MATH425H/PHYS407H Studio Calculus/Physics Schedule

Fall 2006




Instructors:
Teaching Assistants:
Syllabus: pdf (150 kB)



Joint Phys/Calc classes are in blue

Physics classes are in green

Calculus classes are in red

SWBAT := Students Will Be Able To

The reading assignments are to be completed before class

Week 1

Mon, 08/28/2006 J01 First Day of Class
  • Introduction, the goals, group work, the subjects, the daily rules
  • Computer Resources: Blackboard, MasteringPhysics, MyMathLab, MATLAB
Tue, 08/29/2006 P01 Position, Time, and Average Velocity
SWBAT:
  • Describe the physical meaning of positive and negative values of x and t and average velocity.
  • Represent x(t) in different ways (table, plot, stroboscopic picture, words) and translate between representations.
Reading: Knight Introduction, Ch. 1 and Ch. 2.1 - 2.2
Activity: "Describing Motion"
Wed, 08/30/2006 C01 Average Rate of Change, MATLAB
  • Calculate rate of change as the ratio.
  • Estimate rate of change as the slope of the secant line.
  • Think graphically about the secant line becoming a tangent line
  • Recognize tables, formulas and graphs as all different representations of a function.
  • Distinguish between total change and average rate of change.
  • Do simple array calculations with MATLAB.
Reading: Hass Ch. 2.1
Thu, 08/31/2006 P02 Representations of Motion
  • Calculate average acceleration and jerk.
  • Go between simple plots of x, v, and a.
  • Go between actual physical motions and plots.
Reading: Knight Ch. 2.3 - 2.8
Tutorial: "Representations of Motion"
Fri, 09/01/2006 C02 Sequences and Convergence
  • Definition of a sequence as an ordered list of numbers.
  • Graphical understanding that the slopes of the secant line, as Δt decreases, is a sequence.
  • Formal definition of a limit.
  • Algebraic form of the average rate of change, and the sequence it creates as Δt decreases.
Reading: Hass Ch. 8.1

Week 2

Mon, 09/04/2006 N01 Labor Day, no classes
Tue, 09/05/2006 P03 Vector Addition and Subtraction (Dr. Gertrud Kraut)
  • Understand motion in 2 dimensions by adding/subtracting vectors.
  • Go between component and angle and magnitude form.
  • Add two vectors numerically and graphically.
  • Subtract two vectors numerically and graphically.
Reading: Knight Ch. 3
Activity: "Moving in Two Dimensions" and "Substracting Vectors"
Wed, 09/06/2006 C03 Definition of Derivative
  • Calculate average rate of change.
  • Recognize the derivative as the slope of the secant line.
  • Take the limits of the average rate of change for a polynomial.
  • Recognize different notations for derivative.
Reading: Hass Ch. 2.1, 3.1, 3.3
Thu, 09/07/2006 P04 Acceleration in 1-D (Prof. Silas Beane)
  • Calculate acceleration from ticker tape data.
  • Explain errors in calculating acceleration with noisy data.
  • Calculate acceleration using vector subtraction.
  • Explain why acceleration and velocity are independent.
Reading: Knight Ch. 2.5 - 2.8
Activity: "Calculating Velocity and Acceleration"
Tutorial: "Acceleration in 1D"
Fri, 09/08/2006 C04 Derivative of Polynomials
  • Take derivatives of sums of functions.
  • Derive the general form of the derivative of a polynomial.
Reading: Hass Ch. 2.7, 3.1 - 3.3

Week 3

Mon, 09/11/2006 C05 Anti-Derivatives
  • Recognize anti-derivatives as the inverse of a derivative.
  • Find velocity from acceleration.
  • Find position for non-constant acceleration.
Reading: Hass Ch. 4.8
Tue, 09/12/2006 P05 Acceleration in Two Dimensions
  • Calculate acceleration in 2-D using video data.
  • See that motion in the 2 directions is independent.
  • Gain practice in solving standard projectile problems.
Reading: Knight Ch. 6.1 - 6.3
Activity: "Projectile Motion Lab"
Wed, 09/13/2006 C06 Shifting Functions and their Derivatives
  • Take derivatives of shifted functions.
  • Take anti-derivatives of shifted functions.
Reading: Hass Ch. 1.2, 3.1
Thu, 09/14/2006 P06 Emily's Walk
  • Attack a more complex problem.
  • Make assumptions and simplifications and justify them.
  • Describe paths as parametric curves.
  • Putting together vectors, functions, derivatives and anti-derivatives.
Activity: "Emily's Walk" and "Emily's Walk - Redux"
Fri, 09/15/2006 J02 Kinematics Problem Solving
  • Apply the GOAL format for problem solving.
  • Use GOAL format to solve problems involving anti derivatives, derivatives, and vector additions.

