Lectures on Algebra:

(a) Exponential Functions. Definition of exponential function. Extension to negative, zero, rational, and irrational exponents Properties of graphs of exponential functions. Base e exponential functions. Applications to simple population problems. Doubling time. Applications to radioactive problems. Half life.

(b) Introduction to Functions. Simple description of functions, domain, range, arithmetic operations, composition, decomposition, substitution.

(d) Inverse Functions Simple description of inverse functions. Domain, range, graph, slope, existence, horizontal line test.

Correction: there is a typo around minute 8:50 where I write y goes to (y-2)/3. the correct form is y goes to (y-3)/2.

(e) Logarithmic Functions, inverse of exponential functions Simple description logarithms, rules of logarithms, base 10 and base e, graphs.

Lecture 0: A Quick Preview of Trigonometry Angles, vertex, ray, opening, initial side, terminal side, positive or counter-clockwise direction, negative or clockwise direction, winding number, standard position, quadrants, circumference of a circle, measuring angles, degrees, radian, grad, circle, cycle, rotation, round, length of an arc, area of a sector, six trig functions in terms of adjacent, opposite, and hypotenuse, solving a right triangle, six trig functions for arbitrary angles, trig identities: Pythagorean, ratio, negative, sum of angles.

Lecture 1: The Six Trig Functions

Lecture 2: reciprocal identities, cofunction identities, famous angles (30,45,60 degrees)

Lecture 3: degrees, minutes, seconds, calculating inverse trig functions, applications: height of a mountain

Lecture 4: regular polygon problem (1.2, 29), arbitrary angles,

Lecture 5: trig functions of arbitrary angles, given angles or coordinates

Lecture 6: trig functions of arbitrary angles, given equation of terminal line, reference angle, sign of trig functions

Lecture 7: Cicle as a Number Line, Radians, Arc Length

Lecture 8: Radians, Arc Length, angular speed

Lecture 9: A brief review of graphing concepts from college algebra: point plotting, x and y-intercepts, symmetry, asymptotes, domain, range, etc

Lecture 10: Graph of Sine and Cosine

Lecture 11: Graph of Sine, Cosine, and Tangent using unit circle,

Lecture 12: Graph of Cosecant, Secant, and Cotangent using reciprocal identities, graph of Cotangent using the unit circle,

Lecture 13: Negative angle and Reflection Identities, Sin(-x), Sin(Pi-x), Sin(Pi+x), etc

Lecture 14: Graph of transformed Sine and Cosine functions: a*Sin(b*x+c)+d

Lecture 15: Graph of transformed Sine and Cosine functions: a*Sin(b*x+c)+d

Lecture 16: Examples for Graph of transformed Sine and Cosine functions: a*Sin(b*x+c)+d

Lecture 17: Identities (Pythagorean)

Lecture 18: Identities (reciprocal, negative angle, examples)

Lecture 19: Examples for Transformations and Lecture on Identities (cosine of sum and difference)

Lecture 20: Examples for Basic Identities and Lecture on Identities (sine or tangent of sum and difference)

Lecture 21: Proof of identity for Law of Cosine and cosine of difference of angles

Lecture 22: Examples for basic algebra on trig functions, trig identities for sum or difference

Lecture 23: Cofunction and Double angle identities

Lecture 24: Half angle identities

Lecture 25: review (no video control)

Lecture 26: review

Lecture 27: Inverse functions, inverse sine

Lecture 28: inverse cosine

Lecture 29: inverse tangent

Lecture 30a: example of inverse functions, Solving Trig equations, basic cases

Lecture 30b: review of Inverse Trig Functions. arcsin, arccos, arctan, graphs, and special values.

Lecture 30c: Review of Problems on Inverse Trig Functions.

Lecture 31: example problems on inverse functions

Lecture 32: example problems on solving equations

Lecture 33: Solving arbitrary triangles, Law of Sines

Lecture 34: Solving arbitrary triangles, Law of Sines

Lecture 35: Examples from solving trig equations and solving triangles

Lecture 36: The Law of Cosines

Lecture 37: Introduction to complex numbers

Lecture 38: Trig form of complex numbers, multiplication, power, division

Lecture 39: Root of complex numbers