Online Notes (Partial)
I present a lot of material, although in less detail than my full notes (above), for free online. Check out your class below!
Algebra 1
(Coming Later!)
Algebra 2
(Coming Later!)
Geometry
(Coming Later!)
Trigonometry
(Coming Later!)
Calculus 1
See Topics
- Chapter 1- Various Important Functions
- Review of Earlier Functions
- Linear Functions (Lines)
- Quadratic Functions (Parabolas)
- General Polynomial Functions
- Exponential Functions
- Logarithmic Functions
- Trigonometric Functions
- Inverse Functions
- Piecewise Functions
- Hyperbolic Trigonometric Functions
- Review of Earlier Functions
- Chapter 2- Limits
- Introduction to Limits
- Right and Left Hand Limits
- Definition of the Limit
- Graphical Limits
- Tabular Limits
- Direct Substitution
- Properties of Limits
- Indeterminate Forms
- Analytical Procedures for Computing Limits
- Factoring and Cancellation
- Addition of Fractions
- Conjugate Multiplication
- Infinite Limits
- Epsilon-Delta Definition of the Limit
- Squeeze-Theorem
- Chapter 3- Continuity
- Introduction to Continuity
- Definition of Continuity
- Continuous Functions
- Discontinuities in Graphs
- Discontinuities in Functions
- Chapter 4- The Derivative: Introduction and Basic Methods
- Chapter 5- The Derivative: Advanced Methods
- Trig Function Derivatives
- Inverse Trig Derivatives
- Hyperbolic Trig Derivatives
- Exponential Derivatives
- Logarithmic Derivatives
- Implicit Differentiation
- Logarithmic Differentiation Method
- Partial Derivatives
- Chapter 6- Applications of Derivatives
- Intermediate Value Theorem
- Mean Value Theorem
- Rolle’s Theorem
- Introduction to Extrema
- Local Extrema
- The First Derivative Test
- Absolute Extrema
- Optimization
- Higher order Derivatives
- Second Derivative Test
- Concavity and Inflection Points
- Rectilinear Motion: Position, Velocity and Acceleration
- Introduction to Differential Equations
- A Few Basic Examples
- Local Linearity and Euler’s Method
- L’Hôpital’s rule
- Related Rates
- Chapter 7- The Integral: Introduction and Basic Methods
- Introduction to the Area Under Curves
- Area Approximation techniques: Riemann Sums
- Left and Right Endpoint Rectangles
- Center-Aligned Rectangles
- The Trapezoid Rule
- Simpson’s Rule
- The Exact Area Using Riemann Sums
- The Antiderivative
- The Indefinite Integral
- The Integration Power Rule
- Properties of Integrals
- The Definite Integral
- The Fundamental Theorem of Calculus
- Integral Definition Summary (With Examples)
- Chapter 8- Advanced Integration Techniques
- Advanced Power Rule Problems
- Reverse Chain Rule
- U-Substitution
- Long Division
- Completing the Square
- More Examples
- Chapter 9- Integration Applications
- Average Values
- Arc Length
- Area Between Curves (Over x)
- Area Between Curves (Over y)
- Volumes of Revolution
- Disk Method
- Washer Method
- Cylindrical Shell Method
- Multiple Integral Examples
- Volumes of Known Cross Section
- Rectilinear Motion Revisited
Calculus 2
(Coming Later!)
Calculus 3
(Coming Later!)
Differential Equations
(Coming Later!)