#math

Notes from Bainbridge High School's calculus classes. Written in a combination of Markdown, HTML, and LaTeX.

#Multi-Variable Calculus

#Vectors and Matrices

• Vectors, Determinants, and Planes
• Matrices and Systems of Equations
• Parametric Equations for Curves

#AP Calculus

• Limits and Continuity
  • [2-0] Limits Review
• Derivatives
  • [3-1 + 3-2] Definition of the Derivative
  • [3-3] Differentiation Rules
  • [3-4] Rates of Change
  • [3-5] Derivatives of Trigonometric Functions
  • [3-5-5] The Squeeze Theorem and Limits of Composite Functions
  • [3-6] The Chain Rule
  • [3-8] Derivatives of Inverse Functions
  • [3-9] Derivatives of Exponential and Logarithmic Functions
• Applications of Derivatives
  • [4-1] Extreme Values of Functions
  • [4-2] Mean Value Theorem
  • [4-3] Using Derivatives to Analyze Graphs of Functions
  • [4-6] Related Rates

• The Definite Integral
  • [5-1] Estimating with Finite Sums
  • [5-2] Riemann Sums and Definite Integrals
  • [5-5] The Trapezoidal Rule
  • [5-3] Definite Integrals and Antiderivatives
  • [5-4] Fundamental Theorem of Calculus
  • [5-6] The Indefinite Integral
  • [5-7] Implicit Differentiation and Separation of Variables
• [current unit] Antidifferentiation and Mathematical Modeling
  • [6-1] Slope Fields and Euler's Method
  • [6-2] Antidifferentiation by Substitution
  • [6-3] Antidifferentiation by Parts
  • [6-4] Antidifferentiation by Trigonometric Identities
  • [6-5] Growth and Decay
• [also current unit] Applications of Definite Integrals
  • [7-3] Volume as an Integral
  • [7-4] Finding the Length of a Curve
  • [7-5] Work and Force
• [?-?] L'Hopital's Rule

• [bc unit] Sequences and Improper Integrals

#Honors Precalculus

• Functions and Graphs
  • Intro to Functions
  • Properties of Functions
  • Absolute Value and Piecewise
  • Transformations of Functions
• Polynomial, Power, and Rational Functions
  • Linear and Quadratic Functions
  • Power Functions
  • Graphing Rational Functions
  • Division and Finding All Zeros
  • Higher Degree Polynomials
  • Simplifying and Solving Rational Expressions
• Exponential, Logistic, and Logarithmic Functions
  • Logarithmic Functions
  • Solving Exponential and Logs
  • Solving Non Simple Exponential Functions
  • Applications of Exponential, Logarithmic, and Logistic Functions
• Trigonometric Functions
  • Angles and Arc Length
  • Graphs of Tangent and Reciprocal Functions
  • Right Triangle Trigonometry
  • Solving Trig Equations
  • Inverse Trig Functions
• Trigonometric Identities (Analytic Trigonometry)
  • Fundamental Trig Identities
  • Prove Trig Identities
  • Sum and Difference Identities
  • Law of Sines and Cosines
  • Multiple Angle Identities
• Vectors, Parametric, and Polar Equations (Applications of Trigonometry)
  • Vectors in the Plane
  • Dot Product of Vectors in the Plane
  • Intro to Polar Coordinates
• Systems of Matrices
  • Matrices
  • Partial Fractions
• Analytic Geometry (in Two and Three Dimensions)
  • Classification and Rotation of Conics
  • Polar Equations of Conics
  • Eccentricity and Orbits
  • 3D Space and Vectors
• Discrete Mathematics
  • Permutations and Combinations
  • Binomial Theorem
  • Probability
  • Sequences
  • Series
• Intro to Calculus
  • More on Limits and using calculator for Numerical Derivatives and Integrals