Tutoring Curriculum

Hey there! Are you ready to dive into our Calculus course at Gwinnett Math Tutoring? This course is designed to enhance your understanding of calculus and prepare you for advanced mathematical studies. Here’s what you’ll be learning:

• Topic 1 – Functions Review

  • Lines; Functions and graphs; Exponential functions; Parametric equations; Functions and logarithms; Trigonometric functions.

• Topic 2 – Limits and Continuity

  • Rates of change and limits; Limits at infinity; Continuity; Rates of change and tangent lines.

• Topic 3 – Derivatives

  • Differential functions; Rules for differentiation; Velocity and rates of change; Chain rule; Implicit differentiation; Derivatives of inverse trigonometric functions; Derivatives of exponential and logarithmic functions.

• Topic 4 – Applications of Derivatives

  • Extreme values of functions; Mean value theorem; First and second derivatives; Modeling and optimization; Newton’s method; Related rates.

• Topic 5 – The Definite Integral

  • Estimating with finite sums; Definite integrals; Antiderivatives; Fundamental theorem of calculus; Trapezoid rule.

• Topic 6 – Differential Equations and Mathematical Modeling

  • Slope fields and Euler’s method; Antidifferentiation by parts; Exponential growth and decay; Logistic growth.

• Topic 7 – Applications of Definite Integrals

  • Integral as a net change; Areas in the plane; Volume; Length of curves; Scientific applications and statistics.

• Topic 8 – L’Hopital’s Rule and Improper Integrals

  • Sequences; L’Hopital’s Rule; Relative rates of growth; Improper integrals.

• Topic 9 – Infinite Series

  • Power series; Taylor series; Taylor’s theorem; Radius of convergence.

• Topic 10 – Parametric, Vector, and Polar Functions

  • Parametric functions; Vectors; Polar functions.

• Topic 11 – Extended Explorations

  • Induction; Hyperbolic functions.

Each topic includes engaging lectures, plenty of practice problems, group activities, and a quiz to test your understanding. Homework assignments will reinforce what we learn in class, and I’ll be available to provide extra help whenever you need it. For those looking for a greater challenge, there are additional resources to explore.

Are you ready to enhance your math skills and conquer Calculus? Let’s start this journey together and achieve great success!