This week we will focus on...
Week 1 Learning Objectives:
Upon successful completion of this week, students will:
(1.) Define the limit of a function.
(2.) Evaluate the limit of a function numerically.
(3.) Evaluate the limit of a function graphically.
(4.) Evaluate the limit of a function algebraically.
(5.) Define a continuous function.
(6.) Define a discontinuous function.
(7.) Solve applied problems involving the limit of a function.
(8.) Solve applied problems involving function continuity.
This week we will focus on...
Week 2 Learning Objectives:
Upon successful completion of this week, students will:
(1.) Review the slope concept.
(2.) Interpret the slope of a secant line of a function as the Difference Quotient of the function.
(3.) Interpret the slope of a tangent line of a function as the Derivative of the function.
(4.) Solve applied problems on the slope of a function.
This week we will focus on...
Week 3 Learning Objectives:
Upon successful completion of this week, students will:
(1.) Differentiate functions by Limits.
(2.) Differentiate functions by Rules (Power Rule and Sum/Difference Rule).
(3.) Solve applied problems on the differentiation of functions by Limits.
(4.) Solve applied problems on the differentiation of functions by Rules (Power Rule and Sum/Difference
Rule).
This week we will focus on...
Week 4 Learning Objectives:
Upon successful completion of this week, students will:
(1.) Differentiate functions using the Product Rule.
(2.) Differentiate functions using the Quotient Rule.
(3.) Differentiate functions using the Chain Rule.
(4.) Solve applied problems on the differentiation of functions using the Product Rule.
(5.) Solve applied problems on the differentiation of functions using the Quotient Rule.
(6.) Solve applied problems on the differentiation of functions using the Chain Rule.
This week we will focus on...
Week 5 Learning Objectives:
Upon successful completion of this week, students will:
(1.) Find the higher-order derivatives of functions.
(2.) Discuss natural exponential functions. (exponential functions with the Euler number base,
e).
(3.) Discuss natural logarithmic functions (logarithmic functions with the Euler number base, e).
(4.) Solve applied problems involving higher-order derivatives.
(5.) Solve applied problems involving natural exponential functions.
(6.) Solve applied problems involving natural logarithmic functions.
This week we will focus on...
Week 6 Learning Objectives:
Upon successful completion of this week, students will:
(1.) Differentiate natural exponential functions.
(2.) Differentiate natural logarithmic functions.
(3.) Solve applied problems involving uninhibited growth models.
(4.) Solve applied problems involving limited growth models.
This week we will focus on...
Week 7 Learning Objectives:
Upon successful completion of this week, students will:
(1.) Solve applied problems involving exponential decay models.
(2.) Differentiate exponential functions.
(3.) Differentiate logarithmic functions.
(4.) Solve applied problems involving exponential functions.
(5.) Solve applied problems involving logarithmic functions.
This week we will focus on...
Week 8 Learning Objectives:
Upon successful completion of this week, students will:
(1.) Explain the First Derivative Test.
(2.) Determine the relative extrema of functions using the First Derivative Test.
(3.) Explain the Second Derivative Test.
(4.) Determine the relative extrema of functions using the Second Derivative Test.
(5.) Sketch graphs using information from the First and/or Second Derivative Tests.
(6.) Solve applied problems involving the relative extrema of functions.
This week we will focus on...
Week 9 Learning Objectives:
Upon successful completion of this week, students will:
(1.) Explain the Extreme Value Theorem.
(2.) Determine the absolute extrema of functions on closed intervals by evaluating critical points and
end points.
(3.) Solve applied problems involving the absolute extrema of functions.
This week we will focus on...
Week 10 Learning Objectives:
Upon successful completion of this week, students will:
(1.) Differentiate implicit functions.
(2.) Determine the rate of change of one function on relation to the rate of change of another function.
(3.) Solve applied problems using implicit differentiation.
(4.) Solve applied problems involving related rates.
This week we will focus on...
Week 11 Learning Objectives:
Upon successful completion of this week, students will:
(1.) Explain the concept of the antiderivative of a function.
(2.) Apply the Power Rule to determine antiderivatives of functions.
(3.) Compute areas enclosed by straight-line functions using mensuration formulas.
(4.) Verify these areas by recalculating them with definite integrals.
(5.) Evaluate areas under curves using definite integrals and Riemann sums.
(6.) Solve applied problems involving the antiderivatives of functions using Power Rule.
This week we will focus on...
Week 12 Learning Objectives:
Upon successful completion of this week, students will:
(1.) Explain the properties of definite integrals.
(2.) Apply algebraic substitution techniques to determine antiderivatives of functions
(Integration by Algebraic Substitution).
(3.) Solve applied problems involving the properties of definite integrals.
(4.) Solve applied problems involving Integration by Algebraic Substitution.
This week we will focus on...
Week 13 Learning Objectives:
Upon successful completion of this week, students will:
(1.) Explain the concept of consumer surplus.
(2.) Explain the concept of producer surplus.
(3.) Integrate growth models.
(4.) Integrate decay models.
(5.) Solve applied problems involving consumer surpluses.
(6.) Solve applied problems involving producer surpluses.
(7.) Solve applied problems involving growth models.
(8.) Solve applied problems involving decay models.