Difference between revisions of "MAT3613"

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(Edited Week II: tweaked prereqs of Exact DE and Bernoulli)
(Edited Week VIII-IX: Added topics and took out breaks)
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* [[VariationOfParameters2Ord|Variation of Parameters (2nd Order)]]
 
* [[VariationOfParameters2Ord|Variation of Parameters (2nd Order)]]
 
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 +
* Integration techniques
 +
:- [[DirectIntegration|Direct Integration]]
 +
:- [[IntegrationBySubstitution|Integration by Substitution]]
 +
:- [[IntegrationByParts|Integration by Parts]]
 +
:- [[IntegrationOfRationalFunctions|Integration of Rational Functions]]
 
* [[QuadraticEquations|Quadratic Equations]].
 
* [[QuadraticEquations|Quadratic Equations]].
* [[LinearDE1Ord|Linear Differential Equations (1st Order)]].
 
 
* [[SystemsOfLinearEquations|Systems of Linear Equations]].
 
* [[SystemsOfLinearEquations|Systems of Linear Equations]].
 
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* [[VariationOfParameters2Ord|Variation of Parameters (2nd Order)]] (continued)
 
* [[VariationOfParameters2Ord|Variation of Parameters (2nd Order)]] (continued)
 
||
 
||
 
+
* Integration techniques
 +
:- [[DirectIntegration|Direct Integration]]
 +
:- [[IntegrationBySubstitution|Integration by Substitution]]
 +
:- [[IntegrationByParts|Integration by Parts]]
 +
:- [[IntegrationOfRationalFunctions|Integration of Rational Functions]]
 +
* [[QuadraticEquations|Quadratic Equations]].
 +
* [[SystemsOfLinearEquations|Systems of Linear Equations]].
 
||
 
||
 
* Apply variation of parameters technique for second-order ODEs.
 
* Apply variation of parameters technique for second-order ODEs.
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* [[MethodOfUndeterminedCoefficients2Ord|Method of Undetermined Coefficients (2nd Order)]]
 
* [[MethodOfUndeterminedCoefficients2Ord|Method of Undetermined Coefficients (2nd Order)]]
 
||
 
||
 
+
* [[QuadraticEquations|Quadratic Equations]].
 +
* [[SystemsOfLinearEquations|Systems of Linear Equations]].
 
||
 
||
 
* Apply method of undetermined coefficients technique for second-order ODEs.
 
* Apply method of undetermined coefficients technique for second-order ODEs.
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|Week VIII
 
|Week VIII
 
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+
* [[Nonlinear2OrdODEs|Non-linear 2nd Order ODEs]]
 +
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* Ahmad and  Ambrosetti 2014, Ch. 5
 
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* SPRING BREAK
+
* [[AlgebraicEquations|Algebraic Equations]]
 +
* [[ReductionOfTheOrder|Reduction of the Order]]
 +
* Integration techniques
 +
:- [[DirectIntegration|Direct Integration]]
 +
:- [[IntegrationBySubstitution|Integration by Substitution]]
 +
:- [[IntegrationByParts|Integration by Parts]]
 +
:- [[IntegrationOfRationalFunctions|Integration of Rational Functions]]
 
||
 
||
 
+
* Methods for nonlinear second-order ODEs.
 +
* Apply reduction of the order method to some nonlinear second-order ODEs.
 +
|-
 +
|Week VIII
 +
||
 +
* Ahmad and Ambrosetti 2014, Ch. 5
 +
||
 +
* [[VariationOfParametershOrd|Variation of Parameters (Higher Order)]]
 +
||
 +
* [[VariationOfParameters2Ord|Variation of Parameters (2nd Order)]]
 +
||
 +
* Apply variation of parameters technique for higher-order ODEs
 +
|-
 +
|Week VIII
 +
||
 +
* Ahmad and Ambrosetti 2014, Ch. 5
 +
||
 +
* [[MethodOfUndeterminedCoefficientshOrd|Method of Undetermined Coefficients (Higher Order)]]
 +
||
 +
* Methods for higher-order ODEs
 +
* [[MethodOfUndeterminedCoefficients2Ord|Method of Undetermined Coefficients (2nd Order)]]
 
||
 
||
 
+
* Apply method of undetermined coefficients technique for higher-order ODEs
 
|-
 
|-
 
|Week IX
 
|Week IX
 
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+
* [[LinearDEhOrd|Linear Differential Equations (Higher Order)]]
 
