Samuelson Mathxp

Math 20-2 (Block 1)

2011-01-26T16:00:00.001-07:00

There are six units of study in Math 20-2. Each student will receive a detailed course outline describing these units; an abbreviated version is shown below. The complete course outline can be seen by clicking on Math 20 Blog in the right-hand sidebar.

Unit I: Quadratic Functions/Equations 25%

Unit II: Angle Properties/Trigonometry 25%

Unit III: Radicals 20%

Unit IV: Inductive/Deductive Reasoning 10%

Unit V: Statistical Reasoning 10%

Unit VI: Proportional Reasoning 10%

Our semester is approximately 90 days in length; the pacing in the course is determined by that and the relative emphasis of each unit. Students can expect to have some homework throughout; this shouldn't be a huge burden provided we can stay on pace within each unit.

Summative evaluation for the course work will consist of Quizzes/Projects (20%) and Unit Exams (80%); this will determine the student's in-class mark. Formative evaluation will occur within each class; this can be intrinsic (through their own reflection on completed tasks) AND extrinsic (feedback from peers or myself). To arrive at the FINAL mark in Math 20-2, this in-class mark will have a 60% weighting; the Final Exam will make up the remaining 40%.

Math 31 (Block 2)

2011-01-26T15:00:00.005-07:00

Differential Calculus

Required Component

Pre-calculus & Limits

Derivatives & Derivative Theorems

Applications of Derivatives

Elective Component

Numerical Methods

Calculus Theorems

Applications to Physical Sciences/Engineering

Calculus of Log & Exponential Functions

Applications to Business & Economics

Applications to Biological Sciences

Integral Calculus

Required Component

Integrals

Integral Theorems

Applications of Integrals

Elective Component

Numerical Methods

Calculus Theorems

Volumes of Revolution

Further Methods of Integration

Applications to Physical Sciences/Engineering

Calculus of Log & Exponential Functions

Applications to Biological Sciences

Evaluation

Year’s Work

Quizzes/Projects: 25%

Exams: 75%

Final Mark

Year’s Work: 65%

Final Exam: 35%

My intention is to enter into applications of differential and integral calculus as quickly as possible without compromising the basic notions that underlie this discipline. A healthy comprehension of these notions is critical in gaining the necessary understanding that will lead to success in this discipline beyond high school.

Having said that, it is also very important that students have the opportunity to model “real-life” scenarios and apply the theory they have learned. In order to accomplish this, repetitive drills on basic notions will be by-passed; there will be ample opportunity to become well-versed in these procedures through said applications.

Much of the “pre-calculus” requirement has already been completed; any additional requirements will be dealt with as needed. Limits of rational functions will be addressed after students have had the opportunity to explore limits in the context of rates of change of functions (derivatives through first principles) and area under those functions (Riemann Sums).

The historical significance of differential and integral calculus will also be called upon periodically so that students may develop an appreciation for how this discipline evolved from its founders, Isaac Newton and Gottfried Wilhelm Leibniz.

Various rules of differentiation and integration will be derived and explored. Stationary points, points of inflection, and their meaning will be determined and applied in appropriate contexts. These points will also aid in curve sketching; this will be picked up periodically throughout the semester when deemed appropriate.

Students will learn very early that differential and integral calculus are essentially “inverses” of one another. Anti-derivatives will be determined as they relate to simple motion problems; I would like to introduce slope fields at this point as well since this lends itself very nicely to the families of curves that arise with indefinite integrals.

Determining areas bounded by functions is also part of the required component in our course. Riemann Sums will be introduced when deemed appropriate and integrals will be derived from there. The examples chosen will be limited to polynomial functions of degree 3; the summation of Riemann Sums can be cumbersome but it is very worthwhile, in my opinion, as it provides a solid base of reasoning behind the integration rules that will ultimately be utilized.

As far as electives are concerned, various calculus theorems will be introduced and applied when necessary, as will numerical methods of differential and integral calculus; these numerical methods will not be relied upon however.

I would definitely like to explore volumes and surface areas of revolution this semester, and possibly fluid dynamics (time permitting).

I wish us all a very happy and productive semester!

Math 10C (Block 3)

2011-01-26T15:00:00.000-07:00

There are four units of study in Math 10C. Each student will receive a detailed course outline describing these units; an abbreviated version is shown below. The complete course outline can be seen by clicking on Math 10C Blog in the right-hand sidebar.

