MATH 270 Advanced Math for the Sciences (3)

Catalog Description:

This course covers applied material in four areas of advanced mathematics that are foundational for scientific work: matrices, vector spaces, Fourier series, and ordinary differential equations. Topics in these areas are taught with an emphasis on building intuition and proficiency with mathematical methods for modeling scientific processes. (Offered spring semester only.)

 

Prerequisites:


MATH 112 Calculus II or Prerequisite/Corequisite one of MATH 210 Fundamentals of Vector Calculus or MATH 211 Calculus III

Required Course Materials:


Dennis G. Zill and Warren S. Wright, Advanced Engineering Mathematics, 5th edition, Jones and Bartlett Learning Company, 2014

Course Coordinator:


Angela C. Hare, Ph.D., Professor of Mathematics

Course Audience:


Required course for students studying in Chemistry and Engineering.

Course Objectives:

 

Students completing this course should be able to:

  1. Develop the ability to solve ordinary differential equations of first or second order.
  2. Develop the ability to model certain physical phenomenon using ordinary differential equations.
  3. Develop proficiency and understanding of matrices and their applications.
  4. Demonstrate proficiency with Fourier Series in applied settings.
  5. Develop an understanding of complex numbers.

Topics:

 

  1. First-order differential equations: A) separable variables, B)exact equations, C) linear equations, D) integrating factors
  2. Second-order differential equations:  A) reduction of order, B) undetermined coefficients, C) variation of parameters.
  3. Laplace transforms and their application to solving differential equations.
  4. Numerical and graphical methods:  A) direction fields, B) Euler’s method.
  5. Applications:  A) simple harmonic motion, B) damped and forced motion, C) mixture problems, D) population growth, E) radioactive decay. 
  6. Power series solutions for ordinary and singular points
  7. Fourier Series
  8. Complex Numbers: A) powers and roots, B) Sets in the complex plane, C) functions of a complex variable, D) Cauchy-Riemann Equations

 

Revised: February 2013

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