Date 
Sections 
Topics 
Prerequisite Skills 
Student Learning Outcomes

Week I

 Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3


  Direct Integration
  Integration by Substitution
  Integration by Parts
  Partial Fractions

 Explain the basic notion of the order of a differential equation.

Week I

 Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3


  Direct Integration
  Integration by Substitution
  Integration by Parts
  Partial Fractions

 Explain the basic notion of solutions of differential equations.

Week I

 Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3


  Direct Integration
  Integration by Substitution
  Integration by Parts
  Partial Fractions

 Explain the basic notion of the initial values problem.

Week I

 Ahmad and Ambrosetti 2014, Chaps. 1, 2, 3


  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


  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


  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


  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



 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. 13

 Overview of the solutions methods discussed so far (Chapters 13).

  Direct Integration
  Integration by Substitution
  Integration by Parts
  Partial Fractions
  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 SecondOrder ODEs using the Wronskian.

Week VI

 Ahmad and Ambrosetti 2014, Ch. 5



 Apply of the reduction of the order technique for secondorder 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 nonlinear classes of differential equations of the second and higher order.

Week VI

 Ahmad and Ambrosetti 2014, Ch. 5



 Determine Wronskian for a secondorder 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 nonhomogeneous classes of differential equations of the second and higher order.
 Determine linear and nonlinear classes of differential equations of the second and higher order

Week VI

 Ahmad and Ambrosetti 2014, Ch. 5


  Direct Integration
  Integration by Substitution
  Integration by Parts
  Partial Fractions

 Apply of the variation of parameters technique for secondorder ODEs.

Week VII

 Ahmad and Ambrosetti 2014, Ch. 5


  Direct Integration
  Integration by Substitution
  Integration by Parts
  Partial Fractions

 Apply variation of parameters technique for secondorder ODEs.

Week VII

 Ahmad and Ambrosetti 2014, Ch. 5



 Apply method of undetermined coefficients technique for secondorder ODEs.

Week VIII

 Ahmad and Ambrosetti 2014, Ch. 5


  Direct Integration
  Integration by Substitution
  Integration by Parts
  Partial Fractions

 Methods for nonlinear secondorder ODEs.
 Apply reduction of the order method to some nonlinear secondorder ODEs.

Week VIII

 Ahmad and Ambrosetti 2014, Ch. 5



 Apply variation of parameters technique for higherorder ODEs

Week VIII

 Ahmad and Ambrosetti 2014, Ch. 5



 Apply method of undetermined coefficients technique for higherorder ODEs

Week IX

 Ahmad and Ambrosetti 2014, Ch. 6



 Methods for linear higherorder ODEs

Week X

 Ahmad and Ambrosetti 2014, Chaps. 5, 6

 Overview of the solutions methods for second and higher order differential equations.

  Variation of Parameters (Higher Order)
  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



Apply power series method to evaluate solutions of firstorder and secondorder ODEs.

Week XI

 Ahmad and Ambrosetti 2014, Chaps. 10



Apply power series method to evaluate solutions of firstorder and secondorder ODEs.

Week XII

 Ahmad and Ambrosetti 2014, Ch. 11



 Definition and main properties of the Ltransform.

Week XIII

 Ahmad and Ambrosetti 2014, Ch. 11



 Apply the theorem(s) for inverse Ltransform.

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

 Overview of the solutions methods discussed.


 Apply all solutions methods discussed.
