Math 131, Spring 2012


Instructor:

  • Yang Qi (yangqi@math.tamu.edu)


Course description & prerequisites:

  • Description: Limits and continuity; rates of change, slope; differentiation: the derivative, maxima and minima; integration: the definite and indefinite integral techniques; curve fitting.
  • Prerequisites: High school algebra I and II and geometry.
  • Calculator policy: This course requires that you have a TI-83 or TI-84 (Plus or Silver) calculator or the TI-Nspire (non-CAS version). It will be allowed on most quizzes and exams. During in-class quizzes, calculators cannot be shared.
  • Textbook: James Stewart, Single Variable Calculus: Concepts & Contexts, 4th edition, 2010.


Learning outcomes:

This course is focused on quantitative literacy in mathematics found in the natural and social sciences and everyday life. Upon successful completion of this course, students will be able to:

  • Logically formulate mathematical variables and equations to quantitatively create mathematical models representing problems in everyday life.
  • Recognize and construct graphs of basic functions, including polynomials, exponentials, logarithms, and trigonometric functions and use them to model real-life situations.
  • Identify patterns in numeric data to calculate limits and derivatives of functions numerically.
  • Compute limits of functions numerically, graphically, and algebraically.
  • Justify whether a function is continuous or not using the mathematical definition of continuity.
  • Compute derivatives using the limit definition of the derivative.
  • Understand the derivative as a rate of change in order to quantitatively apply it to everyday life. For example, recognize that derivatives can be used to find the velocity and acceleration of an object given its position function.
  • Compute derivatives of polynomials, rational, trigonometric, exponential, and logarithmic functions.
  • Apply the product rule, quotient rule, and chain rule to take derivatives of compositions of functions.
  • Compute the linear approximation of a function and use it in applications of approximation and error estimation.
  • Investigate the relationship between a function and its first and second derivatives, and use the information obtained from its derivatives to identify pertinent information about the function.
  • Find the local and absolute extrema of functions, including optimization applications such as minimizing the cost of fencing in a particular area of land.
  • Compute antiderivatives and understand the concept of integration as it relates to area.
  • Apply the definite integral to quantitatively determine solutions to problems in everyday life including areas between curves, average value of a function, and total distance traveled.
  • Recognize and appreciate the derivative (rate of change) and the definite integral (accumulation of change) and utilize the Fundamental Theorem of Calculus as the bridge between the two.
  • Apply the substitution method to compute integrals.


Core objectives:

  • Critical thinking, communication skills, empirical and quantitative skills


Lecture notes:


Quizzes:


Exams:


Reviews and solutions:


Useful links: