8. Integration Techniques
Integration by Parts
Trig Integrals
powers of sines and cosines
powers of tangents and secants
Trig Substitution
Partial Fraction
Irreducible Quadratics
Division and Polynomials
Strategy for Integration
Approximate Integration
Integrals without Fundamental Theorem?
Improper Integrals
Domain as x --> infinity
Toward Vertical Asymptote
9. Applications of Integration
Arc Length
Area of Surface of Revolution
More Applications
11. Parametric Equations and Polar Coordinates
Curves defined parametrically
Calculus with Parametric Curves
Polar Coordinates
Areas in Polar Coordinates
Length in Polar Coordinates
12. Infinite Sequences and Series
Sequences
Definition of Convergent Sequence
Strategies for Showing Convergence/Divergence
Examples of Sequences
Recursive Sequences
Series
Definition of Convergent Series
Interesting Issues near the Edge
Integral Test
Comparison Tests
Alternating Series
Absolute Convergence; Root & Ratio Tests
Strategy for Series
Power Series
Functions as Power Series
Taylor Series
exp(x), sin(x), ...
Multiply Taylor Series?
Applications of Taylor Series
Fourier Series
13. Vectors and Geometry of Space
3d coordinate system
Vectors
Dot Product
Cross Product
Sample Surfaces
Continuous Functions are Integrable
Partitions
Upper Sums
Lower Sums
Riemann Sums
Unifom Continuity
14. Vector Functions
15. Partial Derivatives
Functions of Several Variables
Limits and Continuity
All Directions; Wild Approach?
Homogeneous Zero Examples
Partial Derivatives
Definition!
Geometrical Significance
Chain Rule
Can be complicated
Do some examples!
Tangent Planes and Linear Approximation
Subtle Change in Definition
Taylor Series in Several Variables?
Directional Derivatives and Gradient Vector
Maximum and Minimum Values
Constrained Optimization; Lagrange Multipliers
One Constraint
Two Constraints
Geometrical Insights Underlying Method
