|
|
Michael Lambrou
|
|
- Outline
- Numerical Sequences
- Convergence of sequences
|
|
|
Michael Lambrou
|
|
|
|
Michael Lambrou
|
|
- Outline
- Criteria for series convergence
- Ratio and root test
|
|
|
Michael Lambrou
|
|
- Outline
- Sequences of functions
- Derivatives and integrals of limits
- Series of functions
|
|
|
Michael Lambrou
|
|
- Outline
- Power Series
- Radius of convergence
- Differentiation and integration of power series
|
|
|
Michael Lambrou
|
|
- Outline
- Maclaurin series
- Polynomial approximation
- Taylor expansion of functions
|
|
|
Michael Lambrou
|
|
- Outline
- Trigonometric expansion of functions
- Orthogonal functions
- Behaviour at discontinuties
|
|
|
Michael Lambrou
|
|
- Outline
- Functions of two variables
- Graph
|
|
|
Michael Lambrou
|
|
- Outline
- Limit of functions of two variables
- Continuity
- Partial derivatives
- Higher - order partial derivatives
|
|
|
Michael Lambrou
|
|
- Outline
- Differentiability of functions
- Chain rules
- Directional derivatives
|
|
|
Michael Lambrou
|
|
- Outline
- Functions of many variables
- Partial derivatives
- Chain Rules
- Cylindrical and spherical transformations
|
|
|
Michael Lambrou
|
|
- Outline
- Maxima, minima, saddle points
- Criteria for extrema
- Extrema on the boundary
|
|
|
Michael Lambrou
|
|
- Outline
- Extrema under constraints
- Lagrange multipliers
|
|
|
Michael Lambrou
|
|
- Outline
- Volume approximation by rectangles
- Double integrals
- Integration
|
|
|
Michael Lambrou
|
|
- Outline
- Double integrals over regions
- Iteration of integrals
- Techniques of integration
|
|
|
Michael Lambrou
|
|
- Outline
- Change of variables into polars
- Change of variable formula for polars
- General change of variables
- Jacobians
|
|
|
Michael Lambrou
|
|
- Outline
- Triple integrals over a rectangular domain
- Triple integrals over general domains
- Volumes as triple integrals
|
|
|
Michael Lambrou
|
|
- Outline
- Techniques of evaluating triple integrals
- Iteration of integrals
|
|
|
Michael Lambrou
|
|
- Outline
- Volume of solids
- Mass of solids
- Center of mass
- Moment fo inertia
- Pappus Theorem
|
|
|
Michael Lambrou
|
|
- Outline
- Idea of differential equations
- Separation of variables
- Homogeneous equations
|
|
|
Michael Lambrou
|
|
- Outline
- First order linear differential equations
- Integrating factor
- Exact equations
|
|
|
Michael Lambrou
|
|
- Outline
- Second order differential equations
- Homogeneous equations
- Application
|
|
|
Michael Lambrou
|
|
- Outline
- Second order linear inhomogeneous differential equations
- Particular solutions
- Undetermined coefficients
|
|
|
Michael Lambrou
|
|
- Outline
- Higher order linear differential equations
- Homogeneous case
- Inhomogeneous case
- Methods of variation of parameters
|
|
|
Michael Lambrou
|
|
- Outline
- Linear systems of differential equations
- Method of D operators
|