Week 4

Mon, 09/18/2006 C07 Slope and Concavity
  • Understand the relationship between concavity and the second derivative.
  • Go between plots of position, acceleration and velocity.
Reading: Hass Ch. 4.3 and 4.4
Tue, 09/19/2006 P07 Physics Review
Activity: "Kinematics Problem Solving" Part 1 and 2
Wed, 09/20/2006 C08 Calculus Review
Thu, 09/21/2006 P08 Relations between Velocity and Acceleration in 2-D (! relevant to first exam !)
  • Show that speeding up, slowing down, or staying at constant speed in two dimensions depends on the angle between v and a vectors.
  • Show that acceleration for an object going in a circle depends directly on velocity and indirectly on radius.
Reading: Knight Ch. 7.1, 7.2 and graphs in 7.6
Activity: "Emily's Walk - Redux"
Tutorial: "Motion in two dimensions"
Fri, 09/22/2006 J03 First Exam
Calculus: Thursday 12:40pm - 2:00pm in Hamilton Smith 129
Physics: Friday 9:10am - 11:00am in DeMeritt 104 & 106

Week 5

Mon, 09/25/2006 C09 Quotient and Product Rules
  • Apply the product, quotient rules.
  • Take derivatives of quotients and products of polynomials and rational functions.
Reading: Hass Ch. 3.2
Tue, 09/26/2006 C10 Composition and Chain Rule
  • Take derivatives of composite functions of polynomial or rational functions.
Reading: Hass Ch. 1.2 and 3.5
Wed, 09/27/2006 P09 Introduction to Forces (! In DeMeritt 104 !)
  • Identify some common forces.
  • Add forces as vectors.
  • Begin to draw a correct free body diagram.
Reading: Knight Ch. 4.1 - 4.3, and 4.7
Activity: "How Do Forces Combine?"
Tutorial: "Forces" Part III
Thu, 09/28/2006 P10 Newton's 1st and 2nd Law
  • Recognize that a constant velocity requires no net force.
  • Recognize that the acceleration is proportional to the net force.
Reading: Knight Ch. 4.4 - 4.6 and 5.1 - 5.3
Activity: "Investigating Force, Acceleration, and Velocity"
Fri, 09/29/2006 P11 Normal Force and Third Law Pairs
  • Identify third law pairs.
  • Calculate the normal force in many situations, especially those for which the normal force is not equal to the weight.
Reading: Knight Ch. 8.1 - 8.4
Activity: "Banging Cars" and "Third Law Pairs"

Week 6

Mon, 10/02/2006 C11 Exponential Functions
  • Use the series definition.
  • Recognize exp as the solution of a differential equation.
  • Apply the rules for the exponential function.
  • Determine the derivative/antiderivative of the exponential functions.
Reading: Hass Ch. 1.4, 1.5, and 3.2
Tue, 10/03/2006 P12 Examining more Forces
  • Draw free body diagrams.
  • Identify forces that act directly on the body.
Reading: Knight Ch. 8.5 - 8.6
Activity: "Examining Forces" and "Atwood Machine Problem"
Tutorial: "Forces" Part III
Wed, 10/04/2006 C12 General Inverse Functions and the log Function
  • Understand and recognize inverse functions.
  • Compute derivatives of the inverse functions.
  • Recognize the Log functions as the inverse of exponential functions.
  • Apply the log rules.
  • Use derivative/antiderivative of log.
Reading: Hass Ch. 3.2 and 5.7
Thu, 10/05/2006 P13 Investigating Friction (Prof. James Harper)
  • Identify statics and kinetic friction.
  • Identify the direction in which friction acts.
Reading: Knight Ch. 5.4 - 5.6
Activity "Thinking about Friction"
Fri, 10/06/2006 J04 Newton's Method
  • Apply Newton's method to find roots.
  • Estimate the approximation error.
Reading: Knight Ch. 6.4 and Hass Ch. 4.7
Activity: "Newton's Method" and "Nasty Canasty vs. Monty Gue"

