BSc: Differential Equations.f23 - Revision history

I.konyukhov: /* Differential Equations */

2023-08-31T18:12:23Z

Differential Equations

← Older revision		Revision as of 18:12, 31 August 2023
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	* J.L.Brenner, Problems in DifferentialEquations(adapted from ”Problems in differential equations” by A.F.Filippov)		* J.L.Brenner, Problems in DifferentialEquations(adapted from ”Problems in differential equations” by A.F.Filippov)
	* S.G.Glebov, O.M.Kiselev, N.Tarkhanov. Nonlinear equations with small parameter. Volume I:Oscillations and resonances		* S.G.Glebov, O.M.Kiselev, N.Tarkhanov. Nonlinear equations with small parameter. Volume I:Oscillations and resonances
		+	<!--
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	== Activities and Teaching Methods ==		== Activities and Teaching Methods ==
	{\| class="wikitable"		{\| class="wikitable"
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	=== The retake exam ===		=== The retake exam ===
	Retakes will be run as a comprehensive exam, where the student will be assessed the acquired knowledge coming from the textbooks, the lectures, the labs, and the additional required reading material, as supplied by the instructor. During such comprehensive oral/written the student could be asked to solve exercises and to explain theoretical and practical aspects of the course.		Retakes will be run as a comprehensive exam, where the student will be assessed the acquired knowledge coming from the textbooks, the lectures, the labs, and the additional required reading material, as supplied by the instructor. During such comprehensive oral/written the student could be asked to solve exercises and to explain theoretical and practical aspects of the course.
		+	-->

I.konyukhov: /* Grading */

2023-08-31T18:11:40Z

Grading

← Older revision		Revision as of 18:11, 31 August 2023
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	\| Attendance and In-class participation \|\| 7		\| Attendance and In-class participation \|\| 7
	\|}		\|}
		+	<!--
−
	=== Recommendations for students on how to succeed in the course ===		=== Recommendations for students on how to succeed in the course ===
	* Participation is important. Attending lectures is the key to success in this course.		* Participation is important. Attending lectures is the key to success in this course.
	* Review lecture materials before classes to do well.		* Review lecture materials before classes to do well.
	* Reading the recommended literature is obligatory, and will give you a deeper understanding of the material.		* Reading the recommended literature is obligatory, and will give you a deeper understanding of the material.
		+	-->

	== Resources, literature and reference materials ==		== Resources, literature and reference materials ==

I.konyukhov: /* Intended Learning Outcomes (ILOs) */

2023-08-31T18:11:06Z

Intended Learning Outcomes (ILOs)

← Older revision		Revision as of 18:11, 31 August 2023
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	* Apply numerical methods to approximate solutions to differential equations.		* Apply numerical methods to approximate solutions to differential equations.
	* Understand the concept of eigenvalues and eigenvectors and use them to solve systems of linear differential equations.		* Understand the concept of eigenvalues and eigenvectors and use them to solve systems of linear differential equations.
−
	<!--		<!--
	=== What is the main purpose of this course? ===		=== What is the main purpose of this course? ===

I.konyukhov: /* Intended Learning Outcomes (ILOs) */

2023-08-31T18:10:53Z

Intended Learning Outcomes (ILOs)

← Older revision		Revision as of 18:10, 31 August 2023
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	* Understand the concept of eigenvalues and eigenvectors and use them to solve systems of linear differential equations.		* Understand the concept of eigenvalues and eigenvectors and use them to solve systems of linear differential equations.

		+	<!--
	=== What is the main purpose of this course? ===		=== What is the main purpose of this course? ===

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	* predict the number of terms in series solution of the equation depending on the given accuracy,		* predict the number of terms in series solution of the equation depending on the given accuracy,
	* implement a certain numerical method in self-developed computer software.		* implement a certain numerical method in self-developed computer software.
		+	-->

	== Grading ==		== Grading ==

I.konyukhov: /* Intended Learning Outcomes (ILOs) */

2023-08-31T18:06:47Z

Intended Learning Outcomes (ILOs)

← Older revision		Revision as of 18:06, 31 August 2023
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	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 numerical 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 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 numerical 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.
−

	=== ILOs defined at three levels ===		=== ILOs defined at three levels ===

I.konyukhov: /* Intended Learning Outcomes (ILOs) */

2023-08-31T18:06:34Z

Intended Learning Outcomes (ILOs)

