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3685 Highway 6 South, Sugar Land, TX 77478
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(832) 387-6250

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
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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!