MATH 2770  Differential Equations Credit Hours: 4.00 Prerequisites: MATH 2000 and MATH 2760 with grade C or better, or equivalent college courses
MATH 2770 is part of the sequence of courses required for most engineering, science, and mathematics majors and includes first order differential equations and their applications, higher order differential equations and their applications, differential operators, the Laplace Transform, systems of linear differential equations, series solutions of differential equations, and numerical methods for solving differential equations.
Billable Contact Hours: 4
Search for Sections OUTCOMES AND OBJECTIVES Outcome 1: Upon completion of this course, students will be able to solve separable, exact, firstorder linear, and Bernoulli ordinary differential equations (ODE’s) by analytical and numerical methods.Objectives:  Identify separable ODEs and employ appropriate techniques to solve separable ODEs.
 Identify exact ODEs and employ appropriate techniques to solve exact ODEs.
 Identify firstorder linear ODEs and employ appropriate techniques to solve firstorder linear ODEs.
 Identify Bernoulli ODEs and employ appropriate techniques to solve Bernoulli ODEs.
 Identify separable ODEs and employ appropriate techniques to solve separable ODEs.
 Use the improved Euler formula to calculate numerical solutions over intervals to any of the above types of ODEs with initial conditions.
Outcome 2: Upon completion of this course, students will be able to apply differential equations to solve mathematical problems. Objectives:  Solve continuous growth and decay models.
 Solve cooling and warming models.
 Solve mixture models.
 Solve series circuit models.
 Solve orthogonal trajectory models.
Outcome 3: Upon completion of this course, students will be able to solve homogeneous and nonhomogeneous higher order linear equations using the methods of undetermined coefficients and variation of parameters. Objectives  Solve homogeneous higher order ODEs using the superposition principle.
 Solve homogeneous higher order ODEs using the operator notation and by the annihilator approach.
 Solve nonhomogeneous higher order ODEs using the method of undetermined coefficients.
 Solve nonhomogeneous higher order ODEs using the method of variation of parameters.
Outcome 4: Upon completion of this course, students will be able to solve initial value problems using the Laplace transform. Objectives  Demonstrate knowledge of the values of the Laplace transform function.
 Demonstrate knowledge of the values of the inverse Laplace transform function.
 Demonstrate knowledge of the technique utilizing these functions to solve initial value problems.
Outcome 5: Upon completion of this course, students will be able to solve homogeneous and nonhomogeneous systems by the Laplace transform, by using operators, and by using eigenvalues and eigenvectors. Objectives  Demonstrate knowledge of the technique utilizing the Laplace and inverse Laplace transforms to solve systems of ODEs with initial conditions.
 Demonstrate knowledge of the technique utilizing operator notation to solve systems of ODEs.
 Demonstrate knowledge of the technique utilizing matrix notation to solve systems of ODEs.
Outcome 6: Upon completion of this course, students will be able to solve differential equations by power series and by Frobeneous’s method. Objectives:  Find power series solutions about an ordinary point.
 Use Frobenius’ method to find series solutions about a regular singular point.
COMMON DEGREE OUTCOMES (CDO) • Communication: The graduate can communicate effectively for the intended purpose and audience. • Critical Thinking: The graduate can make informed decisions after analyzing information or evidence related to the issue. • Global Literacy: The graduate can analyze human behavior or experiences through cultural, social, political, or economic perspectives. • Information Literacy: The graduate can responsibly use information gathered from a variety of formats in order to complete a task. • Quantitative Reasoning: The graduate can apply quantitative methods or evidence to solve problems or make judgments. • Scientific Literacy: The graduate can produce or interpret scientific information presented in a variety of formats.
CDO marked YES apply to this course: Critical Thinking: YES Quantitative Reasoning: YES COURSE CONTENT OUTLINE  First Order Ordinary Differential Equations
 Separable ODEs
 Exact ODEs
 HomogeneousofOrdern ODEs
 Linear ODEs
 Bernoulli ODEs
 Applications of First Order ODEs
 HigherOrdered ODEs
 Reduction of Order
 Homogeneous Linear ODEs with Constant Coefficients
 Undetermined Coefficients
 Variation of Parameters
 CauchyEuler Equations
 Series Solutions at Ordinary Points
 Series Solutions at Singular Points
 Initial Value Problems
 Direct solution of IVPs
 Laplace Transform and the Solution of an IVP of a Single ODE
 Laplace Transform and the Solution of an IVP of a System of ODEs
 Matrix Methods
 Homogeneous Linear Systems with Constant Coefficients
 Variation of Parameters for Systems of ODEs
 Numerical Methods
 Eulers Methods
 RungeKutta 4th Order Method
Primary Faculty Halfaf, Matt Secondary Faculty Williams, Paul Associate Dean McMillen, Lisa Dean Pritchett, Marie
Official Course Syllabus  Macomb Community College, 14500 E 12 Mile Road, Warren, MI 48088
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