Unit I: Algebra & Numbers 30%
Unit II: Measurement 20%
Unit III: Relations & Functions 20%
Unit IV: Linear Equations & Systems 30%

Our semester is approximately 90 days in length; the pacing in the course is determined by that and the relative emphasis of each unit. Students can expect to have some homework throughout; this shouldn't be a huge burden provided we can stay on pace within each unit.

Summative evaluation for the course work will consist of Quizzes/Projects (30%) and Unit Exams (70%); this will determine the student's in-class mark. Formative evaluation will occur within each class; this can be intrinsic (through their own reflection on completed tasks) AND extrinsic (feedback from peers or myself). To arrive at the FINAL mark in Math 10C, this in-class mark will have a 70% weighting; the Final Exam will make up the remaining 30%.

Math 20-1 (Block 4)

2011-01-26T13:00:00.000-07:00

There are four units of study in Math 20-1. Each student will receive a detailed course outline describing these units; an abbreviated version is shown below. The complete course outline can be seen by clicking on Math 20 Blog in the right-hand sidebar.

Unit I: Quadratic Functions/Equations 25%
Unit II: Systems of Equations/Inequations (Linear & Quadratic) 20%
Unit III: Radical, Rational, Absolute Value & Reciprocal Functions 30%
Unit IV: Sequences/Series & Trigonometry 25%

Our semester is approximately 90 days in length; the pacing in the course is determined by that and the relative emphasis of each unit. Students can expect to have some homework throughout; this shouldn't be a huge burden provided we can stay on pace within each unit.

Summative evaluation for the course work will consist of Quizzes/Projects (20%) and Unit Exams (80%); this will determine the student's in-class mark. Formative evaluation will occur within each class; this can be intrinsic (through their own reflection on completed tasks) AND extrinsic (feedback from peers or myself). To arrive at the FINAL mark in Math 20-1, this in-class mark will have a 60% weighting; the Final Exam will make up the remaining 40%.

Crossroads Guitar Festival - 2004/2007/2010

2010-06-26T08:22:00.016-06:00

Describe a collection of geometric progressions contained within one (or more) of the tracks below; represent as exponental AND sinusoidal functions. The Math of Music (1)

Sonny Landreth with Eric Clapton (2010)
Robert Randolf with Joe Bonamassa (2010)
ZZ Top (2010)
Jeff Beck (2010)
Vince Gill with James Burton (2010)
Eric Clapton (2010)

Sheryl Crow with Eric Clapton (2007)
Steve Winwood (2007)
Buddy Guy (2007)

Jimmie Vaughan with Eric Clapton & Robert Randolf (2004)
J.J. Cale with Eric Clapton - After Midnight (2004)
J.J. Cale with Eric Clapton - Call Me The Breeze (2004)

The 25th Rock & Roll Hall of Fame Concerts - 2009

2009-10-29T20:20:00.011-06:00

Describe a collection of geometric progressions contained within one (or more) of the tracks below; represent as exponental AND sinusoidal functions. The Math of Music (2)

Crosby, Stills and Nash
Stevie Wonder with Sting
Paul Simon with David Crosby & Graham Nash
Bruce Springsteen with John Fogerty (Fortunate Son)
Bruce Springsteen with John Fogerty (Oh, Pretty Woman)

Elvis Presley - 1968/1970/1973

2006-02-25T19:17:00.049-07:00

Describe a collection of geometric progressions contained within one (or more) of the tracks below; represent as exponental AND sinusoidal functions. The Math of Music (3)

Elvis.......in my opinion, the coolest cat to ever walk the face of this planet.

'68 COMEBACK SPECIAL
Trouble/Guitar Man (1968)
Baby What You Want Me To Do (1968)
Jaihouse Rock (1968)
Hound Dog/All Shook Up (1968)

THAT'S THE WAY IT IS
Mystery Train/Tiger Man (1970)
I Got A Woman (1970)
Polk Salad Annie (1970)
Suspicious Minds (1970)

ALOHA FROM HAWAII
See See Rider (1973)
Johnny B. Goode (1973)
Long Tall Sally/Whole Lotta Shakin' Goin' On (1973)
A Big Hunk O' Love (1973)
An American Trilogy (1973)

The Promised Land (1973)