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Precalculus Lectures
Prerequisites: Algebra Skills and Equations and Inequalities
Algebra Skills (51:01)
Equations and Inequalities (54:49)
Functions
Functions and Function Notation (87:34)
Domain and Range (27:21)
Behavior of a Function's Graph (19:12)
Composite Functions (39:51)
Transformation of Functions (59:16)
Absolute Value Functions (16:59)
Inverse Functions (41:24)
Linear Functions
Linear Functions (26:00)
Graphs of Linear Functions (16:17)
Modeling with Linear Functions (7:24)
Fitting Linear Models to Data (17:11)
Polynomials and Rational Functions
Complex Numbers (28:19)
Quadratic Functions (40:28)
Power Functions and Polynomial Functions (32:39)
Graphs of Polynomial Functions (28:42)
Dividing Polynomials (4:14)
Zeros of Polynomial Functions (37:19)
Rational Functions (49:57)
Modeling Using Variation (18:13)
Exponential and Logarithmic Functions
Exponential Functions (31:25)
Graphs of Exponential Functions (8:33)
Logarithmic Functions (5:49)
Graphs of Logarithmic Functions (26:25)
Logarithmic Properties (15:17)
Exponential and Logarithmic Equations (32:08)
Logistic Models (5:58)
Fitting Exponential Models to Data (8:06)
Trigonometric Functions
Angles (25:57)
Unit Circle: Sine and Cosine Functions (15:08)
The Other Trigonometric Functions (13:26)
Right Angle Trigonometry (25:12)
Graphs of Trigonometric Functions and Inverse Trigonometric Functions
Graphs of Sine and Cosine Functions (29:04)
Graphs of the Other Trigonometric Functions (10:33)
Inverse Trigonometric Functions (16:56)
Trigonometric Identities and Equations
Sum and Difference Identities (11:39)
Double Angle, Half Angle and Reduction Formulas (12:33)
Sum-to-Product and Product-to-Sum Formulas (3:03)
Solving Other Trigonometric Equations (36:58)
Laws of Sines and Cosines, Polar Coordinates, Parametric Equations and Vectors
Law of Sines (13:57)
Law of Cosines and Heron's Formula (8:54)
Polar Coordinates (25:10)
Graphs in Polar Coordinates (32:38)
Polar Form of Complex Numbers (29:31)
Parametric Equations (4:49)
Graphs of Parametric Equations (5:03)
Vectors (36:04)
System of Equations and Inequalities, Matrices and Partial Fractions
System of Linear Equations: Two Variables (30:34)
Systems of Nonlinear Equations and Inequalities (19:09)
Partial Fractions (26:05)
Matrices and Matrix Operations (13:32)
Solving Systems: Gaussian Elimination (25:32)
Solving Systems: Inverse Matrices (13:31)
Solving Systems: Cramers Rule (25:09)
Analytic Geometry
Ellipse (26:25)
Hyperbola (37:06)
Parabola (30:23)
Rotation of Axes (8:51)
Conic Sections in Polar Coordinates (19:03)
Sequences, Probability and Counting Theory
Sequences and Sequence Notation (17:11)
Arithmetic Sequences (14:19)
Geometric Sequences (8:55)
Series and Series Notation (29:55)
Counting Principles, Permutations and Combinations (18:28)
Binomial Theorem (22:11)
Probability (26:30)
Introduction to Calculus
Finding Limits: Numerical and Graphical Approaches (18:31)
Properties of Limits (5:34)
Continuity (11:10)
Derivatives (26:51)
Parabola
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