For REQUIRED SYLLABUS information that is to be included on all syllabi starting Spring 2018, 201830 go to https://internal.cccs.edu/wp-content/uploads/documents/GT-MA1-Required-Syllabus-Info.docx. :

 1.     Recognize and classify differential equations.

 2. Use graphical approaches to analyze solution curves.

 3. Solve first and second order linear, homogeneous and nonhomogeneous differential equations using classical techniques.

 4. Solve first and second order linear homogeneous and linear nonhomogeneous differential equations using Laplace Transforms and power series.

 5. Solve 2 by 2 linear homogeneous systems of differential equations.

 6. Apply a numerical method to differential equations

 7. Apply differential equation modeling to various engineering problems.

 REQUIRED TOPICAL OUTLINE

 

 I.      Recognize and classify differential equations.

 a. Classification by type

 b. Classification by order

 c. Classification by linearity

 II. Use graphical approaches to analyze solution curves.

 a. Slope fields

 b. Phase lines

 III. Solve first and second order linear, homogeneous and nonhomogeneous differential equations using classical techniques.

 a. Separation of variables

 b. Integrating factor method

 c. Method of undetermined coefficients

 d. Method of variation of parameters

 e. Exact equations

 f. Auxiliary equations including distinct roots, repeated roots, and imaginary roots

 g. Linear independence

 h. Wronskian Determinants to prove linear independence

 i. Existence and Uniqueness Theorem

 IV. Solve first and second order linear homogeneous and linear nonhomogeneous differential equations using Laplace Transforms and power series.

 a. Laplace transforms of elementary functions

 b. Laplace transforms of periodic functions and derivatives

 c. Laplace transforms of inverse transforms

 d. Power series solutions

 V. Solve 2 by 2 linear homogeneous systems of differential equations.

 a. Matrix forms for systems of differential equations

 b. Distinct real, repeated and complex eigenvalues

 VI. Apply a numerical method to differential equations

 a. Euler's Method

 b. Numerical approximation methods using technology

 VII. Apply differential equation modeling to various engineering problems.

 a. Growth and decay

 b. Newton’s Law of Cooling

 c. Mass-spring oscillators and mechanical vibrations

 d. Mixture problems with multiple and single tanks