After completing this course, you will be able to:
Limits and Continuity:
- Calculate and evaluate limits and represent these concepts graphically, algebraically, numerically and in words.
- Apply knowledge of limits and continuity to analyze and solve real-world problems.
- Determine when the use of technology is appropriate for solving problems related to limits and continuity, and how to apply the technology.
Derivatives and Differentiation:
- Explain the definition of derivative and how it is related to tangent lines and rates of change, and to compute derivatives from the limit definition.
- Compute derivatives using all of the standard rules, displaying, in particular, a strong mastery of the Chain Rule.
- Compute derivatives of trigonometric functions and compute closely related trigonometric limits.
- Explain the concept of an implicitly defined function, and use the technique of implicit differentiation to differentiate functions that are defined implicitly.
- Model and solve related rates problems.
Applications of the Derivative:
- Solve problems related to rates of change.
- Identify and describe properties of functions and their graphs.
- Apply the properties of functions and their graphs to real life problem situations.
Integration:
- Calculate anti-derivatives by using some basic rules.
- Evaluate anti-derivatives using the substitution technique.
- Define the definite integral.
- Evaluate a few definite integrals using the definition as a limit of Riemann sums.
- State the Fundamental Theorem of Calculus.
- Apply the Fundamental Theorem of Calculus to evaluate definite integral.
- Unit 1: The Limit of a Function
- Unit 2: Limit Laws and Continuity
- Unit 3: Introduction to Derivatives
- Unit 4: Advanced Derivatives
- Unit 5: Applications of Derivative 1
- Unit 6: Applications of Derivative 2
- Unit 7: Antiderivatives and the Definite Integral
- Unit 8: Integration
Your final grade will be based on the following breakdown. Please note that each instructor may choose to make modifications.
- Attendance Verification 1%
- Participation & Discussions 5%
- Homework (x4) 10%
- Math Learning Project 4%
- Lesson Quizzes (x16) 10%
- Online Exams (x4) 40%
- Proctored Midterm Exam 15%
- Final Exam 15%
* The midterm and/or the final will be proctored.
You will need access to one of the following graphing calculators to complete the activities in MATH 1501: TI-83 or TI-84 with computer cable or TI-83 Plus or TI-84 Plus.
It is also important to note that you will be required to submit your worked examples -hand written or produced in Word- for the Online Exams. For that reason, you must have access to some type of recording device to capture and submit your work:
- Microsoft Word to demonstrate your work in a text format or
- Digital camera, phone camera, scanner or webcam to submit a photo copy of your hand-written work.