Advanced Calculus Demystified
by David Bachman
| Pages 274 | PDF | 2.5 MB |
Content,
Functions of Multiple Variables
- Functions
- Three Dimensions
- Introduction to Graphing
- Graphing Level Curves
- Putting It All Together
- Functions of Three Variables
- Parameterized Curves
- Quiz
Fundamentals of Advanced Calculus
- Limits of Functions of Multiple Variables
- Continuity
- Quiz
Derivatives
- Partial Derivatives
- Composition and the Chain Rule
- Second Partials
- Quiz
Integration
- Integrals over Rectangular Domains
- Integrals over Nonrectangular Domains
- Computing Volume with Triple Integrals
- Quiz
Cylindrical and Spherical Coordinates
- Cylindrical Coordinates
- Graphing Cylindrical Equations
- Spherical Coordinates
- Graphing Spherical Equations
- Quiz
Parameterizations
- Parameterized Surfaces
- The Importance of the Domain
- This Stuff Can Be Hard!
- Parameterized Areas and Volumes
- Quiz
Vectors and Gradients
- Introduction to Vectors
- Dot Products
- Gradient Vectors and Directional Derivatives
- Maxima, Minima, and Saddles
- Application: Optimization Problems
- LaGrange Multipliers
- Determinants
- The Cross Product
- Quiz
Calculus with Parameterizations
- Differentiating Parameterizations
- Arc Length
- Line Integrals
- Surface Area
- Surface Integrals
- Volume
- Change of Variables
- Quiz
Vector Fields and Derivatives
- Definition
- Gradients, Revisited
- Divergence
- Curl
- Quiz
Integrating Vector Fields
- Line Integrals
- Surface Integrals
- Quiz
Integration Theorems
- Path Independence
- Green’s Theorem on Rectangular Domains
- Green’s Theorem over More General Domains
- Stokes’ Theorem
- Geometric Interpretation of Curl
- Gauss’ Theorem
- Geometric Interpretation of Divergence
- Quiz
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