Week 7

Mon, 10/09/2006 N02 Fall break, no classes
Tue, 10/10/2006 C13 (Monday schedule) Series, Power Series, Taylor-MacLaurin Series
  • Recognize a power series.
  • Understand power series convergence.
  • Calculate Taylor polynomials for rational, log, end exp functions.
  • Linearize a function.
  • Estimate approximation errors.
Reading: Hass Ch. 3.10, 4.7, 8.7, and 8.8
Wed, 10/11/2006 C14 More on Taylor Series and Binomial Theorem
  • Use the binomial theorem.
  • Calculate series expressions for basic trig functions.
  • Estimate approximation errors.
Reading: Hass 8.9 and 8.10
Thu, 10/12/2006 P14 Uniform Circular Motion
  • Explain why a force is needed to travel in a circle.
  • Verify that the larger the circle, the smaller the acceleration.
  • Verify that the larger the velocity, the larger the acceleration.
  • Give examples of different types of forces (normal etc.) that can provide centripetal acceleration.
Reading: Knight Ch. 7.3 - 7.6
Activity: "Moving in a Circle at Constant Speed" and "Forces and Circular Motion at Constant Speed"
Fri, 10/13/2006 J05 (Mid-semester) Terminal Velocity
  • Measure drag force on a coffee filter.
Reading: Knight Ch. 5.5
Activity: "Drag Force on a Coffee Filter"

Week 8

Mon, 10/16/2006 C15 Riemann Sums, Integrals, and the Fundamental Theorem of Calculus I
  • Understand Riemann sums as the area under a curve.
  • Calculate Riemann sums for simple functions.
  • Recognize the definition of an integral.
Reading: Hass Ch. 5.1 - 5.2
Tue, 10/17/2006 P15 Physics Review
Wed, 10/18/2006 C16 Calculus Review
Thu, 10/19/2006 P16 Balance Point - Center of Mass
  • Be able to find the center of mass of a two-dimensional object using symmetry and intuition.
  • Be able to find the center of mass of a one-dimensional object using symmetry, intuition, superposition, or Riemann sums.
Reading: Knight Ch. 13.2
Activity: "Balance Point"
Fri, 10/20/2006 J06 Second Exam
Calculus: Thursday 12:40pm - 2:00pm in Hamilton Smith 129
Physics: Friday 9:10am - 11:00am in DeMeritt Hall 104 & 106

Week 9

Mon, 10/23/2006 C17 Riemann Sums, Integrals, and the Fundamental Theorem of Calculus II
  • Approximate integrals.
  • Understand integral through the limit process.
  • Understand the relationship between integration and differentiation.
Reading: Hass Ch. 5.3 - 5.4, and 6.5
Tue, 10/24/2006 P17 Conservation of Momentum
  • Recognize that F_net must be zero on a system in order for linear momentum to be conserved.
  • Determine if F_net is zero in several situations.
Reading: Knight Ch. 9.1 - 9.6
Activity: "Proof of Conservation of Momentum" and "Recognizing Conservation of Momentum"
Wed, 10/25/2006 C18 Center of Mass
  • Calculate the center of mass of a one-dimensional object with non-uniform density.
  • Calculate the center of mass of a two-dimensional object (defined by an upper and lower curve) of uniform density.
Reading: Hass Ch. 6.7
Thu, 10/26/2006 P18 Work and Dot Product
  • Understand the relationship between work and kinetic energy, and in particular know that the sign of the work indicates a speeding up or slowing down.
  • Estimate the dot product given a graphical representation of vectors.
  • Calculate the dot product using both a_x b_x + a_y b_y + a_z b_z and abcosθ.
Reading: Knight Ch. 10.1 - 10.2 and Ch. 11.1 - 11.3
Tutorial: "Work and the Work-Energy Theorem"
Fri, 10/27/2006 J07 Euler's Method and Air Drag
  • Numerically solve simple differential equations.
  • Solve the differential equation for air drag.
  • Recognize Euler's method as the numerical equivalent to slope fields.
Activity: "Drag Force on a Coffee Filter" (curve fitting part), "Air Drag and Euler's Method"

Week 10

Mon, 10/30/2006 C19 Work Integrals
  • Recognize parametric curves.
  • Calculate the work due to a constant force on a parametric curve using ds = sqrt(dx^2+dy^2).
  • Show that the work due to gravity is always "mgh" regardless of the path taken.
Tue, 10/31/2006 P19 Work and Conservative Forces - Proof of Work-Energy Theorem
  • Explain the distinction between conservative and non-conservative forces.
  • Use calculus to prove the work-energy theorem.
Reading: Knight Ch. 10.3 - 10.5 and 11.4 - 11.7
Activity: "Forces and Work" and "Proof of Work-Energy Theorem"
Wed, 11/01/2006 C20 Unconstrained Optimization
Thu, 11/02/2006 C21 Constrained Optimization I
  • Minimize or maximize a function subject to a constraint.
  • Be able to "solve" constrained optimization "by eye".
Fri, 11/03/2006 J05 Project Day

