The Calculus Course develops the studentsâ€™ understanding of calculus concepts by providing exposure to calculus methods and applications. Calculus is designed to strengthen and enhance conceptual understanding of the mathematical reasoning used when modeling and solving real-world problems. Calculus Topics include: (1) Introduction to Limits, (2) Differentiation, (3) Various Applications of Differentiation, (4) Integrations, and (5) Using Transcendental Functions.

- An Introduction to Limits and Limit Notation
- One-Side Limits and One-Sided Limit Notation
- Function Behavior Where Limits Do Not Exist
- Finding Limits by Direct Substitution
- Properties of Limits
- Finding Limits of Trigonometric Functions by Direct Substitution
- What is Indeterminate Form
- Two Functions that Agree at All But One Point
- Dividing Out and Rationalizing to Find Limits
- The Squeeze Theorem
- Two Special Trigonometric Limits
- Continuous vs. Discontinuous (Removable vs. Non-Removable Discontinuity)
- Properties of Continuity and Correlation Between Functions Domain and Continuity
- Intermediate Value Theorem
- Infinite Limits and Vertical Asymptotes
- Properties of Infinite Limits
- Limits as x Approaches Infinity
- Limits and x Approaches Infinity, Part 2
- Formal Definition of a Limits

- Secant Lines and Tangent Lines to a Curve
- The Derivative of a Function
- Finding the Derivative of a Function
- Finding the Slope of a Curve at a Point
- Differentiability and Continuity
- Basic Differentiation Rules (Constant and Power Rule)
- Basic Differentiation Rules (Constant Multiple Rule)
- The Sum and Difference Differentiation Rule
- Derivatives of Sine and Cosine Functions
- Finding the Equation of the Tangent Line of a Function at a Given Point
- Finding the Horizontal Tangent Lines of a Function
- Rates of Change (Average Velocity vs. Instantaneous Velocity)
- The Product Rule
- The Quotient Rule
- Derivatives of Trigonometric Functions
- Higher Order Derivatives
- The Chain Rule
- Using the Chain Rule with Other Differentiation Rules
- Using the Chain Rule with Trigonometric Functions
- Introduction to Implicit Differentiation
- Finding the Derivative Using Implicit Differentiation
- Introduction to Related Rates
- Related Rates Classic Problems

- Definition of Extrema
- The Extreme Value Theorem
- Definition of Relative Extrema
- Using Critical Numbers to Find Extrema Values
- Rolle's Theorem
- The Mean Value Theorem
- Increasing, Decreasing, and Constant Intervals
- The First Derivative Test
- Applying the First Derivative Test
- Concavity
- Points of Inflection
- The Second Derivative Test
- Applied Minimum and Maximum Problems
- Approximating the Zeros of a Function Using Newton's Method
- Linear (Tangent Line) Approximations
- Differentials
- Propagated Error and Relative Error

- Definition of Antiderivatives and Representations of Antiderivatives
- Integration Rules
- Applying Integration Rules
- Finding Particular Solutions
- Solving Vertical Motion Problems
- Approximating the Area Under a Curve with Rectangles
- Approximating the Area Under a Curve with Trapezoids
- Increasing the Number of Rectangles to Estimate the Area Under a Curve
- Summation Notation Review
- Riemann Sums
- Definition of the Area of a Region
- Definition of Definite Integrals
- Properties of Definite Integrals
- Finding Area Under a Function Using Geometric Shapes
- Deriving the Fundamental Theorem of Calculus
- Applying the Fundamental Theorem of Calculus
- The Average Value of a Function on an Interval
- The Mean Value Theorem for Integrals
- Finding Antiderivatives Using U-Substitution
- Using a Change in Variables, Part 1
- Using Change in Variables, Part 2
- Change in Variables for Definite Integrals
- Integration of Even and Odd Functions
- Simpson's Rule

- Definition of Natural Log and Properties of the Natural Log
- Derivatives of the Natural Logs
- Using Natural Logs to Differentiate
- Derivatives with Absolute Value of Natural Logs
- Log Rules for Integration
- Integrals of Trigonometric Functions
- Inverse Functions
- Existence of an Inverse Function
- Finding the Inverse of a Function
- The Natural Exponential Function
- The Derivative of the Natural Exponential Function
- Integration Rules for Exponential Functions
- Exponential and Logarithmic Functions with Base a
- Derivatives of Exponential and Logarithmic Functions with Base a
- Proving the Power Rule for Real Exponents
- Applications of Exponential Functions
- Inverse Trigonometric Functions
- Derivatives of Inverse Trig Functions
- Integrals Involving Inverse Trig Functions
- Definition of Hyperbolic Functions
- Derivatives of Hyperbolic Trig Functions
- Integrals of Hyperbolic Trig Functions