차례

1. Functions, Tangent lines and limits.
   1. Tangent lines to a function
   2. Secant line to tangent line.
   3. Limit of sin(1/x) as x approaches 0 does not exists.
   4. Slope of Secant line.
   5. Zeno's Paradox
   6. 2.2:Left and Right Limits
   7. 2.5:Evaluating Limits Algebraically- Squeeze Theorem
   8. 2.6: Limit of sin(x)/x as x approaches 0
   9. 2.4: Piecewise Function Continuity
   10. Piecewise Function with parameters (a parabola and a cubic)
   11. Exponential Taylor Polynomial
2. Derivatives
   1. How oscillating secant line does not converge to a tangent line
   2. How oscillating secant line does not converge to a tangent line
   3. How oscillating secant line converges to a tangent line
   4. 3.1: Definition of Derivative for Oscillating Limits
   5. 3.4: Total Distance
   6. Product Rule
3. Related Rates-Word Problems
   1. Ferris wheel
   2. 3.10: Police Chase
4. One-dimensional Implicit Functions
   1. Implicict Function
   2. Implicict Function
5. Linear Approximation
   1. Linear approximation
6. Optimization
   1. 4.7: Optimization- Maximize the area of a rectangle inscribed in an ellipse
   2. 4.7: Optimization. Maximum area of a rectangle inscribed in a functions. Drag Point A
   3. 4.7: Optimization of length, corridors and poles
   4. 4.7: Optimization of distance in a police chase
   5. 4.7: Optimization: Inscribe a rectangle in a triangle 3.2: Quadratic Functions
   6. 4.7: Optimization: Area isosceles triangle inscribed in a circle
   7. 4.7: Optimization, Bending a Wire
   8. Approximating using the Second Order Taylor Polynomials
   9. Optimization: closest point to (a,0) from y=1/x^2
7. Integrals.
   1. The area under a positive curve. Click play
   2. Improper Integrals
   3. Area and Symmetry of the Graphs
   4. Area Entrapped by x-axis and the graph between a and b
8. Integral Word Problems
   1. Throwing a ball at an angle
9. Volume of Solids with Cross Sections
   1. Volume of a solid with a triangular base and circle cross sections
   2. Solid Between Two Cylinders
   3. Triangular Cross Sections
   4. Pyramid Volume
   5. Spring K
   6. Circle-Cross-Section over paraboloids
   7. Circle-Cross-Section over paraboloids upward shifted
   8. Circle-Cross-Section over paraboloids upward Not Shifted
   9. Summer 2025 Neither x nor y simple nor dzdxdy nor dzdydx simple
   10. Summer 2025 Neither x nor y simple. But dzdzdy or dzdydx simple
   11. Cross Sectional Square within graph of y=a^2-x^2/2
   12. Cross Sectional Square within graph of y=x^2
10. Volume of Rotation
    1. Volume of Rotation - Shells - Two Curves
    2. Volume of Rotation - Riemann Sum
    3. Volume of Rotation - Washer - Two Curves
    4. Width d of a semi-sphere
11. Polar, Cylindrical and Spherical Integration
    1. Achieve Homework 15.4
    2. The Unit Vectors in Physics, Cylindrical Coordinates
    3. The Unit Vectors in Physics, Spherical Coordinates
    4. 15.4: Spherical Coordinates
    5. 15.6: Rescaling in Polar Transformation
    6. 15.4: Shell Analogy for Cylindrical Transformations When r and z are theta Independent
    7. 15.4: Disk Analogy for Cylindrical Transformations When r and z are theta Independent
    8. 15.4: Polar Transformations
    9. Cone in Spherical Coordinates is a Rotation
12. Double Integral
    1. 3d Riemann Sum
    2. Fubinni's 3d Riemann Sum
    3. 15.2: y-simple Double Integral
    4. 15.2: The 3D Double Integral
13. Solids for triple integrals
    1. Triple Integral Lecture 15.3 With Extra Walls
    2. 15.3: Triple integral
    3. 15.3: Non-Simple Region Triple Integral
    4. 15.3: Triple Integral Lecture
    5. 15.3: Triple Integral, Orange Slice
    6. 15.3: Triple Integrals Paraboloid
    7. Section 15.3: Group Work 6, Question 1
    8. 15.3: Group Work 6, Question 2
    9. Group Work 6 Question 3
    10. 15.3: None Simple Region Triple Integral Lecture Example 5
    11. 15.3: Triple Integral, Orange Slice 2
    12. Example bounded by z+y=2, z=1-x^2 in first octant.
    13. 15.3: Worksheet 11
    14. 15.3: Tetrahedron
    15. 15.3: Worksheet 12
14. Parametric equations
    1. Parametric Heart, Click Play and watch. Precalculus Section 8.7
    2. Trace of a point on a wheel. Move the slider back and forth. Precalculus Section 8.7
    3. Two Cylinders
    4. 12.5: Parametric Equation of Line in 3D
    5. Two tangent circles and point on the inner circle
    6. Two tangent circles and a point on the inner circle moving forward
15. Special curves
    1. 13.1:Helix
    2. 13.1: Conical spiral
    3. Parallel, intersecting and Skew Lines
    4. Parametrization Examples
    5. Parametrized Curve of Intersection of a Cylinder with a Plane
    6. Make a Helix on a Piece of Paper
16. Graphs of Multivariable Functions
    1. Vase shape
    2. The reciprocal
    3. Natural Log
    4. Graph of x^2+(y-2)^2
    5. Graph of 1/(x^2+y^2-1)
    6. Graph of z=ln(x+y+2)
17. Line Integral
    1. Line Integral
18. Surfaces
    1. Saddle point
    2. 3D Discontinuity, xy/(x^2+y^2)
    3. 3d Discontinuity, x^2/(x^2+y^2)
    4. 3d, Discontinuity, x^2y/(x^4+y^2)
    5. Non-differentiable Surface
    6. Differentiable Surfaces, Zoom in
    7. Hessian
    8. 14.7: Optimization of Closed/Bounded Regions
    9. Octants
    10. Quadric Surfaces-Hyperboloids 1-Sheet, 2 -Sheets and Cones
    11. Quadrics: How to draw paraboloids by stacking the Cross sections
    12. Quadrics: Cylinder
    13. Half Cylinders in Cylindrical Coordinates.
19. Vector Fields
    1. 16.1: Rotating Vector Field in 3D
    2. 17.2:Disks Capturing Rotating Vector Field in 3D
    3. 16.5: A Disk Capturing a Radial Vector Field in 3D
    4. 17.3: A Cube Capturing Radially Outward and Inward Vector Field in 3D
    5. 16.5: A Disk Capturing a Vector Field in 3D
    6. Stokes' (circulation of a surface)
    7. Oriented Oval and Disk (Stokes)
20. Parametric Surfaces
    1. Deformation of Curve <y^2,y,y^2> when cylindar x=y^2 is fattened.
    2. Cut the top half of the first page and roll into a surface over the curve of the second curve