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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.
Extras:
Here you can test
your knowledge of linear and quadratic functions by this association
game.
(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.
Lectures on Trigonometry
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