Calculus Summer Acceleration Program

This course is designed for students to get ahead of the curve in Calculus (non AP), AP Calculus AB or Calculus I. Students will receive one-on-one instruction in topics covered in Calculus and have the opportunity to test their skills with live-time exams and assignments to prepare them for the upcoming coursework. This program will run from June 10th-August 7th. The course overview and select materials are available below. Please contact me with any questions regarding availability, pricing, and course content.

Course Content

The study of Calculus involves seeking answers to two critical questions. The first asks how we estimate change at a specific instant in time, and the second asks how we can estimate the area beneath a curve. With numerous real-world applications, Calculus is a fundamental component to many STEM fields as it helps provide answers optimization and efficiency problems. My process focuses on the linking the conceptual and mathematical underpinnings of Calculus prepare students for a successful semester at any level of the subject. I will provide personally-made, detailed notes that will serve as the structure of each lesson, homework assignments to ensure confidence in each topic, and exams to evaluate the level of understanding of the content. I look forward to exploring these fascinating topics with my students and providing them with the tools to feel confident on day one of Calculus!

  • Topics to be Covered:

    1.1: Intro to Calculus

    1.2: Average and Instantaneous Rates of Change

    1.3: Limits

    • Estimating Limits Algebraically, Graphically, and in Tabular form

    • The Precise Definition of a Limit (Calculus I Only)

    • Limits of Composite Functions

    • Algebraic Manipulations to Estimate Limits

    1.4: One-Sided Limits and Limits Involving Infinity

    1.5: The Squeeze Theorem

    1.6: Continuity

    • Review Categories of Discontinuities (Infinite, Removable, Non-removable)

    • Determining Continuity on an Interval

    • Asymptotic Behavior and Algebraic Manipulations to Eliminate Discontinuities

    1.7: Intermediate Value Theorem

  • Topics to be Covered:

    2.1: The Formal Definition of a Derivative:

    • Derivatives at a Point and as a Function

    2.2: Rules of Differentiation - Click for Notes Sample

    • Power Rule

    • Constant Multiple Rule

    • Product Rule

    • Quotient Rule

    • Exponent and Radical Properties

    2.3: Derivative of Trigonometric Functions

    • Unit Circle and Trigonometric Review

    • Formal Derivation and Proofs

    2.4: Graphing Derivative and Parent Functions

    2.5: Higher Order Derivatives (the nth-derivative)

  • Topics to be Covered:

    3.1: The Chain Rule

    3.2: Implicit Differentiation

    3.3: Derivatives of Inverse Functions and Inverse Trigonometric Functions

    3.4: Related Rates and Linearization

    • Applications of the Derivative in Physics, Economics, and Biology Contexts

    3.5: L’Hospital’s Rule and Indeterminant Forms

    3.6: Extrema on a Closed Interval and Mean Value Theorem

    3.7: Monotonic Functions - Applications of the First Derivative

    3.8: Concavity and Graphing Functions - Applications of the Second Derivative

    • Curve Sketching

    3.9: Optimization Problems

    • Geometric and Economic Applications

  • Topics to be Covered:

    4.1: Anti-Derivatives

    • Rules for Indefinite Integrals

    4.2: Reimann Sum - Approximating Area Under Curves

    4.3: Definite Integrals

    4.4: Sigma Notation

    4.5: The Fundamental Theorem of Calculus!

    4.6: Substitution Rules - U-Sub