Differential Equations

Course Description: This course will introduce the student to the solution of elementary differential equations and standard applications of differential equations in science. It will include the solution of first order linear differential equations with applications to exponential growth and decay problems, mixture problems, orthogonal trajectories, etc., solutions to second order differential equations with applications to harmonic motion, and the LaPlace transform.

Textbook: Edwards, C. H, Penney, D. E, & Calvis, D. T (2019). Differential equations and Boundary Value Problems, Pearson.

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Unit 1: First Order Differential Equations and Applications

• 1.1 Differential Equations

• 1.2-1.3 Integrals as Solutions and Slope Fields

• 1.4 Separable Equations

• 1.5 Linear Fist-Ordered Equations

• 1.6a Homogeneous Equations

• 1.6b Bernoulli Equations

• 1.6c Exact Equations

• 2.1 Population Models

• 2.3 Acceleration Velocity Models

Unit 2: Higher Order Differential Equations and Applications

• 3.1 Second Ordered Linear Equations

• 3.2 General Solutions of Linear Equations

• 3.3 Homogeneous Equations with Constant Coefficients

• 3.5a Nonhomogeneous Equations and Undetermined Coefficients

• 3.5b Variation of Parameters

• 3.4a Mechanical Vibrations Free Undamped Motion

• 3.4b Mechanical Vibrations Free Damped Motion

• 3.6 & 3.7 Forced oscillations and RCL Circuits

Unit 3: Solving with Laplace Transforms and Power Series

• 7.1 Laplace Transforms

• 7.3 Partial Fractions and Laplace Transforms

• 7.2 Solving Differential Equations with Laplace Transforms

• 8.1 Power Series as a Solution to Differential Equations

• 8.2 Ordinary Points

• 8.3 Singular Points

Unit 4: Systems of Differential Equations

• 4.2a Homogeneous Systems of Differential Equations

• 4.2b Nonhomogeneous Systems of Differential Equations 

• 5.1 Matrices and Linear Systems

• 5.2 The Eigenvalue Method for Homogeneous Systems

• 5.5 Multiple Eigenvalue Solutions

• 5.7 Nonhomogeneous Linear Systems