Note: F,S,Su 4 cr. LEC 4 PREREQUISITE: M151, ACT 27 or better, SAT 620 or better, MPLEX level 5 within the past 12 months.

Functions

  • elementary transcendental functions
  • limits and continuity
  • differentiation
  • applications of the derivative
  • curve sketching
  • integration theory

Course Learning Outcomes

Upon completion of this course, a student will be able to:

  • Explain the definition of limit, how to compute it in elementary cases, and how to determine the limits of transcendental, rational and piecewise defined functions;
  • Define infinite limits, limits at infinity, asymptotes, indeterminate forms and how to use L’Hopital’s Rule;
  • Explain the limit definition of continuity;
  • Explain the limit definition of the derivative of a function, how it related to the function itself, and how to use it to compute derivatives;
  • Use derivatives to find tangent lines to curves and velocity for particle motion;
  • Apply the power, sum, product, quotient and chain rules of differentiation;
  • Use the derivatives of exponential, logarithmic , trigonometric and hyperbolic functions;
  • Explain implicit and logarithmic differentiation;
  • Apply the Intermediate and Mean Value Theorems;
  • Graphically analyze functions including using continuity and differentiation to determine local and global extrema, concavity, and inflection points;
  • Use the derivative to solve challenging related rate and optimization word problems;
  • Explain Newton’s Method for estimating zeros of a function;
  • Explain the Riemann integral, areas under graphs, antiderivatives the Fundamental Theorem of Calculus;
  • Apply integration using the method of substitution

Core 2.0 Quantitative Reasoning (Q)

Students completing a Core 2.0 Quantitative Reasoning (Q) course should demonstrate an ability to:

  • Interpret and draw inferences from mathematical models such as formulas, graphs, diagrams or tables.
  • Represent mathematical information numerically, symbolically and visually.
  • Employ quantitative methods in symbolic systems such as, arithmetic, algebra, or geometry to solve problems.