Course Outline - Calculus I: Differential Calculus

Description

Calculus I: Differential Calculus gives students the opportunity to explore the concepts and techniques developed by Newton, Leibniz, and others in an effort to examine motion and rates of changes. Topics to be covered in this course include:

Function Review from Pre-Calculus
Limits and Continuity of Functions
Derivatives and Their Applications

Lesson Structure: Suggested Time

Chapter 1: A Quick Review of Functions Varying depending on background (5–7 days)

Lesson 1: Review of Linear Function
Lesson 2: Functions and Graphs
Lesson 3: Exponential Functions
Lesson 4: Parametric Equations
Lesson 5: Functions and Logarithms
Lesson 6: Trigonometric Functions
Review

Chapter 2: Limits and Continuity (10 days)

Lesson 1: Rates of Change (2 days)
Lesson 2: Limits Involving Infinity (2 days)
Lesson 3: Continuity (2 days)
Lesson 4: Rates of Change and Tangents (2 days)
Review/Test (2 days)

Chapter 3: Derivatives (30 days)

Lesson 1: Derivative of a Function (3 days)
Lesson 2: Differentiability (3 days)
Lesson 3: Rules for Differentiation (4 days)
Lesson 4: Velocity and Other Rates of Change (3 days)
Lesson 5: Derivatives of Trigonometric Functions (3 days)
Lesson 6: Chain Rule (3 days)
Lesson 7: Implicit Differentiation (2 days)
Lesson 8: Derivatives of Inverse Trig Functions( 2 days)
Lesson 9: Derivatives of Transcendental Functions (4 days)
Review/Test (3 days)

Chapter 4: Applications (25 days)

Lesson 1: Extreme Values of Functions (5 days)
Lesson 2: Mean Value Theorem (2 days)
Lesson 3: Graphical Relationships (4 days)
Lesson 4: Modeling and Optimization (5 days)
Lesson 5: Linearization and Newton's Method (3 days)
Lesson 6: Related Rates (3 days)
Review/Test (3 days)

Semester Review and Test