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| | ! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes | | ! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes |
| | |- | | |- |
| − | |Week I | + | |Week 1 |
| | || | | || |
| − | * Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3 | + | * |
| | || | | || |
| − | * [[Order of Differential Equations]] | + | * |
| | || | | || |
| − | * Integration techniques | + | * |
| − | :- [[Direct Integration]]
| |
| − | :- [[Integration by Substitution]]
| |
| − | :- [[Integration by Parts]]
| |
| − | :- [[Partial Fractions]]
| |
| | || | | || |
| − | * Explain the basic notion of the order of a differential equation. | + | * Learning outcome |
| − | |-
| |
| − | |Week I
| |
| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3
| |
| − | ||
| |
| − | * [[Solutions of Differential Equations]]
| |
| − | ||
| |
| − | * Integration techniques
| |
| − | :- [[Direct Integration]]
| |
| − | :- [[Integration by Substitution]]
| |
| − | :- [[Integration by Parts]]
| |
| − | :- [[Partial Fractions]]
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| − | ||
| |
| − | * Explain the basic notion of solutions of differential equations.
| |
| − | |-
| |
| − | |Week I
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| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3
| |
| − | ||
| |
| − | * [[Initial Value Problem|Initial Value Problem (IVP)]]
| |
| − | ||
| |
| − | * Integration techniques
| |
| − | :- [[Direct Integration]]
| |
| − | :- [[Integration by Substitution]]
| |
| − | :- [[Integration by Parts]]
| |
| − | :- [[Partial Fractions]]
| |
| − | ||
| |
| − | * Explain the basic notion of the initial values problem.
| |
| − | |-
| |
| − | |Week I
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| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3
| |
| − | ||
| |
| − | * [[Cauchy Problem]]
| |
| − | ||
| |
| − | * Integration techniques
| |
| − | :- [[Direct Integration]]
| |
| − | :- [[Integration by Substitution]]
| |
| − | :- [[Integration by Parts]]
| |
| − | :- [[Partial Fractions]]
| |
| − | ||
| |
| − | * 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
| |
| − | ||
| |
| − | * [[Separation of Variables (1st Order)]]
| |
| − | ||
| |
| − | * Integration techniques
| |
| − | :- [[Direct Integration]]
| |
| − | :- [[Integration by Substitution]]
| |
| − | :- [[Integration by Parts]]
| |
| − | :- [[Partial Fractions]]
| |
| − | ||
| |
| − | * 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
| |
| − | ||
| |
| − | * [[Homogeneous Differential Equations|Homogeneous Differential Equations (1st Order)]]
| |
| − | ||
| |
| − | * Integration techniques
| |
| − | :- [[Direct Integration]]
| |
| − | :- [[Integration by Substitution]]
| |
| − | :- [[Integration by Parts]]
| |
| − | :- [[Partial Fractions]]
| |
| − | ||
| |
| − | * 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
| |
| − | ||
| |
| − | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]]
| |
| − | ||
| |
| − | * Integration techniques
| |
| − | :- [[Direct Integration]]
| |
| − | :- [[Integration by Substitution]]
| |
| − | :- [[Integration by Parts]]
| |
| − | :- [[Partial Fractions]]
| |
| − | ||
| |
| − | * 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
| |
| − | ||
| |
| − | * [[Integrating Factor]]
| |
| − | ||
| |
| − | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]]
| |
| − | ||
| |
| − | * 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
| |
| − | ||
| |
| − | * [[Bernoulli Equations (1st Order)]]
| |
| − | ||
| |
| − | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]]
| |
| − | ||
| |
| − | * Determine Bernoulli of the first order.
| |
| − | * Apply direct methods to evaluate exact solutions of Bernoulli of the first order.
| |
| − | |-
| |
| − | |Week III
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| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Ch. 3
| |
| − | ||
| |
| − | * [[Exact Differential Equations|Exact Differential Equations (1st Order)]]
| |
| − | ||
| |
| − | * [[Integrating Factor]] for exact equations.
