• Learning Outcomes for 3450:221 Analytic Geometry and Calculus I 

    Students are expected to be able to

    • Communicate mathematical results through the proper use of mathematical notation and words
    • Learn the definition of the limit of a function, how to calculate limits using the limit laws, and the definition of continuity
    • Learn the definition of the derivative of a function and how to differentiate polynomial, exponential, trigonometric, and logarithmic functions, as well as products, quotients and compositions of these functions.
    • Learn applications of the derivative
    • Learn the definitions of the definite and indefinite integral, the Fundamental Theorem of Calculus, and the substitution rule
  • Topical Outline
    • Exponential Functions
    • Inverse Functions and Logarithms
    • The Tangent and Velocity Problem
    • The Limit of a Function
    • Calculating Limits using the Limit Laws
    • The Precise Definition of a Limit
    • Continuity
    • Limits at Infinity: Horizontal Asymptotes
    • Derivatives and Rates of Change
    • The Derivative as a Function
    • Derivatives of Polynomials and Exponential Functions
    • The Product and Quotient Rules
    • Derivatives of Trigonometric Functions
    • The Chain Rule
    • Implicit Differentiation
    • Derivatives of Logarithmic Functions
    • Exponential Growth and Decay
    • Related Rates
    • Linear Approximations and Differentials
    • Hyperbolic Functions
    • Maximum and Minimum Values
    • The Mean Value Theorem
    • How Derivatives Affect the Shape of a Graph
    • Indeterminate Forms and l’Hopital’s Rule
    • Summary of Curve Sketching
    • Optimization Problems
    • Newton’s Method
    • Antiderivatives
    • Areas and Distances
    • The Definite Integral
    • Definite Integral
    • The Fundamental Theorem of Calculus
    • Indefinite Integrals and the Net Change Theorem
    • The Substitution Rule