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* Preparation for remote instruction.
+
* Ahmad and  Ambrosetti 2014, Ch. 6
 
||
 
||
 
+
* [[LinearDE1Ord|Linear Differential Equations (1st Order)]]
 +
* [[VariationOfParametershOrd|Variation of Parameters (Higher Order)]].
 +
* [[MethodOfUndeterminedCoefficientshOrd|Method of Undetermined Coefficients (Higher Order)]].
 
||
 
||
 
+
* Methods for linear higher-order ODEs
 
|-
 
|-
 
|Week X
 
|Week X

Revision as of 07:07, 7 July 2020

Topics List

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week I
  • Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3
  • Integration techniques
- Direct Integration
- Integration by Substitutions
- Integration by Parts
- Integration of Rational Functions
  • Explain the basic notion of the order of a differential equation.
Week I
  • Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3
  • Integration techniques
- Direct Integration
- Integration by Substitution
- Integration by Parts
- Integration of Rational Functions
  • Explain the basic notion of solutions of differential equations.
Week I
  • Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3
  • Integration techniques
- Direct Integration
- Integration by Substitution
- Integration by Parts
- Integration of Rational Functions.
  • Explain the basic notion of the initial values problem.
Week I
  • Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3
  • Integration techniques
- Direct Integration
- Integration by Substitution
- Integration by Parts
- Integration of Rational Functions
  • Explain the Cauchy Problem
  • Explain the basic notion of existence and uniqueness of a solution to the Cauchy Problem.
Week I
  • Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3
  • Integration techniques
- Direct Integration
- Integration by Substitution
- Integration by Parts
- Integration of Rational Functions
  • Determine separable differential equations of the first order.
  • Apply direct methods to evaluate exact solutions of separable differential equations of the first order.
Week II
  • Ahmad and Ambrosetti 2014, Chaps. 1 and 3
  • Integration techniques
- Direct Integration
- Integration by Substitution
- Integration by Parts
- Integration of Rational Functions
  • Determine homogeneous differential equations of the first order.
  • Apply direct methods to evaluate exact solutions of homogeneous differential equations of the first order (substitutions).
  • Use some differential equations as mathematical models in biology, population dynamics, mechanics and electrical circuit theory problems.
Week II
  • Ahmad and Ambrosetti 2014, Chaps. 1 and 3
  • Integration techniques
- Direct Integration
- Integration by Substitution
- Integration by Parts
- Integration of Rational Functions
  • Determine linear differential equations of the first order.
  • Use some differential equations as mathematical models in biology, population dynamics, mechanics and electrical circuit theory problems.
Week II
  • Ahmad and Ambrosetti 2014, Chaps. 1 and 3
  • Apply integrating factor to solve linear differential equations of the first order.
  • Use some differential equations as mathematical models in biology, population dynamics, mechanics and electrical circuit theory problems.
Week III
  • Ahmad and Ambrosetti 2014, Ch. 3
  • Determine Bernoulli of the first order.
  • Apply direct methods to evaluate exact solutions of Bernoulli of the first order.
Week III
  • Ahmad and Ambrosetti 2014, Ch. 3
  • Determine Exact Differential Equations of the first order.
  • Apply direct methods to evaluate exact solutions of Exact Differential Equations of the first order.
  • Use the integrating factor technique for exact equations.
Week IV
  • Ahmad and Ambrosetti 2014, Chaps. 1-3
  • Overview of the solutions methods discussed so far (Chapters 1-3).
  • Integration techniques
- Direct Integration
- Integration by Substitution
- Integration by Parts
- Integration of Rational Functions
- Separation of Variables (1st Order)
- Homogeneous Differential Equations (1st Order)
- Linear Differential Equations (1st Order)
- Bernoulli Equations (1st Order)