← Older revision		Revision as of 18:06, 31 August 2023
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	== Intended Learning Outcomes (ILOs) ==		== Intended Learning Outcomes (ILOs) ==

		+	=== Course objectives ===
⚫	=== What is the main purpose of this course? ===

	Upon completion of this course, students should be able to:		Upon completion of this course, students should be able to:
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	* Apply numerical methods to approximate solutions to differential equations.		* Apply numerical methods to approximate solutions to differential equations.
	* Understand the concept of eigenvalues and eigenvectors and use them to solve systems of linear differential equations.		* Understand the concept of eigenvalues and eigenvectors and use them to solve systems of linear differential equations.
		+
		⚫	=== What is the main purpose of this course? ===
		+
		+	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 numerical 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.
		+

	=== ILOs defined at three levels ===		=== ILOs defined at three levels ===

I.konyukhov: /* What is the main purpose of this course? */

2023-08-31T17:59:34Z

What is the main purpose of this course?

← Older revision		Revision as of 17:59, 31 August 2023
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	=== What is the main purpose of this course? ===		=== What is the main purpose of this course? ===

		+	Upon completion of this course, students should be able to:
−	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 numerical 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.
		+	* Realize conditions of existence for the equations of the first order and solve first-order ordinary differential equations using various techniques such as separation of variables, integration factors.
		+	* Solve second-order linear differential equations with constant coefficients using techniques such as the characteristic equation and the method of undetermined coefficients and applications of Laplace transform for the linear equations.
		+	* Define the resonant conditions for the linear and nonlinear equations of the second order equation.
		+	* Apply the Lyapunov's stability theory for the linear and nonlinear systems.
		+	* Know the properties of the solutions of first-order partial differential equations.
		+	* Apply numerical methods to approximate solutions to differential equations.
		+	* Understand the concept of eigenvalues and eigenvectors and use them to solve systems of linear differential equations.

	=== ILOs defined at three levels ===		=== ILOs defined at three levels ===

I.konyukhov: /* Course activities and grading breakdown */

2023-08-31T17:56:34Z

Course activities and grading breakdown

← Older revision		Revision as of 17:56, 31 August 2023
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	\| Midterm \|\| 20		\| Midterm \|\| 20
	\|-		\|-
−	\| Interim Assessment\|\| 20	+	\| Interim Assessment\|\| 20 pts (2 tests by 10 pts)
	\|-		\|-
	\| Final exam \|\| 30		\| Final exam \|\| 30
	\|-		\|-
−	\| Computational assignment \|\| 25	+	\| Computational assignment \|\| 30
	\|-		\|-
−	\| In-class participation \|\| 5	+	\| Attendance and In-class participation \|\| 7
	\|}		\|}

I.konyukhov: /* Course Topics */

2023-08-31T17:51:28Z

Course Topics

@@ Line 12: / Line 12: @@
 ! Section !! Topics within the section
 |-
-| First-order equations and their applications||
+| Differential equations of the first order||
 |-
 |-
-| Higher-order equations and systems ||
+| Nonlinear equations and Lyapunov's stability ||
 |}
 == Intended Learning Outcomes (ILOs) ==

I.konyukhov: /* Open access resources */

2023-08-31T17:34:05Z

Open access resources

← Older revision		Revision as of 17:34, 31 August 2023
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	=== Open access resources ===		=== Open access resources ===
	* Elementary Differential Equations by William F. Trench. Brooks/Cole Thomson Learning, 2001 [https://digitalcommons.trinity.edu/mono/8/ link]		* Elementary Differential Equations by William F. Trench. Brooks/Cole Thomson Learning, 2001 [https://digitalcommons.trinity.edu/mono/8/ link]
−	* Stephen L. Campbell and Richard Haberman, Introduction to differential equations with dynamical systems.	+	* Stephen L. Campbell and Richard Haberman, Introduction to differential equations with dynamical systems
	* J.L.Brenner, Problems in DifferentialEquations(adapted from ”Problems in differential equations” by A.F.Filippov)		* J.L.Brenner, Problems in DifferentialEquations(adapted from ”Problems in differential equations” by A.F.Filippov)
−	* S.G.Glebov, O.M.Kiselev, N.Tarkhanov. Nonlinear equations with small parameter. Volume I:Oscillations and resonances.	+	* S.G.Glebov, O.M.Kiselev, N.Tarkhanov. Nonlinear equations with small parameter. Volume I:Oscillations and resonances

	== Activities and Teaching Methods ==		== Activities and Teaching Methods ==