Syllabus
Syllabus
Textbook: Advanced Engineering Mathematics, by Erwin Kreyszig, 8th edition, John Wiley & Sons, INC.
Course Prerequisites : Calculus II.
Major Topics Covered in the Course:
Ordinary differential equations (ODE's): the concept.
Solutions of ODE's.
First order ODE's.
Second order ODE's.
Higher order ODE's.
Systems of ODE's.
Series Solutions of ODE's.
Laplace transform.
Course Objectives and Relation to the Program Educational Objectives:
Students will demonstrate the ability to:
1. Solve ordinary differential equations.
2. Solve systems of ODEs.
3. Solve ODEs using power series.
4. Solving ODEs using Laplace transform.
Contribution to the Professional Component: Mathematics, Basic Sciences (100 %).
Expected Level of Proficiency for Students Entering the Course: Mathematics (Strong).
Will This Course Involve Computer Assignments? No.
Will This Course Have TA(s) When is it Offered? No.
Level of Contribution to Program Outcomes:
Strong: a,k.
Average: e.
Week: d.
Upon completion of this course, students will have had an opportunity to learn about the following:
1- Solve different types of first order ODEs including separable, exact and linear equations.
2- Show existence and uniqueness of solutions.
3. Solve second order and higher order linear differential equations.
Solve linear systems of ordinary differential equations.
Find series solutions of ordinary differential equations.
Evaluate Laplace transform.
ABET – Student Outcomes (1-7)
1. an ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics.
2. an ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors.
3. an ability to communicate effectively with a range of audiences.
4. an ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts.
5. an ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives.
6. an ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions.
7. an ability to acquire and apply new knowledge as needed, using appropriate learning strategies.
Chapter 4: Introduction to systems of ODE's. See also chapter 6 for solving systems using Laplace.
9-10-2024 video: A short Introduction and Separable 1st order ODE's
16-10-2024 video: Exact equations and Reduced to exact
23-10-2024 video: Introduction to second order ODEs
30-10-2024 videos: Reduction of order 1 Reduction of order 2 Reduction of order 3 Comment about a mistake in the notes
6-11-2024 videos: Cauchy-Euler Equation Existence and uniqueness. Wronskian
13-11-2024: Higher order ODEs: Introduction
20-11-2024: Power series solution- Introduction
27-11-2024: Frobenious Method Frobenious: Another Example
11-12-2024: Laplace I: Problem solving Laplace II: Problem solving
18-12-2024: Laplace III: Dirac delta function
8-1-2025: Laplace IV: Laplace of f(t)/ t