**Calculus**

**AP Calculus Tutoring Available in Sugar Land, TX**

**CALCULUS AB AND BC**

**Limits and Continuity**

- Definition of Limits of Functions
- Evaluating Limits Graphically, Numerically and Analytically
- Continuity and its relation with left and right side limits
- Evaluating Infinite Limits, Asymptotes

**Derivatives**

- Definition of derivative as slopes of functions
- Differentiability vs Continuity
- Differentiating functions from first principles
- Differentiation Rules for
- Different types of functions
- Addition, Subtraction, Product and Quotients of Functions

- Chain Rules for Derivatives
- Higher Order derivatives
- Implicit Differentiation

**Applying Derivatives**

- Word Problems on Related Rates, and Tangents and Normals to Curves
- Rolle’s Theorem (RT) and Mean Value theorem (MVT)
- First Derivative Test for Increasing and Decreasing Functions
- Second Derivative Test for Concavity of Functions
- Finding Extrema (Maxima and Minima) of Curves
- Curve sketching using derivatives
- Optimization Problems
- Derivatives of Inverse Functions

**Simple Differential Equations**

- Slope Fields, Euler’s Method
- Setting up Differential Equations on Growth and Decay
- Separation of Variables
- Setting up and Solving General First Order Differential Equations

**Integration**

- Meaning of Anti-derivative
- Indefinite Integration – Rules
- Definite Integrals: Area under the curve – Riemann Sum, Trapezoidal rule, Newton’s method
- Fundamental Theorems of Calculus
- Integration by Substitution including Trigonometric Integrals and Trigonometric substitutions
- Differentiation and Integration of simple transcendental functions like Exponential including variable base, Logarithmic

**More Integration Techniques**

- Basic Rules in Integration: Integration by Parts
- Partial Fractions
- Other Integration Techniques – Indeterminate forms using L’Hospital’s Rule
- Improper Integrals
- L’Hospital’s Rule

**Applications of Integration**

- Areas and Volumes of curves
- Arc Lengths and Surfaces of Revolution
- Work
- Moments and Centroids
- Conics and Parametric Equations using polar coordinates
- Polar Graphs
- Polar Equations of Conics
- Kepler’s laws

**CALCULUS BC ONLY**

**Infinite Series and Infinite Limits**

- Review of Sequences and Series: Infinite Series and Infinite Limits
- Convergence and L’Hospital’s Rule
- p-Series
- Harmonic Series
- Alternating Series
- Ratio and Root Tests
- Taylor Polynomials and approximations
- Power series and their use in expansion of functions
- Taylor and Maclaurin Series

**Vectors and 3-d Geometry**

- Vectors and coordinates in 2-d plane and 3-d space
- Dot and Cross Product of vectors
- Lines and planes in 3-d

Call 832-387-6250 today to learn more about our AP Calculus tutoring!