Contents
Precalculus
- Square Root
- Absolute Values
- Quadratic Functions
- Complex Numbers
- Complex Plane
- De Moivre’s Theorem
- Roots of a Complex Number
- Euler’s Formula
- Polar Coordinates
- Spherical Polar Coordinates
- Polar Rectangles
- Movement of Graphs
Limits
- The number “e” as a Limit
- Squeeze theorem
- Important Limit Values
- L’Hospital’s Rule
- Continuity
- Ratio Test
Functions
- Even / Odd Functions
- Periodic Functions
- One-to-One Function
- Composite Functions
- Inverse Functions
- Exponential Functions
- Logarithmic Functions
- Natural Logarithms
- Trigonometric Functions (Review)
- Trigonometric Functions / Applications to Triangles
- Inverse Trigonometric Functions
- Hyperbolic Functions
- Inverse Hyperbolic Functions
- Parametric Equations
- Implicit Functions
Taylor Series Expansion
- Binomial Theorem / Multinomial Theorem
- Taylor and Maclaurin Series
- Proof of Taylor Series Expansion
- Approximating Functions by Taylor Polynomials
Space Vectors
- Dot Products
- Cross Products
- Length of The Cross Products
- Geometric Interpretation of Cross Products
- Scalar Triple Products
- Vector Projections
Derivative
- Theorems of Derivative
- Tangent and Normal Lines
- Differentiation Formulas (Review)
- Implicit Differentiation
- General Leibniz Rule
Integrals
Techniques of Integration
- Integration by Parts
- Trigonometric Integrals
- Integration of Rational Functions
- Substitution Rule : involving Irrational Functions / Trigonometric Functions / \(\mathrm{e}^{x}\)
- Trigonometric Substitution
Applications of Integration
- Arc Length
- Volume
- Area of a Surface of Revolution