PreCalculus Videos Lectures

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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,