BSc: Differential Equations.f22 - Revision history

I.konyukhov: /* Final assessment */

2022-06-28T08:16:31Z

Final assessment

← Older revision		Revision as of 08:16, 28 June 2022
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	=== Final assessment ===		=== Final assessment ===
−	~~'''~~Section 1~~'''~~	+	==== Section 1 ====
	# Determine the type of the first order equation and solve it with the use of appropriate method.		# Determine the type of the first order equation and solve it with the use of appropriate method.
	# Find the integrating factor for the given equation.		# Find the integrating factor for the given equation.
	# Solve the initial value problem of the first order.		# Solve the initial value problem of the first order.
	# Construct a mathematical model of the presented real world problem in terms of differential equations and answer for the specific question about it.		# Construct a mathematical model of the presented real world problem in terms of differential equations and answer for the specific question about it.
		⚫	==== Section 2 ====
−
⚫	~~'''~~Section 2~~'''~~
	# For the given initial value problem with the ODE of the first order implement in your favorite programming Euler, improved Euler and general Runge-Kutta methods of solving.		# For the given initial value problem with the ODE of the first order implement in your favorite programming Euler, improved Euler and general Runge-Kutta methods of solving.
	# Using the developed software construct corresponding approximation of the solution of a given initial value problem (provide the possibility of changing of the initial conditions, implement the exact solution to be able to compare the obtained results).		# Using the developed software construct corresponding approximation of the solution of a given initial value problem (provide the possibility of changing of the initial conditions, implement the exact solution to be able to compare the obtained results).
	# Investigate the convergence of the numerical methods on different grid sizes.		# Investigate the convergence of the numerical methods on different grid sizes.
	# Compare approximation errors of these methods plotting the corresponding chart for the dependency of approximation error on a grid size.		# Compare approximation errors of these methods plotting the corresponding chart for the dependency of approximation error on a grid size.
		⚫	==== Section 3 ====
−
⚫	~~'''~~Section 3~~'''~~
	# Compose a characteristic equation and find its roots.		# Compose a characteristic equation and find its roots.
	# Find the general of second order equation.		# Find the general of second order equation.

I.konyukhov: /* Final assessment */

2022-06-24T11:55:32Z

Final assessment

← Older revision		Revision as of 11:55, 24 June 2022
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	=== Final assessment ===		=== Final assessment ===
	'''Section 1'''		'''Section 1'''
		+	# Determine the type of the first order equation and solve it with the use of appropriate method.
−	# Apply the appropriate differentiation technique to a given problem.
−	# Find a ~~derivative~~ of a ~~function~~	+	# Find the integrating factor for the given equation.
		+	# Solve the initial value problem of the first order.
−	# Apply Leibniz formula
		+	# Construct a mathematical model of the presented real world problem in terms of differential equations and answer for the specific question about it.
−	# Draw graphs of functions
−	# Find asymptotes of a parametric function

	'''Section 2'''		'''Section 2'''
		+	# For the given initial value problem with the ODE of the first order implement in your favorite programming Euler, improved Euler and general Runge-Kutta methods of solving.
−	# Apply the appropriate integration technique to the given problem
		+	# Using the developed software construct corresponding approximation of the solution of a given initial value problem (provide the possibility of changing of the initial conditions, implement the exact solution to be able to compare the obtained results).
−	# Find the value of the devinite integral
−	# ~~Calculate~~ the ~~area~~ of the ~~domain~~ or ~~the~~ ~~length~~ ~~of the~~ ~~curve~~	+	# Investigate the convergence of the numerical methods on different grid sizes.
		+	# Compare approximation errors of these methods plotting the corresponding chart for the dependency of approximation error on a grid size.

	'''Section 3'''		'''Section 3'''
		+	# Compose a characteristic equation and find its roots.
−	# Find a limit of a sequence
−	# Find a ~~limit~~ of a ~~function~~	+	# Find the general of second order equation.
		+	# Determine the form of a particular solution of the equation and reduce the order.
		+	# Solve a homogeneous constant coefficient equation.
		+	# Solve a non-homogeneous constant coefficient equation.
		+	# Find the Laplace transform for a given function. Analyze its radius of convergence.
		+	# Find the inverse Laplace transform for a given expression.
		+	# Solve the second order differential equation with the use of a Laplace transform.
		+	# Solve the second order differential equation with the use of Series approach.

