Functions
Properties
Injectivity, Surjectivity, Bijectivity
Inverse Functions
Limits and Continuity
Definition of a Limit
Continuity at a point vs on an interval
Asymptotes (Vertical, Horizontal, Oblique)
Sequences and Series
Sequences
Geometric Sequences
Arithmetic Sequences
Convergence criteria (Squeeze theorem, Monotonicity)
Series
Convergence tests
Power Series
Limits
Table
Continuity of a function
Differential Calculus
Fundamentals
Definition of the Derivative (Limit of difference quotient)
Tangent Line Equation
Leibniz and Newton notation
Differentiability implies Continuity
Product Rule, Quotient Rule, Chain Rule
Derivatives of Elementary Functions (Trig, Hyperbolic, Exp/Log)
Theorems and Applications
Min/max of a function, inflexion point, curvature
Mean Value Theorem
Taylor and Maclaurin Series
L’Hôpital’s Rule (undefined limit)
Optimization (Min/Max problems)
Integral Calculus
Indefinite Integrals
Primitives
Definite Integrals
Riemann Sums definition
Fundamental Theorem of Calculus
Other Integrals
Improper Integrals
Integral with singularity
Integration Methods
Integration by Parts
U-Substitution
Trigonometric Substitution
Partial Fraction Decomposition
Applications (geometry)
Theorem of the mean
Area between curves
Arc Length
Volumes of Revolution (Disk/Washer method)
Guldin’s Rules (Centroids)
Handwritten