MAT3613

From Department of Mathematics at UTSA
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Topics List

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week I
  • Ahmad and Ambrosetti 2014,
  • Chaps. 1,
  • 2, 3
  • nan
  • nan
  • nan
  • Explain the basic notions related to differential equations: the order of a differential equation, solutions, basic concepts of initial values, existence and uniqueness.
  • Determine separable differential equations of the first order. Apply direct methods to evaluate exact solutions of separable differential equations of the first order.
  • nan
  • nan
  • nan
  • nan
  • Integration techniques.
  • nan
  • nan
  • nan
  • nan
  • nan
  • Explain the basic notions related to differential equations: the order of a differential equation, solutions, basic concepts of initial values, existence and uniqueness.
  • Determine separable differential equations of the first order. Apply direct methods to evaluate exact solutions of separable differential equations of the first order.
  • nan
  • nan
  • nan
  • nan
Week II
  • Ahmad and Ambrosetti 2014,
  • Chaps. 1
  • and 3
  • Determine homogeneous and linear differential equations of the first order. Apply direct methods to evaluate exact solutions of homogeneous and linear differential equations of the first order (substitutions, integrating factor method). Use some differential equations as mathematical models in biology, population dynamics, mechanics and electrical circuit theory
  • problems.
  • nan
  • Integration techniques.
  • nan
  • nan
  • Determine homogeneous and linear differential equations of the first order. Apply direct methods to evaluate exact solutions of homogeneous and linear differential equations of the first order (substitutions, integrating factor method). Use some differential equations as mathematical models in biology, population dynamics, mechanics and electrical circuit theory
  • problems.
  • nan
Week III
  • Ahmad and Ambrosetti 2014, Ch.
  • 3
  • nan
  • Determine Bernoulli and exact differential equations of the first order. Apply direct methods to evaluate exact solutions of Bernoulli and exact differential equations of the first order. Use the integrating factor technique for
  • exact equations.
  • nan
  • Integration techniques. Partial derivatives. Linear first- order differential equations.
  • nan
  • nan
  • Determine Bernoulli and exact differential equations of the first order. Apply direct methods to evaluate exact solutions of Bernoulli and exact differential equations of the first order. Use the integrating factor technique for
  • exact equations.
  • nan
Week IV
  • Ahmad and Ambrosetti 2014,
  • Chaps. 1-3
  • 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.
  • Integration techniques. Partial derivatives. Integrating factor methods.
  • First-order differential equations.
  • 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
  • nan
  • Linear dependence and independence of functions. Wronskian of two functions. Wronskian of two solutions of linear second-order ODEs.
  • nan
  • Linear dependence, independenc e of vectors.
  • Determinant s.
  • Linear dependence and independence of functions. Wronskian of two functions. Wronskian of two solutions of linear second-order ODEs.
  • nan
Week VI
  • Ahmad and Ambrosetti 2014, Ch. 5
  • nan
  • nan
  • nan
  • nan
  • nan
  • Determine the type of different classes of differential equations of the second and higher order: linear and nonlinear, equations with constant coefficients, homogeneous and non- homogeneous.
  • Determine fundamental solutions.
  • Apply of the variation of parameters technique for second-order ODEs.
  • nan
  • nan
  • nan
  • Wronskian. Algebraic equations. Determinant s.
  • nan
  • nan
  • nan
  • nan
  • nan
  • Determine the type of different classes of differential equations of the second and higher order: linear and nonlinear, equations with constant coefficients, homogeneous and non- homogeneous.
  • Determine fundamental solutions.
  • Apply of the variation of parameters technique for second-order ODEs.
  • nan
  • nan
  • nan
Week VII
  • Ahmad and Ambrosetti 2014, Ch. 5
  • nan
  • Apply variation of parameters and method of undetermined coefficients techniques for second-order ODEs.
  • nan
  • Variation of parameters. Method of undetermine d coefficients.
  • nan
  • Apply variation of parameters and method of undetermined coefficients techniques for second-order ODEs.
  • nan
Week VIII
  • asdfa
  • asdfsa
  • asdfas
  • asdfsa
Week IX
  • adfaf
  • asdfas
  • asdfas
  • asdfas
Week X
  • Ahmad and Ambrosetti 2014, Ch. 5
  • nan
  • nan
  • Apply variation of parameters and method of undetermined coefficients techniques for higher-order ODEs
  • nan
  • nan
  • Methods for higher-order ODEs.
  • Variation of parameters. Method of undetermine d coefficients.
  • nan
  • Apply variation of parameters and method of undetermined coefficients techniques for higher-order ODEs
  • nan
  • nan
Week XI
  • Ahmad and Ambrosetti 2014,
  • Chaps. 5,
  • 6, 10
  • Evaluate the exact solutions of important classes of differential equations such as second order differential equations as well as some higher order differential equations.
  • nan
  • nan
  • Direct methods for second and higher-order ODEs.
  • nan
  • nan
  • Evaluate the exact solutions of important classes of differential equations such as second order differential equations as well as some higher order differential equations.
  • nan
  • nan
Week XII
  • Ahmad and Ambrosetti 2014, Ch.
  • 11
  • nan
  • nan
  • nan
  • nan
  • Definition and main properties of the Laplace transform.
  • nan
  • nan
  • nan
  • nan
  • nan
  • Improper integrals with infinite limits.
  • nan
  • nan
  • nan
  • nan
  • nan
  • Definition and main properties of the Laplace transform.
  • nan
  • nan
  • nan
  • nan
  • nan
Week XIII
  • Ahmad and Ambrosetti 2014, Ch.
  • 11
  • Apply the theorem(s) for inverse L-transform.
  • nan
  • Derivatives of functions of complex variables.
  • nan
  • Apply the theorem(s) for inverse L-transform.
  • nan
Week XIV
  • Ahmad and Ambrosetti 2014, Ch.
  • 11
  • Apply the Laplace transform as solution technique.
  • nan
  • Properties of the L- transform and inverse L-transform.
  • nan
  • Apply the Laplace transform as solution technique.
  • nan
Week XV
  • Ahmad and Ambrosetti 2014
  • nan
  • Apply the L-transform. Apply all solutions methods discussed.
  • nan
  • Solutions methods discussed.
  • nan
  • Apply the L-transform. Apply all solutions methods discussed.
  • nan
Week XVI
  • Ahmad and Ambrosetti 2014
  • nan
  • Collect HOMEWORK # 3 Overview of the solutions methods discussed.
  • nan
  • Solutions methods discussed.
  • nan
  • Apply all solutions methods discussed.
  • nan
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