Overview
Syllabus
The Velocity Problem | Part I: Numerically.
The Velocity Problem | Part II: Graphically.
A Tale of Three Functions | Intro to Limits Part I.
A Tale of Three Functions | Intro to Limits Part II.
What is an infinite limit?.
Limit Laws | Breaking Up Complicated Limits Into Simpler Ones.
Building up to computing limits of rational functions.
Limits of Oscillating Functions and the Squeeze Theorem.
Top 4 Algebraic Tricks for Computing Limits.
A Limit Example Combining Multiple Algebraic Tricks.
Limits are simple for continuous functions.
Were you ever exactly 3 feet tall? The Intermediate Value Theorem.
Example: When is a Piecewise Function Continuous?.
Limits "at" infinity.
Computing Limits at Infinity for Rational Functions.
Infinite Limit vs Limits at Infinity of a Composite Function.
How to watch math videos.
Definition of the Derivative | Part I.
Applying the Definition of the Derivative to 1/x.
Definition of Derivative Example: f(x) = x + 1/(x+1).
The derivative of a constant and of x^2 from the definition.
Derivative Rules: Power Rule, Additivity, and Scalar Multiplication.
How to Find the Equation of a Tangent Line.
The derivative of e^x..
The product and quotient rules.
The derivative of Trigonometric Functions.
Chain Rule: the Derivative of a Composition.
Interpreting the Chain Rule Graphically.
The Chain Rule using Leibniz notation.
Implicit Differentiation | Differentiation when you only have an equation, not an explicit function.
Derivative of Inverse Trig Functions via Implicit Differentiation.
The Derivative of ln(x) via Implicit Differentiation.
Logarithmic Differentiation | Example: x^sinx.
Intro to Related Rates.
Linear Approximations | Using Tangent Lines to Approximate Functions.
The MEAN Value Theorem is Actually Very Nice.
Relative and Absolute Maximums and Minimums | Part I.
Relative and Absolute Maximums and Minimums | Part II.
Using L'Hopital's Rule to show that exponentials dominate polynomials.
Applying L'Hopital's Rule to Exponential Indeterminate Forms.
Ex: Optimizing the Volume of a Box With Fixed Surface Area.
Folding a wire into the largest rectangle | Optimization example.
Optimization Example: Minimizing Surface Area Given a Fixed Volume.
Tips for Success in Flipped Classrooms + OMG BABY!!!.
What's an anti-derivative?.
Solving for the constant in the general anti-derivative.
The Definite Integral Part I: Approximating Areas with rectangles.
The Definite Integral Part II: Using Summation Notation to Define the Definite Integral.
The Definite Integral Part III: Evaluating From The Definition.
"Reverse" Riemann Sums | Finding the Definite Integral Given a Sum.
Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example.
Fundamental Theorem of Calculus II.
Intro to Substitution - Undoing the Chain Rule.
Adjusting the Constant in Integration by Substitution.
Substitution Method for Definite Integrals **careful!**.
Back Substitution - When a u-sub doesn't match cleanly!.
Average Value of a Continuous Function on an Interval.
Exam Walkthrough | Calc 1, Test 3 | Integration, FTC I/II, Optimization, u-subs, Graphing.
♥♥♥ Thank you Calc Students♥♥♥ Some final thoughts..
Taught by
Dr. Trefor Bazett