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.
College level readiness in reading and writing
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
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.
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