BSc:DifferentialEquations old

Differential Equations

• Course name: Differential Equations
• Course number: XYZ
• Knowledge area: Math

Administrative details

• Faculty: Computer Science and Engineering
• Year of instruction: 2nd year of BS
• Semester of instruction: 1st semester
• No. of Credits: 4 ECTS
• Total workload on average: 144 hours overall
• Class lecture hours: 2 per week
• Class tutorial hours: 2 per week
• Lab hours: 2 per week
• Individual lab hours: 0
• Frequency: weekly throughout the semester
• Grading mode: letters: A, B, C, D

Prerequisites

• Mathematical Analysis I
• Mathematical Analysis II
• Analytic Geometry and Linear Algebra I
• Analytic Geometry and Linear Algebra II

Course outline

The course is designed to provide Software Engineers and Computer Scientists by knowledge of basic (core) concepts, definitions, theoretical results and techniques of ordinary differential equations theory, basics of power series and numeric methods, applications of the all above in sciences. All definitions and theorem statements (that will be given in lectures and that are needed to explain the keywords listed above) will be formal, but just few of these theorems will be proven formally. Instead (in the tutorial and practice classes) we will try these definitions and theorems on work with routine exercises and applied problems. The course is based on a textbook “Elementary Differential Equations” by William F. Trench (2001).

Expected learning outcomes

The course will provide an opportunity for participants to:

• know mathematical theory of linear ordinary differential equations, elements of basic numeric methods;
• understand application value of ordinary differential equations, functional series, and numeric methods;
• get practical (pen-and-paper as well as computer-aided) experience with solving ordinary differential equations and using them for modelling in Science.

Programming related learning outcomes

Course includes computational practice assignment that assumes implementation of three numeric methods,namely:

• Euler method,
• improved Euler method,
• Runge-Kutta method.

Special attention will be paid for the quality and the OO-style of the implementation.

Expected acquired core competences

• Ordinary differential equations (ODE),
• initial value problems;
• linear, first, second and higher-order ODE’s;
• separable and exact ODE’s; order reduction;
• power and Fourier series;
• Newton method for algebraic equations;
• Euler and Runge-Kutta methods for ODE’s;
• Laplace transform;
• partial differential equations.

Required computer resources

Students should have laptops with any programming language installed (while Java is preferred).

Evaluation

• Grading items:
  • In-class participation 1 point per week for each individual contribution in class (i.e. 14 points overall).
  • Final overall in-course participation/contribution (“instructors’ gratitude”) 6 points.
  • Each in-class theory or practice tests – up to 10 points (i.e. 40 points overall).
  • Mid-term exam up to 40 points, final examination up to 40 points (i.e. 80 points overall).
  • computational practice assignment up to 10 points for each task (i.e. up to 30 points for 3 tasks),
• Final grade scale:
  • A: 136..170 points (i.e. 80% at least);
  • B: 102..135 points (i.e. 60% at least);
  • C: 68..101 points (i.e. 40% at least);
  • D: less than 68 points.