MAP 2302 — Differential Equations — Syllabus
Prerequisites: C (2.0) or better in MAC 2313, or C (2.0) or better in MAC 2283.
Course Description: The course meets for approximately 45 hours during a 15-week semester. Successful completion of the course merits 3 semester hours of credit. The schedule outlined below allows time for three midterm exams plus a cumulative final exam, which are the norms for this course. (Note: A “lecture” is defined as a 50-minute time period.)
Text: Fundamentals of Differential Equations, 8th Edition, by Nagle, Saff, and Snider
Course Content
Chapter 1. Introduction (1 week)
1.1 Background
1.2 Solutions and Initial Value Problems
1.3 Direction Fields (optional)
1.4 The Approximation Method of Euler (omit)
Chapter 2. First Order Differential Equations (2-3 weeks)
2.1 Introduction: Motion of a Falling Body
2.2 Separable Equations
2.3 Linear Equations
2.4 Exact Equations
2.5 Special Integrating Factors
2.6 Substitutions and Transformations
Chapter 3. Mathematical Models and Numerical Methods Involving First Order Equations (1 week)
3.1 Mathematical Modeling
3.2 Compartmental Analysis
3.3 Heating and Cooling of Buildings
3.4 Newtonian Mechanics
3.5 Electrical Circuits (omit)
3.6 Improved Euler's Method (omit)
3.7 Higher-Order Numerical Methods: Taylor and Runge-Kutta (omit)
Chapter 4. Linear Second Order Equations (3-4 weeks)
4.1 Introduction: The Mass-Spring Oscillator
4.2 Homogeneous Linear Equations: The General Solution
4.3 Auxiliary Equations with Complex Roots
4.4 Nonhomogeneous Equations: The Method of Undetermined Coefficients
4.5 The Superposition Principle and Undetermined Coefficients Revisited
4.6 Variation of Parameters
4.7 Variable-Coefficient Equations (omit)
4.8 Qualitative Considerations for Variable-Coefficient and Nonlinear Equations
4.9 A Closer Look at Free Mechanical Vibrations
4.10 A Closer Look at Forced Mechanical Vibrations
Chapter 5. Introduction to Systems and Phase Plane Analysis (omit)
5.1 Interconnected Fluid Tanks
5.2 Elimination Method for Systems with Constant Coefficients
5.3 Solving Systems and Higher-Order Equations Numerically
5.4 Introduction to the Phase Plane
5.5 Applications to Biomathematics: Epidemic and Tumor Growth Models
5.6 Coupled Mass-Spring Systems
5.7 Electrical Systems
5.8 Dynamical Systems, Poincaré Maps, and Chaos
Chapter 6. Theory of Higher-Order Linear Differential Equations (1-2 weeks)
6.1 Basic Theory of Linear Differential Equations
6.2 Homogeneous Linear Equations with Constant Coefficients
6.3 Undetermined Coefficients and the Annihilator Method
6.4 Method of Variation of Parameters
Chapter 7. Laplace Transforms (2-3 weeks)
7.1 Introduction: A Mixing Problem
7.2 Definition of the Laplace Transform
7.3 Properties of the Laplace Transform
7.4 Inverse Laplace Transform
7.5 Solving Initial Value Problems
7.6 Transforms of Discontinuous and Periodic Functions
7.7 Convolution
7.8 Impulses and the Dirac Delta Function (omit)
7.9 Solving Linear Systems with Laplace Transforms (omit)
Chapter 8. Series Solutions of Differential Equations (1-2 weeks)
8.1 Introduction: The Taylor Polynomial Approximation
8.2 Power Series and Analytic Functions
8.3 Power Series Solutions to Linear Differential Equations
8.4 Equations with Analytic Coefficients
8.5 Cauchy-Euler (Equidimensional) Equations
8.6 Method of Frobenius
8.7 Finding a Second Linearly Independent Solution (omit)
8.8 Special Functions (omit)
Chapter 9. Matrix Methods for Linear Systems (1-2 weeks)
9.1 Introduction
9.2 Review 1: Linear Algebraic Equations
9.3 Review 2: Matrices and Vectors
9.4 Linear Systems in Normal Form
9.5 Homogeneous Linear Systems with Constant Coefficients
9.6 Complex Eigenvalues (omit)
9.7 Nonhomogeneous Linear Systems (omit)
9.8 The Matrix Exponential Function (omit)
Chapter 10. Partial Differential Equations (omit)
10.1 Introduction: A Model for Heat Flow
10.2 Method of Separation of Variables
10.3 Fourier Series
10.4 Fourier Cosine and Sine Series
10.5 The Heat Equation
10.6 The Wave Equation
10.7 Laplace's Equation
Miscellaneous University/College Policies:
- You are encouraged to take notes and may tape the lectures, but neither your notes nor your tapes are to be sold.
- All unauthorized recordings of class are prohibited. Recordings that accommodate individual student needs must be approved in advance and may be used for personal use during this semester only; redistribution is prohibited.
- Students in need of academic accommodations for a disability may consult with the Office of Students with Disabilities Services (SDS) in SVC 1133 to arrange appropriate accommodations. Students are required to give reasonable notice (typically 5 working days) prior to requesting an accommodation.
- Students who anticipate the necessity of being absent due to the observation of a major religious holiday must provide notice of the date in writing to the instructor by the second class meeting.
- Contingency Course Plan: In the event of an emergency, it may be necessary for USF to suspend normal operations. During this time, USF may opt to continue delivery of instruction through methods that include but are not limited to: Blackboard, Elluminate, Skype, and e-mail messaging and/or alternate scheduling. It is the responsibility of the student to monitor the main USF website, e-mails and MoBull messages for important information about the closure. For information about the continuation of instruction, students are directed to their individual blackboard course sites.
- S-U Policy: Students who want to take this course for a grade of S-U (Satisfactory-Unsatisfactory) must sign the S-U Contract no later than the end of the third week of classes. There will be no exceptions. For further information on S-U grades, please consult the undergraduate catalog. Note: Gordon Rule Math courses cannot be taken for an S-U grade.
- “I” Grade Policy: A grade of “I” indicates incomplete work and will only be assigned when most of the coursework has already been completed with a passing grade. For further information on “I” grades, please consult the undergraduate catalog.
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