Math - Calculus
Topics covered in the first two or three semester of college calculus. Everything from limits to derivatives to integrals to vector calculus. Should understand the topics in the pre-calculus playlist first (the limit videos are in both playlists)
- Polynomial approximation of functions (part 4)
- Approximating functions with polynomials (part 3)
- Polynomial approximation of functions (part 2)
- Polynomial approximation of functions (part 1)
- Sequences and series (part 2)
- Sequences and Series (part 1)
- Solid of Revolution (part 8)
- Solid of Revolution (part 6)
- Solid of Revolution (part 7)
- Solid of Revolution (part 5)
- Solid of Revolution (part 4)
- Solid of Revolution (part 3)
- Solid of Revolution (part 2)
- Solid of Revolution (part 1)
- Introduction to differential equations
- Integrals: Trig Substitution 3 (long problem)
- Integrals: Trig Substitution 2
- Integrals: Trig Substitution 1
- Definite integral with substitution
- Definite Integrals (part 5)
- Definite Integrals (part 4)
- Definite Integrals (area under a curve) (part III)
- Definite integrals (part II)
- Another u-subsitution example
- Introduction to definite integrals
- Indefinite Integration (part 7)
- Integration by Parts (part 6 of Indefinite Integration)
- Indefinite Integration (part IV)
- Indefinite Integration (part V)
- Indefinite Integration (part III)
- Indefinite integrals (part II)
- Mean Value Theorem
- The Indefinite Integral or Anti-derivative
- Ladder rate-of-change problem
- Rates-of-change (part 2)
- Equation of a tangent line
- Introduction to rate-of-change problems
- Optimization Example 4
- Optimization with Calculus 3
- Optimization with Calculus 2
- Optimization with Calculus 1
- Graphing with Calculus
- Calculus Graphing with Derivatives Example
- Calculus: Graphing Using Derivatives
- Calculus: Maximum and minimum values on an interval
- Monotonicity Theorem
- Inflection Points and Concavity Intuition
- Maxima Minima Slope Intuition
- Calculus: Derivative of x^(x^x)
- Trig Implicit Differentiation Example
- More chain rule and implicit differentiation intuition
- More implicit differentiation
- Implicit Differentiation (part 2)
- Implicit Differentiation
- Extreme Derivative Word Problem (advanced)
- Proof: d/dx(e^x) = e^x
- Proofs of Derivatives of Ln(x) and e^x
- Proof: d/dx(ln x) = 1/x
- Proof: d/dx(sqrt(x))
- Proof: d/dx(x^n)
- Derivatives (part 9)
- Derivatives (part 8)
- Derivatives (part 7)
- Calculus: Derivatives 6
- Calculus: Derivatives 5
- Calculus: Derivatives 4: The Chain Rule
- Calculus: Derivatives 3
- Calculus: Derivatives 2
- Calculus: Derivatives 1
- Calculus: Derivatives 2.5 (new HD version)
- Calculus: Derivatives 2 (new HD version)
- Calculus: Derivatives 1 (new HD version)
- Epsilon Delta Limit Definition 2
- Epsilon Delta Limit Definition 1
- More Limits
- Proof: lim (sin x)/x
- Squeeze Theorem
- Limit Examples w/ brain malfunction on first prob (part 4)
- Limit Examples (part3)
- Limit Examples (part 2)
- Introduction to Limits
- Limit Examples (part 1)
- Polynomial approximations of functions (part 5)
- Polynomial approximation of functions (part 6)
- Polynomial approximation of functions (part 7)
- Taylor Polynomials
- Exponential Growth
- AP Calculus BC Exams: 2008 1 a
- AP Calculus BC Exams: 2008 1 b&c
- AP Calculus BC Exams: 2008 1 c&d
- AP Calculus BC Exams: 2008 1 d
- Calculus BC 2008 2 a
- Calculus BC 2008 2 b &c
- Calculus BC 2008 2d
- Partial Derivatives
- Partial Derivatives 2
- Gradient 1
- Gradient of a scalar field
- Divergence 1
- Divergence 2
- Divergence 3
- Curl 1
- Curl 2
- Curl 3
- Double Integral 1
- Double Integrals 2
- Double Integrals 3
- Double Integrals 4
- Double Integrals 5
- Double Integrals 6
- Triple Integrals 1
- Triple Integrals 2
- Triple Integrals 3
- (2^ln x)/x Antiderivative Example
- Introduction to the Line Integral
- Line Integral Example 1
- Line Integral Example 2 (part 1)
- Line Integral Example 2 (part 2)
- Position Vector Valued Functions
- Derivative of a position vector valued function
- Differential of a vector valued function
- Vector valued function derivative example
- Line Integrals and Vector Fields
- Using a line integral to find the work done by a vector field example
- Parametrization of a Reverse Path
- Scalar Field Line Integral Independent of Path Direction
- Vector Field Line Integrals Dependent on Path Direction
- Path Independence for Line Integrals
- Closed Curve Line Integrals of Conservative Vector Fields
- Example of Closed Line Integral of Conservative Field
- Second Example of Line Integral of Conservative Vector Field
- Green's Theorem Proof Part 1
- Green's Theorem Proof (part 2)
- Green's Theorem Example 1
- Green's Theorem Example 2
- Introduction to Parametrizing a Surface with Two Parameters
- Determining a Position Vector-Valued Function for a Parametrization of Two Parameters
- Partial Derivatives of Vector-Valued Functions
- Introduction to the Surface Integral
- Example of calculating a surface integral part 1
- Example of calculating a surface integral part 2
- Example of calculating a surface integral part 3
- Introduction to L'Hopital's Rule
- L'Hopital's Rule Example 1
- L'Hopital's Rule Example 2
- L'Hopital's Rule Example 3