- Exact Differential Equations (1st Order)
  • Determine the type of different classes of differential equations of the first order: separable, linear, homogeneous, Bernoulli, exact.
  • Use direct methods to solve first order differential equations solved and not solved for the first derivative.
Week V
  • Ahmad and Ambrosetti 2014, Ch. 5
  • Understanding of Linear Independence of Functions.
Week V
  • Ahmad and Ambrosetti 2014, Ch. 5
  • Understanding of Linear Dependence of Functions.
Week V
  • Ahmad and Ambrosetti 2014, Ch. 5
  • Showing linear independence of two functions using the Wronskian.
  • Showing linear independence of two solutions of Linear Second-Order ODEs using the Wronskian.
Week VI
  • Ahmad and Ambrosetti 2014, Ch. 5
  • Apply of the reduction of the order technique for second-order ODEs with a given solution.
Week VI
  • Ahmad and Ambrosetti 2014, Ch. 5
  • Determine homogeneous classes of differential equations of the second and higher order.
  • Determine linear and non-linear classes of differential equations of the second and higher order.
Week VI
  • Ahmad and Ambrosetti 2014, Ch. 5
  • Determine Wronskian for a second-order ODE with 2 given solutions.
Week VI
  • Ahmad and Ambrosetti 2014, Ch. 5
  • Determine fundamental solutions.
Week VI
  • Ahmad and Ambrosetti 2014, Ch. 5
  • Determine non-homogeneous classes of differential equations of the second and higher order.
  • Determine linear and non-linear classes of differential equations of the second and higher order
Week VI
  • Ahmad and Ambrosetti 2014, Ch. 5
  • Integration techniques
- Direct Integration
- Integration by Substitution
- Integration by Parts
- Integration of Rational Functions
  • Apply of the variation of parameters technique for second-order ODEs.
Week VII
  • Ahmad and Ambrosetti 2014, Ch. 5
  • Integration techniques
- Direct Integration
- Integration by Substitution
- Integration by Parts
- Integration of Rational Functions
  • Apply variation of parameters technique for second-order ODEs.
Week VII
  • Ahmad and Ambrosetti 2014, Ch. 5
  • Apply method of undetermined coefficients technique for second-order ODEs.
Week VIII
  • Ahmad and Ambrosetti 2014, Ch. 5
- Direct Integration
- Integration by Substitution
- Integration by Parts
- Integration of Rational Functions
  • Methods for nonlinear second-order ODEs.
  • Apply reduction of the order method to some nonlinear second-order ODEs.
Week VIII
  • Ahmad and Ambrosetti 2014, Ch. 5
  • Apply variation of parameters technique for higher-order ODEs
Week VIII
  • Ahmad and Ambrosetti 2014, Ch. 5
  • Apply method of undetermined coefficients technique for higher-order ODEs
Week IX
  • Ahmad and Ambrosetti 2014, Ch. 6
  • Methods for linear higher-order ODEs
Week X
  • Ahmad and Ambrosetti 2014, Ch. 5
  • Apply variation of parameters technique for higher-order ODEs
Week X
  • Ahmad and Ambrosetti 2014, Ch. 5
  • Apply method of undetermined coefficients technique for higher-order ODEs
Week XI
  • Ahmad and Ambrosetti 2014, Chaps. 5, 6, 10
  • Overview of the solutions methods for second and higher order differential equations.
  • Direct methods for second and higher-order ODEs.
  • Evaluate the exact solutions of important classes of differential equations such as second order differential equations as well as some higher order differential equations.
Week XII
  • Ahmad and Ambrosetti 2014, Ch. 11
  • Definition and main properties of the L-transform.
Week XIII
  • Ahmad and Ambrosetti 2014, Ch. 11
  • Apply the theorem(s) for inverse L-transform.
Week XIV
  • Ahmad and Ambrosetti 2014, Ch. 11
  • Apply the Laplace transform as solution technique.
Week XIV
  • Ahmad and Ambrosetti 2014, Ch. 11
  • Apply the Laplace transform as solution technique.
Week XV
  • Ahmad and Ambrosetti 2014
  • Solutions methods discussed.
  • Apply the L-transform.
Week XV
  • Ahmad and Ambrosetti 2014
  • Overview of the solutions methods discussed.
  • Solutions methods discussed.
  • Apply all solutions methods discussed.
Week XVI
  • Ahmad and Ambrosetti 2014
  • Overview of the solutions methods discussed.
  • Solutions methods discussed.
  • Apply all solutions methods discussed.