Stat 122X Elementary Statistics

MATH 2171 Syllabus DIFFERENTIAL EQUATIONS

MATH 2171. Prerequisite: Math 1242 with a grade of C or better

Required Text: Differential Equations: An Introduction to Modern Methods & Applications, First Edition, by James R. Brannan and William E. Boyce and the related Student Solutions Manual

Week Section Section Title or Topics 1 1.1 Some Basic Mathematical Models; Direction Fields 1.2 Solutions of Some Differential Equations 1.3 Numerical Approximations: Euler’s Method 2 1.4 Classification of Differential Equations 2.1 Linear Equations; Method of Integrating Factors 3 2.2 Separable Equations 2.3 Modeling with First Order Equations Review for Test 1 4 Test 1 2.4 Differences Between Linear and Nonlinear Equations 2.5 Autonomous Equations and Population Dynamics 5 2.8 Improved Euler and Runge-Kutta Methods • Projects ?? 3.1 Systems of Two Linear Algebraic Equations (A quick review followed by an introduction to Eigenvalues and Eigenvectors) 3.2 Systems of Two First Order Linear Differential Equations 6 3.3 Homogeneous Linear Systems with Constant Coefficients 3.4 Complex Eigenvalues 7 3.6 Introduction to Nonlinear Systems 3.7 Numerical Methods for Systems of First Order Equations Review for Test 2 8 Test 2 4.1 Definitions and Examples 4.2 Theory of Second Order Linear Homogeneous Equations 9 4.3 Linear Homogeneous Equations with Constant Coefficients 4.4 Characteristic Equations with Complex Roots 4.5 Mechanical and Electrical Vibrations 10 4.6 Nonhomogeneous Equations; Method of Undetermined Coefficients 4.7 Forced Vibrations, Frequency Response, and Resonance 11 4.8 Variation of Parameters Review for Test 3 12 Test 3 5.1 Definition of the Laplace Transform 5.2 Properties of the Laplace Transform 13 5.3 The Inverse Laplace Transform 5.4 Solving Differential Equations with Laplace Transforms 5.5 Discontinuous Functions and Periodic Functions 14 5.6 Differential Equations with Discontinuous Forcing Functions 5.7 Impulse Functions Review for the final exam Final Exam Please note that this syllabus serves only as a general guideline for the set of topics to be covered in this course, and the number and placement of exams.