	=== The retake exam ===		=== The retake exam ===

I.konyukhov: /* Section 3 */

2022-06-24T11:53:14Z

Section 3

← Older revision		Revision as of 11:53, 24 June 2022
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	# In which form a general solution may be found?		# In which form a general solution may be found?
	# What is the form of the particular solution of non-homogeneous equation?		# What is the form of the particular solution of non-homogeneous equation?
		+	# How to compose the Laplace transform for a certain function?
		+	# How to apply the method of Laplace transform for solving ordinary differential equations?
		+	# How to differentiate a functional series?

	=== Final assessment ===		=== Final assessment ===

I.konyukhov: /* Ongoing performance assessment */

2022-06-24T11:52:08Z

Ongoing performance assessment

← Older revision		Revision as of 11:52, 24 June 2022
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	# Which type of the equation have we obtained for the modeled real world problem?		# Which type of the equation have we obtained for the modeled real world problem?
	# Is the equation exact or not?		# Is the equation exact or not?
−

	==== Section 2 ====		==== Section 2 ====

I.konyukhov: /* Ongoing performance assessment */

2022-06-24T11:52:02Z

Ongoing performance assessment

@@ Line 195: / Line 195: @@
 ==== Section 1 ====
-#: the asymptotes of this curve;
+# Is the equation homogeneous or not?
 ==== Section 2 ====
 ==== Section 3 ====
 === Final assessment ===

I.konyukhov: /* Activities and Teaching Methods */

2022-06-24T11:50:38Z

Activities and Teaching Methods

← Older revision		Revision as of 11:50, 24 June 2022
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	\| Development of individual parts of software product code \|\| 0 \|\| 0 \|\| 0		\| Development of individual parts of software product code \|\| 0 \|\| 0 \|\| 0
	\|-		\|-
−	\| Individual Projects \|\| 0 \|\| 0 \|\| 0	+	\| Individual Projects \|\| 0 \|\| 1 \|\| 0
	\|-		\|-
	\| Group projects \|\| 0 \|\| 0 \|\| 0		\| Group projects \|\| 0 \|\| 0 \|\| 0

I.konyukhov: /* Activities and Teaching Methods */

2022-06-24T11:50:16Z

Activities and Teaching Methods

← Older revision		Revision as of 11:50, 24 June 2022
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	\| Problem-based learning (students learn by solving open-ended problems without a strictly-defined solution) \|\| 1 \|\| 1 \|\| 1		\| Problem-based learning (students learn by solving open-ended problems without a strictly-defined solution) \|\| 1 \|\| 1 \|\| 1
	\|-		\|-
−	\| Project-based learning (students work on a project) \|\| 0 \|\| 0 \|\| 0	+	\| Project-based learning (students work on a project) \|\| 0 \|\| 1 \|\| 0
	\|-		\|-
	\| Modular learning (facilitated self-study) \|\| 0 \|\| 0 \|\| 0		\| Modular learning (facilitated self-study) \|\| 0 \|\| 0 \|\| 0

I.konyukhov: /* Open access resources */

2022-06-24T11:49:53Z

Open access resources

← Older revision		Revision as of 11:49, 24 June 2022
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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]
−	* Jerrold E. Marsden and Alan Weinstein, Calculus I, II, and II. Springer-Verlag, Second Edition 1985 [https://www.cds.caltech.edu/~marsden/volume/Calculus/ link]
−	* Zorich, V. A. Mathematical Analysis I, Translator: Cooke R. (2004)

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

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

2022-06-24T11:48:57Z

Course activities and grading breakdown

← Older revision		Revision as of 11:48, 24 June 2022
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	\| Midterm \|\| 20		\| Midterm \|\| 20
	\|-		\|-
		+	\| Interim Assessment\|\| 20
−	\| Quizzes \|\| 28 (2 for each)
	\|-		\|-
−	\| Final exam \|\| 50	+	\| Final exam \|\| 30
	\|-		\|-
		+	\| Computational assignment \|\| 25
⚫	\| In-class participation \|\| ~~7 (including~~ 5 ~~extras)~~
		+	\|-
		⚫	\| In-class participation \|\| 5
	\|}		\|}

I.konyukhov: /* Level 1: What concepts should a student know/remember/explain? */

2022-06-24T11:45:38Z

Level 1: What concepts should a student know/remember/explain?

← Older revision		Revision as of 11:45, 24 June 2022
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	* describe the common goal of the numeric methods,		* describe the common goal of the numeric methods,
	* restate the given ordinary equation with the Laplace Transform.		* restate the given ordinary equation with the Laplace Transform.
−

	==== Level 2: What basic practical skills should a student be able to perform? ====		==== Level 2: What basic practical skills should a student be able to perform? ====