*These notes are from last year which you may use as a resource. Ignore any anoucements made in the notes as they do not apply to you. We may do different examples or skip examples this year. There may be mistakes in the notes. These notes should NEVER be a substitue for your own in class notes unless you are absent.
- Trigonometry Review
- Functions
- Domain & Range
- Function Transformations
- Logarithm Properties
- Log Equations
- Log Graphs
- Continuity
- One-sided Limits
- Limit of a Function
- Continuity and Limits
- Evaluating Limits
Visit: Limit of a hole Demo
- Interval Notation
- Sign Charts
- Increasing/Decreasing
- Log Equations
- Exponential Equations
- Infinity as a Limit
- Undefined Limits
- Tangent Lines
- Secant Lines
- The Derivative
Visit:
- Secant to Tangent Line Demo
- The Derivative Demo
- Function Composition
- Function Decomposition
- Power Rule for Derivatives
- Derivative Rules
- Derivative of \(e^x\) and \(ln(x)\)
- Derivatives of \(\sin(x)\) and \(\cos(x)\)
- Exponential Growth/Decay
- The Tangent Line Equation
- Higher Order Derivatives
- Rational Functions
- Special Limits
- Differentials
- Product Rule for Derivaitves
- Antiderivatives
- Indefinite Integrals
- Polynomial Review
- Implicit Differentiation
- Integral of a Constant
- Integral of \(kf(x)\)
- Integral of \(x^n\)
- Critical Numbers
- The Chain Rule
- Integral of a Sum
- Integral of \(\frac{1}{x}\)
- Units of Derivatives
- Normal Lines
- Maximums and Minimums
- Area Under a Curve
- Upper & Lower Sums
- Left, Right, Midpoint Sums
Visit:
- Lower/Left Sum Demo
- Upper/Right Sum Demo
- Midtpoint Sum Demo
- Sum Below Demo
- Rectangle Height Demo
- Rational Functions Review
- Quotient Rule for Derivatives
- Area Under a Curve as an Infinite Sum
- More Chain Rule
- Alternate Definitiion of the Derivative
- Uisng \(f'\) to Characterize \(f\)
- Using \(f'\) to find Maximums and Minimums
Visit:
- Characterizing f with f' Demo
- Sketching the Derivative Demo 1
- Sketching the Derivative Demo 2
- Related Rates Problems
- Fundamental Theorem of Calculus (FTC)
- Riemann Sums
- The Definite Integral
- Concavity and Inflection Points
- Geometric Meaning of the Second Derivative
- First and Second Derivative Tests
- Derivatives of Composite Functions
- Integraion by Guessing
- Optimization Problems
- Velocity and Acceleration
- Motion Due to Gravity
- More Integration by Guessing
- Properties of the Definite Integral
- Computing Areas
- Numerical Integration on Calculator
- Area Between Two Curves
- Playing Games with \(f, f'\) and \(f''\)
- Work, Distance, and Rates
- Extreme Value Theorem (EVT)
- Derivatives of Inverse Trig Functions
- Falling-Body Problems
- Areas Involving Functions of \(y\)
- \(u\)-Substitution
- Change of Variable
- Even and Odd Functions
- Properties of Limits
- Special Limits
- Solids of Revolution I: Disks
Visit:
- Revolving a Region Demo
- Revolving a Curve Demo
- Disk Cross Sections Demo
- Derivative of \(a^x\)
- Derivative of \(\log_a x\)
- Derivative of \(|f(x)|\)
Visit: Dereivative of |x| at 0 Demo
- Integral of \(a^x\)
- Integral of \(\log_a x\)
- Continuity of Functions
- Particle Motion I
Visit: Velocity, Acceleration, Normal Demo
- L'Hôpital's Rule
- Solids of R evolution II: Washers
Visit:
- Revoloving a Region
- Washer Cross Sections Animations
- Limits and Continuity
- Differentiability
- Logarithmic Differentiation
- Rules for Even and Odd Functions
- Mean Value Theorem (MVT)
- Rolle's Theorem
- Applications of MVT
Watch: Speed Cameras
- Separable Differential Equations
Watch:
Source: Resonance Differential Equation
- Average Value of a Function
- Mean Value Theorem for Integrals
- Particle Motion II
- Derivatives of Inverse Functions
- Solids of Revolution IV: Displaced Axes
- Trapezoidal Rule
- Error Bound
- Derivatives and Integrals of Functions Involving Absolute Value
- Solids Defined by Cross Sections
- Fundamental Theorem of Calculus, Part 2
- Chain Rule with FTC
- Graphs of Solutions of Differential Equations
- Slope Fields
- Implicit Differentiation
