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Course Syllabus

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MA005: Calculus I

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COURSE INTRODUCTION

Course Syllabus

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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

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Certificate Final Exam

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