Calculus Classes 微積分精英班

上課時間表

對象：AP/IB Calculus 學生或大學生

本科由有十數年的教學經驗資深微積分導師任教。加上有系統的教學方法，我們絕對有信心使各學生在學業及考試上有卓越成績。


  • Limits and Rates of Change
    • Estimating limits from tables and graphs.
    • Evaluating limits algebraically.
    • Squeeze theorem.
    • Continuity.

  • Concepts of the Derivative
    • Tangents and other rates of change.
    • Interpretation of the derivative.
    • Estimating the derivative from tables and graphs.
    • Sketching graph of the derivative of a function whose graph is given.
    • Linear approximation.
  • Differentiation.
    • Differentiation formulas- Sum, Product, Quotient Rules.
    • Derivatives of Polynomial and Trigonometric Functions.
    • Chain Rule and Implicit Differentiation.
    • Higher order Derivatives.
    • Related Rates.

  • Applications of Differentiation.
    • Maximum and Minimum Values.
    • Mean Value Theorem.
    • Intervals where function increases/decreases.
    • Concavity and points of inflection.
    • Limits at infinity
    • Optimization problems.
    • Applications in Economics and other disciplines.
    • Differentials and linear approximation.
    • Newton's method.
    • Anti-derivatives.

  • Integrals.
    • The Area problem; Definite Integrals; Riemann Sums.
    • Fundamental Theorem of Calculus.
    • Average value of a function. (Mean value of integrals)
    • Substitution Rule.

  • Applications of Integration.
    • Area between curves.
    • Volumes of Revolution (discs, washers, shell)
    • Volumes of Solids with known cross-sections.
    • Numerical Methods. Trapezoidal Rule.

  • Exponential Functions and their Derivatives.
    • Exponential function. Differentiation /Integration.
    • Logarithmic function. Differentiation / Integration.
    • Applications: Exponential growth and decay.
    • Logistic Growth.
    • Differential Equations.
    • Separation of Variables.
    • Slope (direction) fields.
    • Euler's Method.
    • Inverse Trigonometric Function.
    • Derivatives of Inverse Trigonometric Function.
    • Integrals of Inverse Trigonometric Functions.
    • L'Hopital's Rule.

  • Integration Techniques.
    • Integration by parts.
    • Integration using partial fractions (non repeating factors).
    • Improper Integrals.

  • Parametric and Polar Equations.
    • Derivatives of parametric, polar, and vector functions.
    • Arc Length.
    • Areas and lengths in polar coordinates.

  • Infinite Sequences and Series.
    • Sequences.
    • Series.
    • Integral, Comparison, Ratio Tests.
    • Alternating Series.
    • Absolute and Conditional Convergence.
    • Power Series.
    • Taylor and Maclaurin Series.
    • Error Bound