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Calculus I - MATH 1501

Description

This course includes material on functions, limits, continuity, the derivative, anti-differentiation, the definite integral, and techniques of integration.


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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.
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