MA 151

MA 151 - Calculus I

  1. Review of Functions
    a) Definition and notation; Domain and range
    b) Linear functions, Graphing

  2. Limits and Continuity
    a) Limits: intuitive, analytical and graphical approach
    b) Limits at Infinity
    c) Definition of continuity, Intermediate Value Theorem
    d) Limits and continuity of the trigonometric functions

  3. Differentiation
    a) Tangent line to a curve, instantaneous rate of change
    b)  Limit definition of the derivative
    c) Techniques of differentiation
    d) Derivatives of the trigonometric functions
    e) Chain rule; Implicit differentiation
    f) Differentials and the Tangent Line approximation

  4. Application of the Derivative
    a) Related rates
    b) Relative extrema
    c) Applications of the derivative to curve sketching
    d) Applications of maxima and minima
    e) Rolle's Theorem and the Mean Value Theorem
    f) Rectilinear motion; velocity and acceleration
    g) Newton's Method (optional)

  5. Logarithmic and Exponential Functions
    a) Integration and differentiation involving logarithmic and exponential functions

  6. Integration
    a) Antiderivatives and the indefinite integral
    b) Area and the definite integral
    c) The Fundamental Theorem of Calculus
    d) Change of variables and the Substitution Method
    e) The Mean Value Theorem for Integrals

    Learning Outcome 1: The student will understand the concept of limits and continuity.

    Learning Outcome 2: The student will understand the concept of the derivative.

    Learning Outcome 3: The student will understand the concept of the integral.