Arithmetic Pre-Algebra Algebra I Algebra California Standards Test: Algebra I California Standards Test: Algebra II Geometry
California Standards Test: Geometry Trigonometry Precalculus  Calculus Differential Equations  Linear Algebra Probability
Statistics Physics Chemistry Biology History Finance Banking and Money
Venture Capital and Capital Markets Valuation and Investing Current Economics Credit Crisis Paulson Bailout Geithner Plan Brain Teasers
SAT Preparation GMAT Preparation


Derivatives, Slope, Velocity, Rate of Change Limits, Continuity, Trigonometric Limits Derivatives of Products, Quotients, Sine, Cosine Chain Rule, Higher Derivatives Implicit Differentiation, Inverses Exponential and Log, Logarithmic Differentiation, Hyperbolic Functions Hyperbolic Functions Continued and Exam I Review
Linear and Quadratic Approximations Curve Sketching Max-Min Problems  Related Rates Newton's Method and other Applications  Mean Value Theorem Inequalities Differentials, Antiderivatives
Differential Equations, Separation of Variables Definite Integrals First Fundamental Theorem of Calculus Second Fundametal Theorem of Calculus Applications to Logarithms and Geometry Volumes by Disks and Shells Work, Average Value, Probability
Numerical Integration Exam III Review


The Dot Product Determinants and the Cross Product Matrices and Inverse Matrices Square Systems and Equations of Planes Parametric Equations for Lines and Planes Velocity, Acceleration, and Kepler's Second Law Review 1
Level Curves, Partial Derivatives, and Tangent Plane Approximations Maximum-Minimum Problems and Least Squares The Second Derivative Test, Boundaries, and Infinity  Differentials and the Chain Rule The Gradient, Directional Derivative, and the Tangent Plane  Lagrange Multipliers Non-Independent Variables 
Partial Differential Equations Review Double Integrals Double Integrals in Polar Coordinates Change of Variables Vector Fields and Line Integrals in the Plane Path Independence and Conservative Fields Gradient Fields and Potential Functions
Green's Theorem Flux and the Normal Form of Green's Theorem Simply Connected Regions and Review Triple Integrals in Rectangular and Cylindrical Coordinates Spherical Coordinates and Surface Area Vector Fields in 3D, Surface Integrals, and Flux Divergence Theorem
Divergence Theorem, Applications, and Proof Line Integrals in Space, Curl, Exactness, and Potentials Stoke's Theorem Stoke's Theorem and Review Topological Considerations and Maxwell's Equations Final Review Final Review Continued


The Geometrical View

Euler's Method

First-Order Linear ODEs

First-Order Substitution Methods

First-Order Autonomous ODEs

Complex Exponentials

First Order Linear with Constant Coefficients


 Second-Order Linear ODEs with Constant Coefficients

 Complex Characteristic Roots

 General Second-Order Linear Homogeneous ODEs

 Nonhomogeneous ODEs

 Particular Solutions to Nonhomogeneous ODEs


 Fourier Series

 Fourier Series Continued

 Particular Solutions via Fourier Series

 The Laplace Transform

 Using the Laplace Transform to Solve Linear ODEs

 Convolution Formula

 Using the Laplace Transform to Solve ODEs with Discontinuous Inputs

 Using the Laplace Transform with Impulse Inputs

 First-Order Systems of ODEs

 Homogeneous Linear Systems with Constant Coefficients

 Continuation of Homogeneous Linear Systems with Constant Coefficients

 Sketching Solutions of Homogeneous Linear Systems with Constant Coefficients

 Matrix Methods for Nonhomogeneous Systems

 Matrix Exponentials

 Decoupling Linear Systems with Constant Coefficients

 Non-Linear Autonomous Systems

 Existence and Non-Existence Criteria

 Relations Between Non-Linear Systems and First-Order ODEs


Lecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5 Lecture 6 Lecture 7
Lecture 8 Lecture 9 Lecture 10  Lecture 12 Lecture 13  Lecture 14 Lecture 15
Lecture 18 Lecture 19 Lecture 20 Lecture 22 Lecture 23 Lecture 24 Lecture 25
Lecture 26 Lecture 28 Lecture 29 Lecture 30


The Geometry of Linear Equations

Elimination with Matrices

Multiplication and Inverse Matrices

Factorization into A=LU

Transposes, Permutations, Spaces Rn

Column Space and Nullspace

Solving AX=0, Pivot Variables, Special Solutions

Solving AX=B, Row Reduced Form B

 Independence, Basis, and Dimension

 The Four Fundamental Subspaces

 Matrix Spaces, Rank 1, Small World Graphs

 Graphs, Networks, Incidence Matrices

 Quiz 1 Review

Orthogonal Vectors and Subspaces

Projections onto Subspaces

 Projection Matrices and Least Squares

 Orthogonal Matrices and Gram-Schmidt

 Properties of Determinants

 Determinant Formulas and Cofactors

 Cramer's Rule, Inverse Matrix, and Volume

 Eigenvalues and Eigenvectors

 Diagonalization and Powers of A

 Differential Equations and Exp(At)

 Markov Matrices, Fourier Series

 Quiz 2 Review

 Symmetric Matrix and Positive Definiteness

 Complex Matrices, Fast Fourier Transform

 Positive Definite Matrices and Minima

 Similar Matrices and Jordan Form

 Singular Value Decomposition

 Linear Transformations and Their Matrices

 Change of Basis, Image Compression

Quiz 3 Review

Left and Right Inverses, Pseudoinverse 

Final Course Review 


Part 1 Part 2 Part 3 Part 4 Part 5 Part 6 Part 7
Part 8 Part 9 Part 10  Part 11 Part 12  Part 13 Part 14
Proof The Pigeonhole Principle Construction of GF(8) Euler's Identity The Birthday Paradox Infinity Classification Theorem for Finite Simple Groups