Learning Enhancement Center (LEC)

Virtual Tutoring

Math:

Conceptual videos and worked examples from basic algebra through algebra 2. Includes videos from the former algebra worked examples playlists.

Topics include:

• Introduction to algebra
• Linear equations
• Linear inequalities
• Graphing and analyzing linear functions
• Systems of equations and inequalities
• Multiplying and factoring expressions
• Exponent expressions and equations
• Functions
• Ratios and proportions
• Rational expressions
• Logarithms
• Conic sections
• Matrices
• Imaginary and complex numbers

Linear Algebra

Matrices, vectors, vector spaces, transformations, eigenvectors/values.  Covers all topics in a first year college linear algebra course.  This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

Topics include:

• Vectors and spaces
• Matrix transformations
• Alternate coordinate systems (bases)

Geometry

This is a first year, high-school level course on Geometry (which is based on Euclid's elements).  It revisits many of the basic geometrical concepts studied in earlier courses, but addresses them with more mathematical rigor. There is strong focus on proving theorems and results from basic postulates.

• Introduction to Euclidean geometry
• Angles and intersecting lines
• Congruence
• Similarity
• Right triangles and trigonometry
• Perimeter, area and volume
• Circles
• Special properties and parts of triangles
• Logical reasoning
• Transformations
•  Analytic geometry
• Geometric constructions
• Worked examples

Calculus

Topics covered in the first two or three semesters of college calculus.  Everything from limits to derivatives to integrals to vector calculus.
Should understand the topics in the pre-calculus playlist first (the limit videos are in both playlists)

• Limits
• Taking derivatives
• Derivative applications
• Indefinite and definite integrals
• Solid of revolution
• Sequences, series and function approximation
• AP Calculus practice questions
• Double and triple integrals
• Partial derivatives, gradient, divergence, curl
• Line integrals and Green's theorem
• Surface integrals and Stokes' theorem
• Divergence theorem

Trigonometry and Precalculus

Videos and exercises on trigonometry.
Watch the "Geometry" playlist first if you have trouble understanding the topics covered here.

• Graphing lines
• Functions and their graphs
• Polynomial and rational functions
• Exponential and logarithmic functions
• Basic trigonometry
• Trig identities and examples
• Parametric equations and polar coordinates
• Conic sections
• Systems of equations and inequalities
• Sequences, series and induction
• Probability and combinatorics
• Imaginary and complex numbers
• Hyperbolic functions
• Limits

Differential Equations

Topics covered in a first year course in differential equations.
Need to understand basic differentiation and integration from Calculus playlist before starting here, topics include:

• Second order linear equations
• Laplace transform

Statistics

Topics include:

•         Independent and dependent events
•         Probability and combinatorics
•         Descriptive statistics
•         Random variables and probability distributions
•         Regression
•         Inferential statistics

Science:

Chemistry

• Introduction to the atom
• Orbitals and electrons
• Periodic table, trends, and bonding
• Chemical reactions (stoichiometry)
• Ideal gas laws
• States of matter
• Reaction rates
• Acids and bases
• Oxidation reduction

Physics

Projectile motion, mechanics and electricity and magnetism.  Solid understanding of algebra and a basic understanding of trigonometry necessary.
Topics include:

• Two-dimensional motion
• Forces and Newton's laws of motion
• Work and energy
• Impacts and linear momentum
• Moments, torque and angular momentum
• Gravitation
• Oscillatory motion
• Fluids
• Thermodynamics
• Electricity and magnetism
• Waves and optics

Biology

Covers topics seen in a first year college or high school biology course:

• Cells and cell division
• Heredity and genetics
• Tree of life
• Cellular respiration
• Photosynthesis
• Human biology
• Immunology

Astronomy

Videos attempting to grasp a little bit about our Universe, topics include:

• Scale of the universe
• Stars, black holes and galaxies
• Earth geological and climatic history
• Life on earth and in the universe

Organic Chemistry

Topics covered in college organic chemistry course.
Basic understanding of basic high school or college chemistry assumed (although there is some review).

• Organic structures and acid/base
• Alkanes and cycloalkanes
• Stereochemistry
• Substitution and elimination reactions
• Alkenes and alkynes
• Alcohols, ethers, epoxides, sulfides
• Conjugation, Diels-Alder, and MO theory
• Aromatic compounds
• Aldehydes and ketones
• Carboxylic acids and derivatives
• Amines

Microeconomics

Topics covered in a traditional college level introductory microeconomics course

• Supply, demand and market equilibrium
• Elasticity
• Consumer and producer surplus
• Scarcity, possibilities, preferences and opportunity cost
• Production decisions and economic profit
• Forms of competition
• Game theory and Nash equilibrium

Macroeconomics

Topics covered in a traditional college level introductory macroeconomics course include:

• GDP: Measuring national income
• Inflation - measuring the cost of living
• Aggregate demand and aggregate supply
• The monetary system
• Income and expenditure: Keynesian cross and IS-LM model

Finance and Capitol Markets

Videos on finance and macroeconomics, topics include:

• Interest and debt
• Housing
• Inflation
• Taxes
• Accounting and financial statements
• Stocks and bonds
• Investment vehicles, insurance and retirement
• Money, banking and central banks
• Options, swaps, futures, MBSs, CDOs, and other derivatives
• Current economics

Humanities:

World History

The history of the world, topics include:

• 1900 - present: The recent past
• 1700-1900: Enlightenment and the Industrial Revolution
• 1500-1600: Renaissance and Reformation
• Before 1300: Ancient and Medieval history
• Surveys of history

Art History

Topics include:

• Art History Basics
• - 400 C.E. Ancient cultures
• 400-1300 Medieval Era
• 1300-1400 Proto-Renaissance
• 1400-1500 Renaissance in Italy and the North
• 1500-1600 End of the Renaissance and the Reformation
• 1600-1700 The Baroque
• 1700-1800 Age of Enlightenment
• 1800-1848 Industrial Revolution I
• 1848-1907 Industrial Revolution II
• 1907-1960 Age of Global Conflict
• 1960 -  Age of Post-Colonialism

Videos about how government works in the United States.

Last Updated: 8/18/20