐established equivalency that reasonably approximates not less than one hour of classroom or direct faculty instruction and a minimum of two hours of out‐of‐class student work for approximately fifteen weeks for one semester hour of credit or an equivalent amount of work over a different amount of time. The number of semester hours of credit allowed for each distance education or blended hybrid courses shall be assigned by the college based on the amount of time needed to achieve the same course outcomes in a purely face‐to‐face format. 

Refer to the following policies: 

402.00 Academic Code of Conduct 

263.00 Student Appeal of Course Grades 

403.00 Student Code of Conduct 

Disability Services Program:

Cowley College, in recognition of state and federal laws, will accommodate a student with a documented disability.  If a student has a disability, which may impact work in this class, which requires accommodations, contact the Disability Services Coordinator.