Difference between revisions of "ModelCourses/Differential Calculus"

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==Problem sets==
  
==Problem sets==
−
* '''Set 01 Functions and Change''' Students will be able to
 +
* '''Set 01 Functions and Change''' <br> Students will be able to
 
** Find equations of lines
 
** Find equations of lines
 
** Find equations of perpendicular lines
  
** Find equations of perpendicular lines
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** Find the domain and range of functions
  
** Find the domain and range of functions
   
−
* '''Set 02 Exponential Functions''' Students will be able to
 +
* '''Set 02 Exponential Functions''' <br> Students will be able to
 
** Construct exponential functions based on given numerical data
  
** Construct exponential functions based on given numerical data
 
** Construct exponential functions based on given graphical data
  
** Construct exponential functions based on given graphical data
 
** Find the concavity of a function based on graphical data
  
** Find the concavity of a function based on graphical data
   
−
* '''Set 03 New Functions from Old''' Students will be able to
 +
* '''Set 03 New Functions from Old''' <br> Students will be able to
 
** Evaluate compositions of functions
  
** Evaluate compositions of functions
 
** Determine if a function is invertible or not
  
** Determine if a function is invertible or not
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** Evaluate an inverse function
  
** Evaluate an inverse function
   
−
* '''Set 04 Logarithmic Functions''' Students will be able to
 +
* '''Set 04 Logarithmic Functions''' <br> Students will be able to
 
** Solve exponential equation using logarithms
  
** Solve exponential equation using logarithms
 
** Find doubling times
  
** Find doubling times
 
** Identify the growth rate of an exponential function
  
** Identify the growth rate of an exponential function
   
−
* '''Set 05 Trigonometric Functions''' Students will be able to
 +
* '''Set 05 Trigonometric Functions''' <br> Students will be able to
 
** Find the period and amplitude of trigonometric functions
  
** Find the period and amplitude of trigonometric functions
 
** Find the equation of a function based on the graph
  
** Find the equation of a function based on the graph
 
** Apply concepts to problems in an applied setting
  
** Apply concepts to problems in an applied setting
   
−
* '''Set 06 Powers, Polynomials, and Rational Functions''' Students will be able to
 +
* '''Set 06 Powers, Polynomials, and Rational Functions''' <br> Students will be able to
 
** Find horizontal asymptotes
  
** Find horizontal asymptotes
 
** Find vertical asymptotes
  
** Find vertical asymptotes
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** Apply concepts to problems in an applied setting
  
** Apply concepts to problems in an applied setting
   
−
* '''Set 07 Introduction to Continuity''' Students will be able to
 +
* '''Set 07 Introduction to Continuity''' <br> Students will be able to
 
** Apply the Intermediate Value Theorem
  
** Apply the Intermediate Value Theorem
 
** Determine how to find parameters so that a piece-wise defined function is continuous
  
** Determine how to find parameters so that a piece-wise defined function is continuous
 
** Determine where a function is continuous
  
** Determine where a function is continuous
   
−
* '''Set 08 Limits ''' Students will be able to
 +
* '''Set 08 Limits ''' <br> Students will be able to
 
** Use a graph to estimate limits
  
** Use a graph to estimate limits
 
** Use a table 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
  
** 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 09 Introduction to the derivative''' <br> Students will be able to
 
**
 
**
   
−
* '''Set 10 The Derivative at a Point''' Students will be able to
 +
* '''Set 10 The Derivative at a Point''' <br> Students will be able to
 
**
 
**
   
−
* '''Set 11 The Derivative Function''' Students will be able to
 +
* '''Set 11 The Derivative Function''' <br> Students will be able to
 
**
 
**
   
−
* '''Set 12 Interpretations of the Derivative''' Students will be able to
 +
* '''Set 12 Interpretations of the Derivative''' <br> Students will be able to
 
**
 
**
   
−
* '''Set 13 The Second Derivative''' Students will be able to
 +
* '''Set 13 The Second Derivative''' <br> Students will be able to
 
**
 
**
   
−
* '''Set 14 Differentiability''' Students will be able to
 +
* '''Set 14 Differentiability'''<br> Students will be able to
 
**
 
**
   
−
* '''Set 15 Derivatives of Powers and Polynomials''' Students will be able to
 +
* '''Set 15 Derivatives of Powers and Polynomials''' <br> Students will be able to
 
**
 
**
   
−
* '''Set 16 Derivative of the Exponential Function''' Students will be able to
 +
* '''Set 16 Derivative of the Exponential Function''' <br> Students will be able to
 
**
 
**
   
−
* '''Set 17 The Product and Quotient Rules''' Students will be able to
 +
* '''Set 17 The Product and Quotient Rules''' <br> Students will be able to
 
**
 
**
   
−
* '''Set 18 The Chain Rule''' Students will be able to
 +
* '''Set 18 The Chain Rule''' <br> Students will be able to
 
**
 
**
   
−
* '''Set 19 The Trigonometric Functions''' Students will be able to
 +
* '''Set 19 The Trigonometric Functions''' <br> Students will be able to
 
