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Linear Algebra for MATH 308
Lecture 1: Vectors, Linear Independence, and Spanning Sets
Lecture 2: Operations with Matrices and Vectors
Lecture 3: Systems of Equations
Lecture 4: Determinant
Lecture 5: Eigenvectors and Eigenvalues
Lecture 6: Matrix Inverses and Diagonalization
Lecture 7: Systems of Differential Equations
Lecture 8: Systems of Differential Equations
Math for Quantitative Finance
Several Variables Calculus
Section 1: Functions of Several Variables
Section 2: Limits and Continuity
Section 3: Partial Derivatives
Section 4: Tangent Planes and Linear Approximations
Section 5: The Chain Rule
Section 6: Directional Derivatives and the Gradient Vector
Section 7: Maximum and Minimum Values
Section 8: Lagrange Multipliers
Differential Equations
Section 1: Integrating Factor
Section 2: Separable Equations
Section 3: Compound Interest
Section 4: Variation of Parameters
Section 5: Systems of Ordinary Differential Equations
Section 6: Matrices
Section 7: Systems of Equations, Linear Independence, and Eigenvalues & Eigenvectors
Section 8: Homogeneous Linear Systems with Constant Coefficients
Section 9: Complex Eigenvalues
Section 10: Fundamental Matrices
Section 11: Repeated Eigenvalues
Section 12: Nonhomogeneous Linear Systems
Mathematical Probability
Section 1: Probabilistic Models and Probability Laws
Section 2: Conditional Probability, Bayes’ Rule, and Independence
Section 3: Discrete Random Variable, Probability Mass Function, and Cumulative Distribution Function
Section 4: Expectation, Variance, and Continuous Random Variables
Section 5: Discrete Distributions
Section 6: Continuous Distributions
Section 7: Joint Distribution Function, Marginal Probability Mass Function, and Uniform Distribution
Section 8: Independence of Two Random Variables, Covariance, and Correlation
Section 9: Conditional Distribution and Conditional Expectation
Section 10: Moment Generating Function
Section 11: Markov’s Inequality, Chebyshev’s Inequality, and Weak Law of Large Numbers
Section 12: Convergence and the Central Limit Theorem
Python Instructional Video Series
Double Integrals
How To
How To ... Precalculus
How To ... Calculus
MPE
MPE Practice Problems for Math 147, 151, or 171
MPE Practice Problems for Math 142
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Algebra Series
Domain
Domain of Logarithmic Functions
Domain of Radical Functions
Domain of Rational Functions
Domain of Combinations of Functions
Linear Functions
Solving Linear Equations
Systems of Two Linear Equations in Two Variables
Quadratic Functions
Quadratic Equations
Rational Functions
Operations with Rational Functions
Solving Rational Equations
Radical Functions
Radical Equations
Power and Exponential Functions
Exponential Functions
Solving Exponential Equations
Logarithms
Logarithmic Equations
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Python Instructional Video Series
Python Instructional Video Series
An example-based guide to using Python to solve math problems.
A link to the transcript is included below each video.
#
Video
00
►Watch: Introduction and Installation
Transcript 00
Video 00 Page
01
►Watch: Numerical Calculations in Python
Transcript 01
Video 01 Page
02
►Watch: Using Variables in Python
Transcript 02
Video 02 Page
03
►Watch: Creating and Manipulating Symbolic Expressions
Transcript 03
Video 03 Page
04
►Watch: Solving Equations Symbolically
Transcript 04
Video 04 Page
05
►Watch: Plotting Expressions and Solving Equations Numerically
Transcript 05
Video 05 Page
06
►Watch: Plotting Multiple Expressions in One Graph
Transcript 06
Video 06 Page
07
►Watch: List Comprehension and Numerical, Graphical, and Symbolic Limits
Transcript 07
Video 07 Page
08
►Watch: Finding Derivatives
Transcript 08
Video 08 Page
09
►Watch: Definite and Indefinite Integrals
Transcript 09
Video 09 Page
10
►Watch: Word Problems and the Algorithmic Process for Multistep Problem Solving
Transcript 10
Video 10 Page
11
►Watch: Simplifying Difference Quotients
Transcript 11
Video 11 Page
12
►Watch: Finding and Graphing Tangent Lines to a Curve
Transcript 12
Video 12 Page
13
►Watch: Finding Horizontal Tangent Lines
Transcript 13
Video 14 Page
14
►Watch: List Comprehension and Patterns in Higher Derivatives
Transcript 14
Video 14 Page
15
►Watch: Implicit Plots and Implicit Differentiation
Transcript 15
Video 15 Page
16
►Watch: Parametric Plots and Tangents at a Given
t
-value
Transcript 16
Video 16 Page
17
►Watch: Tangents to Parametrized Curves at a Given Point
Transcript 17
Video 17 Page
18
►Watch: Finding Absolute (Global) Extrema
Transcript 18
Video 18 Page
19
►Watch: Finding Intervals of Increase/Decrease and Concavity
Transcript 19
Video 19 Page
20
►Watch: Approximating Definite Integrals with Riemann Sums
Transcript 20
Video 20 Page
21
►Watch: Areas Between Curves
Transcript 21
Video 21 Page
22
►Watch: Volumes of Revolution
Transcript 22
Video 22 Page
23
►Watch: Work: Hooke’s Law
Transcript 23
Video 23 Page
24
►Watch: Work: Pumping Liquid from a Tank
Transcript 24
Video 24 Page
25
►Watch: Generating and Plotting Sequences
Transcript 25
Video 25 Page
26
►Watch: Generating and Plotting Partials Sums of a Series
Transcript 26
Video 26 Page
27
►Watch: For Loops and Recursive Sequences
Transcript 27
Video 27 Page
28
►Watch: Radius and Interval of Convergence
Transcript 28
Video 28 Page
29
►Watch: Plotting a Function and Partial Sums of its Power Series
Transcript 29
Video 29 Page