| |
| − | * [[Partial Derivatives]]
| |
| − | ||
| |
| − | * 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]]
| |
| − | :- [[Partial Fractions]]
| |
| − | * [[Partial Derivatives]]
| |
| − | * First-order differential equations:
| |
| − | :- [[Separation of Variables (1st Order)]]
| |
| − | :- [[Homogeneous Differential Equations|Homogeneous Differential Equations (1st Order)]]
| |
| − | :- [[Linear Differential Equations|Linear Differential Equations (1st Order)]]
| |
| − | :- [[Bernoulli Equations (1st Order)]]
| |
| − | :- [[Exact Differential Equations|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
| |
| − | ||
| |
| − | * [[Linear Independence of Functions]].
| |
| − | ||
| |
| − | * [[Linear Independence of Vectors]].
| |
| − | ||
| |
| − | * Understanding of Linear Independence of Functions.
| |
| − | |-
| |
| − | |Week V
| |
| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Ch. 5
| |
| − | ||
| |
| − | * [[Linear Independence of Functions|Linear Dependence of Functions]].
| |
| − | ||
| |
| − | * [[Linear Dependence of Vectors]].
| |
| − | ||
| |
| − | * Understanding of Linear Dependence of Functions.
| |
| − | |-
| |
| − | |Week V
| |
| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Ch. 5
| |
| − | ||
| |
| − | * [[Wronskian]]
| |
| − | ||
| |
| − | * [[Linear Independence of Functions]].
| |
| − | * [[Linear Independence of Functions|Linear Dependence of Functions]].
| |
| − | * [[Determinant]].
| |
| − | ||
| |
| − | * 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
| |
| − | ||
| |
| − | * [[Reduction of the Order]]
| |
| − | ||
| |
| − | * [[Wronskian]].
| |
| − | * [[Quadratic Equations]].
| |
| − | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]].
| |
| − | * [[Solutions of Linear Systems]].
| |
| − | ||
| |
| − | * Apply of the reduction of the order technique for second-order ODEs with a given solution.
| |
| − | |-
| |
| − | |Week VI
| |
| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Ch. 5
| |
| − | ||
| |
| − | * [[Homogeneous Differential Equations|Linear Homogeneous Equations]]
| |
| − | ||
| |
| − | * [[Wronskian]].
| |
| − | * [[Quadratic Equations]].
| |
| − | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]].
| |
| − | * [[Solutions of Linear Systems]].
| |
| − | ||
| |
| − | * 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
| |
| − | ||
| |
| − | * [[Abel’s Theorem]]
| |
| − | ||
| |
| − | * [[Wronskian]].
| |
| − | * [[Quadratic Equations]].
| |
| − | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]].
| |
| − | * [[Solutions of Linear Systems]].
| |
| − | ||
| |
| − | * Determine Wronskian for a second-order ODE with 2 given solutions.
| |
| − | |-
| |
| − | |Week VI
| |
| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Ch. 5
| |
| − | ||
| |
| − | * [[Fundamental Solutions]]
| |
| − | ||
| |
| − | * [[Wronskian]].
| |
| − | * [[Quadratic Equations]].
| |
| − | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]].
| |
| − | * [[Solutions of Linear Systems]].
| |
| − | ||
| |
| − | * Determine fundamental solutions.
| |
| − | |-
| |
| − | |Week VI
| |
| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Ch. 5
| |
| − | ||
| |
| − | * [[Linear Differential Equations|Linear Non-homogeneous Equations]]
| |
| − | ||
| |
| − | * [[Wronskian]].
| |
| − | * [[Quadratic Equations]].
| |
| − | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]].
| |
| − | * [[Solutions of Linear Systems]].
| |
| − | ||
| |
| − | * 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
| |
| − | ||
| |
| − | * [[Variation Of Parameters (2nd Order)|Variation of Parameters (2nd Order)]]
| |
| − | ||
| |
| − | * Integration techniques
| |
| − | :- [[Direct Integration]]
| |
| − | :- [[Integration by Substitution]]
| |
| − | :- [[Integration by Parts]]
| |
| − | :- [[Partial Fractions]]
| |
| − | * [[Quadratic Equations]].