**
 
**
   
−
* '''Set 20 The Chain Rule and Inverse Functions''' Students will be able to
 +
* '''Set 20 The Chain Rule and Inverse Functions''' <br> Students will be able to
 
**
 
**
   
−
* '''Set 21 Implicit Functions''' Students will be able to
 +
* '''Set 21 Implicit Functions''' <br> Students will be able to
 
**
 
**
   
−
* Set 22 Hyperbolic Functions
 +
* '''Set 22 Hyperbolic Functions''' <br> Students will be able to
−
* Set 23 Linear Approximation and the Derivative
 +
**
−
* Set 24 Theorems about Differentiable Functions
+
−
* Set 25 Using First and Second Derivatives
 +
* '''Set 23 Linear Approximation and the Derivative''' <br> Students will be able to
−
* Set 26 Optimization
 +
**
−
* Set 27 Families of Functions
 +
−
* Set 28 Optimization Geometry and Modeling
 +
* '''Set 24 Theorems about Differentiable Functions ''' <br> Students will be able to
−
* Set 29 Applications to Marginality (optional)
 +
**
−
* Set 30 Rates and Related Rates
 +
−
* Set 31 L’Hopital’s Rule, Growth, and Dominance
 +
* '''Set 25 Using First and Second Derivatives''' <br> Students will be able to
−
* Set 32 Parametric Equations
+
**
−
* Set 33 Introduction to the definite integral
 +
−
* Set 34 The Definite Integral
 +
* '''Set 26 Optimization''' <br> Students will be able to
−
* Set 35 The Fundamental Theorem and Interpretations
 +
**
−
* Set 36 Theorems about Definite Integrals
+
−
* Set 37 Antiderivatives Graphically and Numerically
 +
* '''Set 27 Families of Functions''' <br> Students will be able to
−
* Set 38 Constructing Antiderivatives Analytically
 +
**
−
* Set 39 Differential Equations
 +
−
* Set 40 Second Fundamental Theorem of Calculus
 +
* '''Set 28 Optimization Geometry and Modeling''' <br> Students will be able to
−
* Set 41 The Equations of Motion
 +
**
  +
  +
* '''Set 29 Applications to Marginality''' <br> Students will be able to
  +
**
  +
  +
* '''Set 30 Rates and Related Rates''' <br> Students will be able to
  +
**
  +
  +
* '''Set 31 L’Hopital’s Rule, Growth, and Dominance''' <br> Students will be able to
  +
**
  +
  +
* '''Set 32 Parametric Equations ''' <br> Students will be able to
  +
**
  +
  +
* '''Set 33 Introduction to the definite integral''' <br> Students will be able to
  +
**
  +
  +
* '''Set 34 The Definite Integral''' <br> Students will be able to
  +
**
  +
  +
* '''Set 35 The Fundamental Theorem and Interpretations''' <br> Students will be able to
  +
**
  +
  +
* '''Set 36 Theorems about Definite Integrals ''' <br> Students will be able to
  +
**
  +
  +
* '''Set 37 Antiderivatives Graphically and Numerically''' <br> Students will be able to
  +
**
  +
  +
* '''Set 38 Constructing Antiderivatives Analytically''' <br> Students will be able to
  +
**
  +
  +
* '''Set 39 Differential Equations''' <br> Students will be able to
  +
**
  +
  +
* '''Set 40 Second Fundamental Theorem of Calculus''' <br> Students will be able to
  +
**
  +
  +
* '''Set 41 The Equations of Motion''' <br> Students will be able to
  +
**

Revision as of 17:50, 9 March 2013

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
    Students will be able to
  • Set 23 Linear Approximation and the Derivative
    Students will be able to
  • Set 24 Theorems about Differentiable Functions
    Students will be able to
  • Set 25 Using First and Second Derivatives
    Students will be able to
  • Set 26 Optimization
    Students will be able to
  • Set 27 Families of Functions
    Students will be able to
  • Set 28 Optimization Geometry and Modeling
    Students will be able to
  • Set 29 Applications to Marginality
    Students will be able to
  • Set 30 Rates and Related Rates
    Students will be able to
  • Set 31 L’Hopital’s Rule, Growth, and Dominance
    Students will be able to
  • Set 32 Parametric Equations
    Students will be able to
  • Set 33 Introduction to the definite integral
    Students will be able to
  • Set 34 The Definite Integral
    Students will be able to
  • Set 35 The Fundamental Theorem and Interpretations
    Students will be able to
  • Set 36 Theorems about Definite Integrals
    Students will be able to
  • Set 37 Antiderivatives Graphically and Numerically
    Students will be able to
  • Set 38 Constructing Antiderivatives Analytically
    Students will be able to
  • Set 39 Differential Equations
    Students will be able to
  • Set 40 Second Fundamental Theorem of Calculus
    Students will be able to
  • Set 41 The Equations of Motion
    Students will be able to
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