LSC-CyFair Math Department

Catalog Description

Linear equations, solutions in series, solutions using Laplace transforms, systems of differential equations and applications to problems in engineering and allied fields.

Course Learning Outcomes

The Student Will:

• Identify homogeneous equations, homogeneous equations with constant coefficients, and exact and linear differential equations.
• Solve ordinary differential equations and systems of equations using: a) Direct integration b) Separation of variables c) Reduction of order d) Methods of undetermined coefficients and variation of parameters e) Series solutions f) Operator methods for finding particular solutions g) Laplace transform methods.
• Determine particular solutions to differential equations with given boundary conditions or initial conditions.
• Analyze real-world problems in fields such as Biology, Chemistry, Economics, Engineering, and Physics, including problems related to population dynamics, mixtures, growth and decay, heating and cooling, electronic circuits, and Newtonian mechanics.

Contact Hour Information

Credit Hours:  3
Lecture Hours:  3
Lab Hours:  1
External Hours:  0
Total Contact Hours:  64

Prerequisites

MATH 2414;
College level readiness in reading and writing

Required Materials

Textbook:

Dennis G. Zill; A First Course in Differential Equations with Modeling Applications, 11th ed.; Cengage, ISBN Numbers:
Textbook Plus Enhanced WebAssign:  9781337604994
Textbook Only:  9781305965720
eBook Only:  9781337515573

Calculator:

Calculators may be required for some assignments/assessments at the discrection of the Instructor.  Refer to class syllabus for details.
Neither cell phones nor PDA’s can be used as calculators.  Calculators may be cleared before tests.

Textbook Sections
 

Chapter 1.  Introduction to Differential Equations

1.1  Definitions and Terminology

Chapter 2.  First-Order Differential Equations

2.2  Separable Equations

2.3  Linear Equations

2.4  Exact Equations

2.5  Solutions by Substitutions

2.6  Numerical Methods

Chapter 4.  Higher-Order Differential Equations

4.1  Preliminary Theory: Linear Equatons

4.2  Reduction of Order

4.3  Homogeneous Linear Equations with Constant Coefficients

4.4  Undetermined Coefficients - Superposition Approach

4.5  Undermined Coefficients - Annihilator Approach

4.6  Variation of Parameters

4.7  Cauchy-Euler Equations

4.8  Green's Functions

4.9  Solving Systems of Linear DEs by Elimination

4.10  Nonlinear Differential Equations

Chapter 6.  Series Solutions of Linear Equations

6.1  Review of Power Series

6.2  Solutions about Ordinary Points

6.3  Solutions about Singular Points

6.4  Special functions

Chapter 7.  The Laplace Transform

7.1  Definition of the Laplace Transform

7.2   Inverse Transforms and Transforms of Derivatives

7.3  Operational Properties I

7.4  Operational Properties II

7.5  The Dirac Delta Function

7.6  Systems of Linear Differential Equation

Chapter 8. Systems of Linear First-Order Differential Equations

8.1  Preliminary Theory - Linear Systems

8.2  Homogeneous Linear Systems

8.3  Nonhomogeneous Linear Systems

Chapter 9. Numerical Solutions of Ordinary Differential Equations

9.1  Euler Methods and Error Analysis

9.2  Runge-Kutta Methods