### MAT1300: Calculus

05/01/2023 to 04/30/2024 • Modified 06/08/2023

### Course Description

This year-long course builds on principles of geometry, algebra, trigonometry, and other prior mathematics courses to take students into the world of limits, derivatives, and special computational techniques such as the power rule and differentiation. It is an important prerequisite for many educational programs in engineering and science. The student will also explore topics related to sequences, series, and the fundamental theorem of calculus as well as differential equations. Students will have access to engaging multimedia video lectures, notes pages for each lesson summarizing the video content, practice problems, and assessments. All video lessons include a transcript and closed captioning in English and Spanish.

#### Prerequisite

Pre-Calculus or Trigonometry

### Schedule

Module 1: Introduction and Limits

• Week 1: Overview and Review
• Week 2: Introduction to Limits
• Week 3: More Limits

Module 2: Limits and Derivatives

• Week 4: Limits and Instantaneous Velocity
• Week 5: Introduction to Derivatives
• Week 6: More Derivatives

Module 3: Rules for Computing Derivatives

• Week 7: Derivative Rules
• Week 8: More Derivative Rules
• Week 9: Derivatives of Trigonometric Functions & Quarter 1 Exam

Module 4: Derivatives and Functions

• Week 10: Exponential and Logarithmic Functions
• Week 11: Implicit Differentiation
• Week 12: Position, Velocity, and More Differentiation

Module 5: Optimization

• Week 13: Optimization Applications
• Week 14: More Optimization and Related Rates
• Week 15: More Related Rates

Module 6: Graphs and Derivatives

• Week 16: Extrema and Concavity
• Week 17: Graphing Using the Derivative
• Week 18: Asymptotes & Quarter 2 Exam

Module 7: Integration

• Week 19: More Asymptotes
• Week 20: Antidifferentiation
• Week 21: Integrating More Functions

Module 8: Area and Motion

• Week 22: Area
• Week 23: Antiderivatives and Motion
• Week 24: Area between Two Curves

Module 9: Indeterminate Forms and Integrating with y

• Week 25: Integrating with Respect to y
• Week 26: L’Hôpital’s Rule
• Week 27: Log Functions & Quarter 3 Exam

Module 10: Derivatives of Inverse Functions

• Week 28: Inverse Functions
• Week 29: Trigonometric Functions
• Week 30: Partial Fractions

Module 11: Integration by Parts and Improper Integrals

• Week 31: Integrating by Parts
• Week 32: Improper Integrals
• Week 33: Average Value and Cross- Sectional Volume

Module 12: Solids of Revolution and Differential Equations

• Week 34: Disk and Washer Methods
• Week 35: Differential Equations
• Week 36: Quarter 4 Exam

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