Math 213 - Calculus and Introduction to Differential Equations

• Prerequisites: Math 211 or 221.
• Frequency: Fall (I), Winter (II)
• Student Body: students in social sciences and finance.
• Credits: 3. Students may not receive full degree credit for both Math 222 and 213 or both Math 234 and 213. (r-N-I)
• Recent Texts: Applied Calculus, by Hughes - Hallett, Gleason, et al, 1st ed. Wiley (1999). Calculus, Single Variable, by Hughes - Hallett, Gleason, et al, 2nd ed. Wiley (1998), Chapter 9 only
• Course Coordinator: Wayne Dickey
• Background and Goals: This course is a sequel to Math 211 for students, primarily in social sciences and finance, who need to develop more techniques than are covered in Math 211. Math 221 is also suitable preparation for Math 213. Students in Math 213 whose calculus background is not very recent will need to review and work problems in elementary calculus. Some class time is assigned for this, but students should be prepared to put considerable effort into review.
  Students in the biological sciences are better served by 231 and/or 232.
• Alternatives: Students in the physical sciences or who will eventually wish to take higher level mathematics courses should not take this course, but should go through the sequence 221-222-234.
• Subsequent Courses: n/a

Content coverage:

• Review of techniques of single-variable calculus: Functions, graphs, definition of derivative, rules for calculating derivatives, exponential and logarithmic functions, maximum - minimum problems, indefinite and definite integrals, the fundamental theorem of calculus, techniques of integration.
• Some business applications of single-variable calculus: Optimization problems, supply and demand, elasticity of demand, consumers' surplus.
• Multivariable calculus: Functions of two variables, limits, partial derivatives, local linearity and the chain rule, implicit differentiation, maximum - minimum problems and business applications, constrained maximum - minimum problems and business applications.
• Taylor approximation: Taylor polynomials, the mean value theorem, Taylor's theorem with remainder, Taylor series and representation of functions by power series.
• First-order differential equations: Exponential growth and decay, separable equations, linear differential equations, qualitative properties, applications in economics and business.