MAT175

MAT175 (Multivariable Mathematics for Economics and Life Sciences) is a survey of topics from Multivariable Calculus, with a very brief introduction to Linear Algebra as time permits. This course is a slower-paced, less comprehensive and less intensive alternative to the two semester sequence MAT201/202, and students who plan to take further mathematics courses at the 200-level or higher should take MAT201 instead. Students who do well in MAT175 can continue in MAT202 in order to learn more about linear algebra, but MAT201 is not an option after completing MAT175.

The main goal of MAT175 is to generalize the ideas of MAT103 (Calculus I – functions and derivatives and their applications along with the notion of the definite integral) to higher dimensions in order to prepare students for upper division work in economics and the sciences. The topics covered in the course include:

  • Geometry in Several Variables: Cartesian Coordinates and Vectors, Dot Product and Cross Product, Curves in the Plane and in 3-space, Lines and Tangent Lines in 3-space, Surfaces in 3-space. This will include a brief treatment of some topics from Linear Algebra (Determinants, Matrices and Gaussian Elimination)
  • Calculus in Several Variables: Partial derivatives, Functions of two or more variables, Limits, Continuity and Derivatives, Linear Approximation, Gradients, Chain Rule, Tangent Planes, Optimization (maxima and minima, saddle points), Constrained Optimization and Lagrange Multipliers.
  • Integration: Review of one-variable integration (Fundamental Theorem of Calculus, u-substitutions, Integration by Parts, Partial Fractions). Integrals involving Infinity, the Logistic Equation, Integrals over 2-dimensional Regions in the xy-plane.

MAT103 (Calculus I) is an absolutely necessary prerequisite for this course. We assume general familiarity with the general properties and the graphical behavior of the standard library of functions (polynomials and roots, rational functions, logarithmic and exponential functions, trigonometric functions and their inverses along with the standard formulas for derivatives and antiderivatives for these functions. Strong working knowledge of techniques for computing derivatives along with applications of the derivative, particularly to optimization (max-min problems) and for understanding rates of change and approximation is absolutely essential in the second half of the course.

Note: Although calculators can be an extremely useful analytic tool, they will not be a part of this course. At this level, they can be a hindrance to developing the independence and foundational knowledge that are the main goals of the course.

Your job as students in this course is to work hard and keep an open mind, asking questions and learning from the contradictions and surprises that you encounter as you try to solve the practice problems and struggle with new ideas.  Our job as instructors is to make sure you have interesting questions to think about, suitable for your current mathematical level, and access to well-informed guides who can help you get the greatest return on your sustained efforts throughout the semester. Lots of help is available including:

  • Instructor Office Hours: A schedule of office hours will be posted on the course web site and no appointment is needed. If the posted office hours conflict with your schedule, discuss this with your instructor – individual appointments can usually be arranged. Remember vague and ill-posed questions are a normal part of the learning process and are very welcome. (If you knew exactly what you were confused about then you probably would not be confused anymore!)
  • Review/Problem Sessions: There will be regular (optional) review/problem sessions with the course instructors/undergraduate course assistants/graduate course assistants. The schedule will be posted on the course web page early in the semester.
  • McGraw Tutoring/Study Hall/Workshops: The McGraw Center in Frist offers free (peer) tutoring and a good space for informal work with other students in the class.  We encourage you to work with them this semester.