Outline
Jila's Calculus class.
This is meant to be used by my calculus I class. It includes appropriates apps and gifs.
Table of Contents
Functions, Tangent lines and limits.
- Tangent lines to a function
- Secant line to tangent line.
- Limit of sin(1/x) as x approaches 0 does not exists.
- Slope of Secant line.
- Zeno's Paradox
- 2.2:Left and Right Limits
- 2.5:Evaluating Limits Algebraically- Squeeze Theorem
- 2.6: Limit of sin(x)/x as x approaches 0
- 2.4: Piecewise Function Continuity
- 6.1: Graphing a Free Harmonic Motion(Spring)
Derivatives
Related Rates-Word Problems
Linear Approximation
Optimization
- 4.7: Optimization- Maximize the area of a rectangle inscribed in an ellipse
- 4.7: Optimization. Maximum area of a rectangle inscribed in a functions. Drag Point A
- 4.7: Optimization of length, corridors and poles
- 4.7: Optimization of distance in a police chase
- 4.7: Optimization: Inscribe a rectangle in a triangle
- 4.7: Optimization: Area isosceles triangle inscribed in a circle
- 4.7: Optimization, Bending a Wire
- Approximating using the Second Order Taylor Polynomials
Integrals.
Integral Word Problems
Volume of Rotation
Polar, Cylindrical and Spherical Integration
- Achieve Homework 15.4
- The Unit Vectors in Physics, Cylindrical Coordinates
- The Unit Vectors in Physics, Spherical Coordinates
- 15.4: Spherical Coordinates
- 15.6: Rescaling in Polar Transformation
- 15.4: Shell Analogy for Cylindrical Transformations When r and z are theta Independent
- 15.4: Disk Analogy for Cylindrical Transformations When r and z are theta Independent
- 15.4: Polar Transformations
Solids for triple integrals
- 3d Riemann Sum
- Fubinni's 3d Riemann Sum
- 15.2: The 3D Double Integral
- Triple Integral Lecture 15.3 With Extra Walls
- 15.3: Triple integral
- 15.3: Non-Simple Region Triple Integral
- 15.3: Triple Integral Lecture
- 15.3: Triple Integral, Orange Slice
- 15.3: Triple Integrals Paraboloid
- Section 15.3: Group Work 6, Question 1
- 15.3: Group Work 6, Question 2
- Group Work 6 Question 3
- 15.3: None Simple Region Triple Integral Lecture Example 5
- 15.3: Triple Integral, Orange Slice 2
- Example bounded by z+y=2, z=1-x^2 in first octant.
- 15.3: Worksheet 11
- 15.3: Tetrahedron
- 15.3: Worksheet 12
Parametric equations
Special curves
Vector Fields
Surfaces
- Saddle point
- 3D Discontinuity, xy/(x^2+y^2)
- 3d Discontinuity, x^2/(x^2+y^2)
- 3d, Discontinuity, x^2y/(x^4+y^2)
- Non-differentiable Surface
- Differentiable Surfaces, Zoom in
- Hessian
- 14.7: Optimization of Closed/Bounded Regions
- Octants
- Vase shape
- The reciprocal
- Natural Log
- Quadric Surfaces-Hyperboloids 1-Sheet, 2 -Sheets and Cones
- Quadrics: How to draw paraboloids by stacking the Cross sections
- Quadrics: Cylinder
- Half Cylinders in Cylindrical Coordinates.
- Cone in Spherical Coordinates is a Rotation
- Stokes' (circulation of a surface)
- Oriented Oval and Disk (Stokes)