ModelCourses/Differential Calculus

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General Description

  • Freshman level differential calculus course
  • Pre-requisite: Pre-Calculus


Possible textbooks include, but are not limited to:

  • Deborah Hughes-Hallett, Andrew Gleason, William McCallum et al. Calculus, Fifth Edition. New York, NY: John Wiley & Sons, Inc., 2009. (or a later edition)

Course Objectives

  • Properties of Elementary Functions
  • Introduction to continuity
  • Introduction to limits
  • Explore differentiation from graphical, numerical and analytical viewpoints
  • Optimization and modeling
  • The definite integral
  • Explore anti-derivatives from graphical, numerical and analytical viewpoints.
  • Fundamental Theorem of Calculus

Problem sets

  • Set 01 Functions and Change Students will be able to
    • Find equations of lines
    • Find equations of perpendicular lines
    • Find equations of parallel lines
    • Find the domain and range of functions
  • Set 02 Exponential Functions Students will be able to
    • Construct exponential functions based on given numerical data
    • Construct exponential functions based on given graphical data
    • Find the concavity of a function based on graphical data
  • Set 03 New Functions from Old Students will be able to
    • Evaluate compositions of functions
    • Determine if a function is invertible or not
    • Interpret the value of an inverse function
    • Evaluate an inverse function
  • Set 04 Logarithmic Functions Students will be able to
    • Solve exponential equation using logarithms
    • Find doubling times
    • Identify the growth rate of an exponential function


  • Set 05 Trigonometric Functions Students will be able to
    • Find the period and amplitude of trigonometric functions
    • Find the equation of a function based on the graph
    • Apply concepts to problems in an applied setting
  • Set 06 Powers, Polynomials, and Rational Functions Students will be able to
    • Find horizontal asymptotes
    • Find vertical asymptotes
    • Find the equation of a polynomial given a graph
    • Apply concepts to problems in an applied setting
  • Set 07 Introduction to Continuity Students will be able to
    • Apply the Intermediate Value Theorem
    • Determine how to find parameters so that a piece-wise defined function is continuous
    • Determine where a function is continuous
  • Set 08 Limits Students will be able to
    • Use a graph to estimate limits
    • Use a table to estimate limits
    • Determine the limit of sums, differences, products and quotients of two functions if the limits of the individual functions are known
  • Set 09 Introduction to the derivative Students will be able to
  • Set 10 The Derivative at a Point Students will be able to
  • Set 11 The Derivative Function Students will be able to
  • Set 12 Interpretations of the Derivative Students will be able to
  • Set 13 The Second Derivative Students will be able to
  • Set 14 Differentiability Students will be able to
  • Set 15 Derivatives of Powers and Polynomials Students will be able to
  • Set 16 Derivative of the Exponential Function Students will be able to
  • Set 17 The Product and Quotient Rules Students will be able to
  • Set 18 The Chain Rule Students will be able to
  • Set 19 The Trigonometric Functions Students will be able to
  • Set 20 The Chain Rule and Inverse Functions Students will be able to
  • Set 21 Implicit Functions Students will be able to
  • Set 22 Hyperbolic Functions
  • Set 23 Linear Approximation and the Derivative
  • Set 24 Theorems about Differentiable Functions
  • Set 25 Using First and Second Derivatives
  • Set 26 Optimization
  • Set 27 Families of Functions
  • Set 28 Optimization Geometry and Modeling
  • Set 29 Applications to Marginality (optional)
  • Set 30 Rates and Related Rates
  • Set 31 L’Hopital’s Rule, Growth, and Dominance
  • Set 32 Parametric Equations
  • Set 33 Introduction to the definite integral
  • Set 34 The Definite Integral
  • Set 35 The Fundamental Theorem and Interpretations
  • Set 36 Theorems about Definite Integrals
  • Set 37 Antiderivatives Graphically and Numerically
  • Set 38 Constructing Antiderivatives Analytically
  • Set 39 Differential Equations
  • Set 40 Second Fundamental Theorem of Calculus
  • Set 41 The Equations of Motion