Difference between revisions of "ModelCourses/Differential Calculus"

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Revision as of 15:54, 9 March 2013

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
Set 06 Powers, Polynomials, and Rational Functions
Set 07 Introduction to Continuity
Set 08 Limits
Set 09 Introduction to the derivative
Set 10 The Derivative at a Point
Set 11 The Derivative Function
Set 12 Interpretations of the Derivative
Set 13 The Second Derivative
Set 14 Differentiability
Set 15 Powers and Polynomials
Set 16 The Exponential Function
Set 17 The Product and Quotient Rules
Set 18 The Chain Rule
Set 19 The Trigonometric Functions
Set 20 The Chain Rule and Inverse Functions
Set 21 Implicit Functions
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

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