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  • MA005: Calculus I
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  • Course data
    Course Introduction
    Course Introduction Video
    Course Syllabus
    Unit 1: Preview and Review
    1.1: Preview of Calculus
    1.2: Lines in the Plane
    1.3: Functions and Their Graphs
    1.4: Combinations of Functions
    1.5: Mathematical Language
    Unit 2: Functions, Graphs, Limits, and Continuity
    2.1: Tangent Lines, Velocities, and Growth
    2.2: The Limit of a Function
    2.3: Properties of Limits
    2.4: Continuous Functions
    2.5: Definition of a Limit
    Unit 2 Assessment
    Unit 3: Derivatives
    3.1: Introduction to Derivatives
    3.2: The Definition of a Derivative
    3.3: Derivatives, Properties, and Formulas
    3.4: Derivative Patterns
    3.5: The Chain Rule
    3.6: Some Applications of the Chain Rule
    3.7: Related Rates
    3.8: Newton's Method for Finding Roots
    3.9: Linear Approximation and Differentials
    3.10: Implicit and Logarithmic Differentiation
    Unit 3 Assessment
    Unit 4: Derivatives and Graphs
    4.1: Finding Maximums and Minimums
    4.2: The Mean Value Theorem and Its Consequences
    4.3: The First Derivative and the Shape of a Function f(x)
    4.4: The Second Derivative and the Shape of a Function f(x)
    4.5: Applied Maximum and Minimum Problems
    4.6: Infinite Limits and Asymptotes
    4.7: L'Hopital's Rule
    Unit 4 Assessment
    Unit 5: The Integral
    5.1: Introduction to Integration
    5.2: Sigma Notation and Riemann Sums
    5.3: The Definite Integral
    5.4: Properties of the Definite Integral
    5.5: Areas, Integrals, and Antiderivatives
    5.6: The Fundamental Theorem of Calculus
    5.7: Finding Antiderivatives
    5.8: First Application of Definite Integral
    5.9: Using Tables to Find Antiderivatives
    Unit 5 Assessment
    Study Guide
    Certificate Final Exam
    Course Feedback Survey
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    MA005: Calculus I

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    Saylor University © 2010-2026 except as otherwise noted. Excluding course final exams, content authored by Saylor University is available under a Creative Commons Attribution 3.0 Unported license. Third-party materials are the copyright of their respective owners and shared under various licenses. See detailed licensing information. Saylor University®, Saylor.org®, and Harnessing Technology to Make Education Free® are trade names of the Constitution Foundation, a 501(c)(3) organization through which our educational activities are conducted.