After completing this course, you will be able to:
- 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 in solving problems related to limits and continuity, and how to apply the technology.
- 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.
- 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.
- 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 0 - Review of Functions and their Properties (optional, non-graded)
- Unit 1 - Limits and Continuity
- Lesson 1.1 - Introduction to Limits
- Lesson 1.2 - Finding Limits
- Lesson 1.3 - Calculating Limits
- Lesson 1.4 - Infinite Limits
- Lesson 1.5 - Continuity and Discontinuity
- Unit 2 - Derivatives and Differentiation
- Lesson 2.1 - The Derivative Concept
- Lesson 2.2 - The Calculus of Derivatives
- Lesson 2.3 - Derivatives of Trigonometric Functions
- Lesson 2.4 - The Chain Rule
- Lesson 2.5 - Implicit Differentiation
- Lesson 2.6 - Related Rates
- Lesson 2.7 - Differentiation of Logarithmic and Exponential Functions
- Unit 3 – Applications of the Derivative
- Lesson 3.1 - Linear Approximation
- Lesson 3.2 - The Mean Value Theorem
- Lesson 3.3 - Derivatives and Graphs of Functions, Part I
- Lesson 3.4 - Derivatives and Graphs of Functions, Part II
- Lesson 3.5 - Average and Instantaneous Rate of Change
- Unit 4 – Integration
- Lesson 4.1 - Antidifferentiation
- Lesson 4.2 - Integration by Substitution
- Lesson 4.3 - Definite Integrals
- Lesson 4.4 - The Fundamental Theorem of Calculus
Your final grade will be based on the following breakdown. Please note that each instructor may choose to make modifications.
- Participation/Discussions – 5%
- Online Quizzes – 15%
- Online Exams (4) – 40%
- Proctored Midterm Exam – 20%
- Proctored Final Exam – 20%
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.