| |
| − | * [[Solutions of Linear Systems]].
| |
| − | ||
| |
| − | * Apply of the variation of parameters technique for second-order ODEs.
| |
| − | |-
| |
| − | |Week VII
| |
| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Ch. 5
| |
| − | ||
| |
| − | * [[Variation Of Parameters (2nd Order)|Variation of Parameters (2nd Order)]] (continued)
| |
| − | ||
| |
| − | * Integration techniques
| |
| − | :- [[Direct Integration]]
| |
| − | :- [[Integration by Substitution]]
| |
| − | :- [[Integration by Parts]]
| |
| − | :- [[Partial Fractions]]
| |
| − | * [[Quadratic Equations]].
| |
| − | * [[Solutions of Linear Systems]].
| |
| − | ||
| |
| − | * Apply variation of parameters technique for second-order ODEs.
| |
| − | |-
| |
| − | |Week VII
| |
| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Ch. 5
| |
| − | ||
| |
| − | * [[Method of Undetermined Coefficients (2nd Order)]]
| |
| − | ||
| |
| − | * [[Quadratic Equations]].
| |
| − | * [[Systems of Linear Equations]].
| |
| − | ||
| |
| − | * Apply method of undetermined coefficients technique for second-order ODEs.
| |
| − | |-
| |
| − | |Week VIII
| |
| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Ch. 5
| |
| − | ||
| |
| − | * [[Non-linear 2nd Order ODEs]]
| |
| − | ||
| |
| − | * [[Algebraic Equations]]
| |
| − | * [[Reduction of the Order]]
| |
| − | * Integration techniques
| |
| − | :- [[Direct Integration]]
| |
| − | :- [[Integration by Substitution]]
| |
| − | :- [[Integration by Parts]]
| |
| − | :- [[Partial Fractions]]
| |
| − | ||
| |
| − | * 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
| |
| − | ||
| |
| − | * [[Variation Of Parameters|Variation of Parameters (Higher Order)]]
| |
| − | ||
| |
| − | * [[Variation Of Parameters|Variation of Parameters (2nd Order)]]
| |
| − | ||
| |
| − | * Apply variation of parameters technique for higher-order ODEs
| |
| − | |-
| |
| − | |Week VIII
| |
| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Ch. 5
| |
| − | ||
| |
| − | * [[Method of Undetermined Coefficients|Method of Undetermined Coefficients (Higher Order)]]
| |
| − | ||
| |
| − | * [[Method of Undetermined Coefficients (2nd Order)]]
| |
| − | ||
| |
| − | * Apply method of undetermined coefficients technique for higher-order ODEs
| |
| − | |-
| |
| − | |Week IX
| |
| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Ch. 6
| |
| − | ||
| |
| − | * [[Linear Differential Equations|Linear Differential Equations (Higher Order)]]
| |
| − | ||
| |
| − | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]]
| |
| − | * [[Variation Of Parameters|Variation of Parameters (Higher Order)]].
| |
| − | * [[Method of Undetermined Coefficients|Method of Undetermined Coefficients (Higher Order)]].
| |
| − | ||
| |
| − | * Methods for linear higher-order ODEs
| |
| − | |-
| |
| − | |Week X
| |
| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Chaps. 5, 6
| |
| − | ||
| |
| − | * Overview of the solutions methods for second and higher order differential equations.
| |
| − | ||
| |
| − | * [[Algebraic Equations]]
| |
| − | * Direct methods for second and higher-order ODEs:
| |
| − | :- [[Variation Of Parameters|Variation of Parameters (Higher Order)]]
| |
| − | :- [[Method of Undetermined Coefficients|Method of Undetermined Coefficients (Higher Order)]]
| |
| − | ||
| |
| − | * 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 X
| |
| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Chaps. 10
| |
| − | ||
| |
| − | * [[Power Series Solutions]]
| |
| − | ||
| |
| − | * [[Power Series Induction]]
| |
| − | ||
| |
| − | Apply power series method to evaluate solutions of first-order and second-order ODEs.
