• Understand what calculus is and how it compares with pre-calculus
• Understand that the tangent line problem is basic to calculus.
• Understand that the area problem is also basic to calculus
• Estimate a limit using a numerical or graphical approach.
• Learn different ways that a limit can fail to exist.
• Study and use formal definition of limit.
• Evaluate a limit using properties of limits.
• Develop and use a strategy for finding limits,
• Evaluate a limit using dividing out and rationalizing techniques.
• Evaluate a limit using the squeeze theorem
• Determine continuity at a point and continuity on an open interval.
• Determine one-sided limits and continuity on a closed interval.
• Use properties of continuity.
• Understand and use the intermediate value theorem.
• Determine infinite limits from the left and from the right
• Find and sketch the vertical asymptotes of the graph of a function.

• Textbook: Calculus Early Transcendental Functions, pages 62-103
• Video lectures for Module 1 (in BConline)
• Power Points lectures for  Module.1 (in BConline)
• Additional learning tools (video, animation, textbook pages, etc) are available in Web Assign, under “eBook” for each topic/exercise in Module 1

• Chapter 2
• PowerPoint

Assessments

• Quizzes #1-5

Test # 1 

All quizzes+homework related to test#1 will be due the same date as the test.

• Find the slope of the tangent line to a curve at a point.
• Use the limit definition to find the derivative of a function.
• Understand the relationship between differentiability and continuity.
• Find the derivative of a function using the constant rule
• Find the derivative of a function using the power rule
• Find the derivative of a function using the constant multiple rules.
• Find the derivative of a function using the sum and difference rules
• Find the derivative of the sine, cosine, and exponential functions.
• Use the derivatives to find rates of change.
• Find the derivative of a function using the product rule.
• Find the derivative of a function using the quotient rule
• Find the derivative of a trigonometric function
• Find a higher-order derivative of a function.
• Find the derivative of a composite function using the chain rule.
• Find the derivative of a function using the general power rule.
• Simplify the derivative of a transcendental function using the chain rule.
• Find the derivative of a function involving the natural logarithmic function.
• Define and differentiate exponential functions that have bases other than e.
• Distinguish between functions written in implicit form and explicit form.
• Use implicit differentiation to find the derivative of a function.
• Find derivatives of functions using logarithmic differentiation.
• Find the derivative of an inverse function.
• Differentiate an inverse trigonometric function.
• Review the basic differentiation rules for elementary functions.
• Find a related rate.
• Use related rates to solve real-life problems.

• Textbook: Calculus Early Transcendental Functions, pages 116-189
• Video lectures for Module 2 (in BConline)
• Power Points lectures for  Module.2 (in BConline)
• Additional learning tools (video, animation, textbook pages, etc) are available in Web Assign, under “eBook” for each topic/exercise in Module 2

• Chapter 3
• PowerPoint

Assessments

• Quizzes #6-12

Test # 2

All quizzes+homework related to test#2 will be due the same date as the test.

• Understand the definition of extrema of a function on an interval.
• Understand the definition of relative extrema of a function on an open interval.
• Find extrema on a closed interval.
• Understand and use the mean value theorem.
• Determine intervals on which a function is increasing or decreasing.
• Apply the first derivative test to find relative extrema of a function.
• Determine intervals on which a function is concave upward or concave downward.
• Find any points of inflection of the graph of a function.
• Apply the second derivative test to find relative extrema of a function.
• Determine (finite) limits at infinity.
• Determine the horizontal asymptotes, if any, of the graph of a function.
• Determine infinite limits at infinity.
• Analyze and sketch the graph of a function.
• Solve applied minimum and maximum problems.
• Understand the concept of a tangent line approximation
•  Compare the value of differential,dy , with actual change in y, Delta y
• Estimate a propagated error using a differential.
• Find the differential of a function using differentiation formulas.

• Textbook: Calculus Early Transcendental Functions, pages 204-280
• Video lectures for Module 3 (in BConline)
• Power Points lectures for  Module.3 (in BConline)
• Additional learning tools (video, animation, textbook pages, etc) are available in Web Assign, under “eBook” for each topic/exercise in Module 3

• Chapter 4
• PowerPoint

Assessments

• Quizzes #13-20

Test # 3

All quizzes+homework related to test#3 will be due the same date as the test.

• Write the general solution of a differential equation.
• Use indefinite integral notation for antiderivative.
• Use basic integration rules to find antiderivatives.
• Find a particular solution of a differential  equation.
• Using sigma notation to write and evaluation a sum.
• Understand the concept of area.
• Approximate the area of a plane region.
• Find the area of a plane region using limits.
• Understand the definition of Riemann sum.
• Evaluate a definite integral using limits.
• Evaluate a definite integral using properties of definite integrals.
• Evaluate a definite integral using the fundamental theorem of calculus.
• Understand and use the mean value theorem for integrals.
• Find the average value of a function over a closed interval.
• Understand and use the second fundamental theorem of calculus.
• Understand and use the net change theorem.
• Use pattern recognition to find an indefinite integral.
• Use a change of variables to find and infinite integral.
• Use the general power rule for integration to find and indefinite integral.
• Evaluate a definite integral involving an even or odd function.
• Approximate a definite integral using the trapezoidal rule.
• Approximate a definite integral using simpson’s rule.
• Use the log rule  for integration to integrate a rational function.
• Integrate trigonometric functions.
• Integrate functions whose antiderivative involve inverse trigonometric functions.
• Use the method of completing the square to integrate a function.
• Use the method of completing the square to integrate a function.
• Review basic integration rules involving elementary functions.

• Textbook: Calculus Early Transcendental Functions, pages 281-357
• Video lectures for Module 4 (in BConline)
• Power Points lectures for  Module4 (in BConline)
• Additional learning tools (video, animation, textbook pages, etc) are available in Web Assign, under “eBook” for each topic/exercise in Module 4

• Chapter 5
• PowerPoint

Assessments

• Quizzes #20-28

Test # 4  

All quizzes+homework related to test#4 will be due the same date as the test.