| |
| − | |-
| |
| − | |Week XI
| |
| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Chaps. 10
| |
| − | ||
| |
| − | * [[Power Series Solutions]] (continued)
| |
| − | ||
| |
| − | * [[Power Series Induction]]
| |
| − | ||
| |
| − | Apply power series method to evaluate solutions of first-order and second-order ODEs.
| |
| − | |-
| |
| − | |Week XII
| |
| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Ch. 11
| |
| − | ||
| |
| − | * [[Laplace Transform]]
| |
| − | ||
| |
| − | * [[Functions]] of Single Variable.
| |
| − | * [[Continuity]] of functions of single variables.
| |
| − | * [[Derivatives]] of functions of single variables.
| |
| − | * [[Improper Integrals]] of functions of single variables with infinite limits.
| |
| − | ||
| |
| − | * Definition and main properties of the L-transform.
| |
| − | |-
| |
| − | |Week XIII
| |
| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Ch. 11
| |
| − | ||
| |
| − | * [[Inverse Laplace Transform]]
| |
| − | ||
| |
| − | * [[Laplace Transform]]
| |
| − | * [[Complex Derivatives]]
| |
| − | ||
| |
| − | * Apply the theorem(s) for inverse L-transform.
| |
| − | |-
| |
| − | |Week XIV
| |
| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Ch. 11
| |
| − | ||
| |
| − | * [[Laplace Transform to ODEs]]
| |
| − | ||
| |
| − | * [[Linear Differential Equations|Linear Equations]]
| |
| − | * [[Laplace Transform]]
| |
| − | * [[Inverse Laplace Transform]]
| |
| − | ||
| |
| − | * Apply the Laplace transform as solution technique.
| |
| − | |-
| |
| − | |Week XIV
| |
| − | ||
| |
| − | * Ahmad and Ambrosetti 2014, Ch. 11
| |
| − | ||
| |
| − | * [[Laplace Transform to ODEs|Laplace Transform to Systems of ODEs]]
| |
| − | ||
| |
| − | * [[Solutions of Linear Systems]].
| |
| − | * [[Laplace Transform]].
| |
| − | * [[Inverse Laplace Transform]].
| |
| − | ||
| |
| − | * Apply the Laplace transform as solution technique.
| |
| − | |-
| |
| − | |Week XV
| |
| − | ||
| |
| − | * Ahmad and Ambrosetti 2014
| |
| − | ||
| |
| − | * Overview of the solutions methods discussed.
| |
| − | ||
| |
| − | * [[Separation of Variables (1st Order)]]
| |
| − | * [[Homogeneous Differential Equations|Homogeneous Differential Equations (1st Order)]]
| |
| − | * [[Linear Differential Equations|Linear Differential Equations (1st Order)]]
| |
| − | * [[Integrating Factor]]
| |
| − | * [[Bernoulli Equations (1st Order)]]
| |
| − | * [[Exact Differential Equations|Exact Differential Equations (1st Order)]]
| |
| − | * [[Reduction of the Order]]
| |
| − | * [[Method of Undetermined Coefficients (2nd Order)]]
| |
| − | * [[Non-linear 2nd Order ODEs]]
| |
| − | * [[Variation Of Parameters|Variation of Parameters (Higher Order)]]
| |
| − | * [[Method of Undetermined Coefficients|Method of Undetermined Coefficients (Higher Order)]]
| |
| − | * [[Linear Differential Equations|Linear Differential Equations (Higher Order)]]
| |
| − | * [[Power Series Solutions]]
| |
| − | * [[Laplace Transform to ODEs]]
| |
| − | * [[Laplace Transform to ODEs|Laplace Transform to Systems of ODEs]]
| |
| − | ||
| |
| − | * Apply all solutions methods discussed.
| |
| | |} | | |} |