Week 11

Mon, 11/06/2006 P20 Conservation Laws - When Do I Use What Method?
  • Recognize when work-energy theorem is appropriate to solve a problem.
  • Recognize when Newton's second law is appropriate to solve a problem.
Reading: Knight Ch. 10.6 - 10.7 and 11.8 - 11.9
Activity: "Proof of Conservation Laws" and "Contrasting Work-Energy Theorem and Newton's 2nd Law"
Tue, 11/07/2006 P21 (Election day) Conservation Lab I (Momentum)
  • Recognize that momentum is conserved.
  • Verify that momentum is nearly conserved.
Reading: Knight Ch. 9.5 - 9.6
Activity: "Conservation Lab I"
Wed, 11/08/2006 C22 Constrained Optimization II
Thu, 11/09/2006 P22 Conservation Lab II (Energy)
  • Recognize that mechanical energy is conserved.
  • Verify that mechanical energy is nearly conserved.
Reading: Knight Ch. 10.6
Activity: "Conservation Lab II"
Fri, 11/10/2006 N03 Veterans Day, no classes

Week 12

Mon, 11/13/2006 C23 Impulse-Momentum Theorem and the FTC
  • Derive the impulse-momentum theorem using the fundamental theorem of calculus.
  • Apply the impulse-momentum theorem to some situations with forces that are not constant in time.
Tue, 11/14/2006 P24 Physics Review (Prof. Olof Echt)
Wed, 11/15/2006 C24 Calculus Review
Thu, 11/16/2006 P25 Introduction to Rotation
  • Understand the value of using angular instead of linear variales.
  • Have some sense why the direction of ω is out of the page.
  • See the analogy with constant linear acceleration problems.
Reading: Knight Ch. 7.1 - 7.2 (review) and 13.1
Tutorial: "Rotational Motion" (parts I and II only!)
Fri, 11/17/2006 J10 Third Exam
Calculus: Thursday 12:40pm - 2:00pm in Hamilton Smith 129
Physics: Friday 9:10am - 11:00am in DeMeritt Hall 104 & 106

Week 13

Mon, 11/20/2006 C25 Trigonometric functions and the unit circle
  • Understand what circular motion is.
  • Know the definition of sin(x) and cos(x), and their derivatives.
  • Recognize sin/cos as basic solutions of the 2nd order differential equation y'' = - ω^2 y.
  • Relate radius vector, velocity vector, and acceleration vector in a circular motion.
Tue, 11/21/2006 P26 Introduction to Moment of Inertia and Torque
  • Recognize that the distance of mass and force from the pivot point affect how an objects rotates.
  • Explain intuitively what torque and moment of inertia are.
Reading: Knight Ch. 13.2 - 13.5 and 13.9
Activity: "Rotational Analogs to Force and Mass" and "Moment of Inertia"
Wed, 11/22/2006 C26 (Friday schedule) Derivatives and Antiderivatives of Trigonometric Functions
Thu, 11/23/2006 N04 Thanksgiving, no classes
Fri, 11/24/2006 N05 Thanksgiving, no classes

Week 14

Mon, 11/27/2006 C27 Working with Vectors
  • Identify a vector from a scalar.
  • Distinguish between different vector notations.
  • Know about unit vectors and coordinate systems.
  • Recognize component notation as a simplification of a linear combination.
  • Know the relation between dot product, length of a vector, and angle/distance between vectors.
  • Differentiate vector valued functions.
Tue, 11/28/2006 C28 Inverse Trigonometric Functions and Hyperbolic Functions I
  • Recognize the inverse trig. and hyp. functions.
  • Take the derivative of inverse trig/hyp funtions.
  • Recognize inverse trig. functions as antiderivatives of some rational and trancendental functions.
Wed, 11/29/2006 P27 Moment of Inertia Calculations
  • Calculate the moment of inertia for point particles.
  • Use parallel-axis theorem and tables to calculate the moment of inertia.
Reading: Knight Ch. 13.4 - 13.5
Activity: "Problem using Torque and Moment of Inertia" and "Atwood Machine Problem - Redux"
Thu, 11/30/2006 P28 Angular Momentum
  • Apply conservation of angular momentum to explain some everyday phenomena.
  • Apply conservation of angular momentum in problem solving.
Reading: Knight Ch. 9.7 and 13.10
Activity: "Spinning our selves!"
Fri, 12/01/2006 P29 Torque Lab
  • Use (1) rotational dynamics and (2) geometry to find the moment of inertia for a large pulley.
Reading: Knight Ch. 13.4 - 13.5
Activity: "Moment of Inertia Experiment"

Week 15

Mon, 12/04/2006 C29 Inverse Trigonometric Functions and Hyperbolic Functions II
  • Know what to do with them.
  • Recognize sinh/cosh as solution of differential equation.
Tue, 12/05/2006 P30 Torque Lab II and Equilibrium
  • Determine the modified atwood machine with a massive pulley.
  • Several standard equilibrium problems.
Reading: Knight Ch. 13.6 - 13.8
Wed, 12/06/2006 P31 Physics Review
Thu, 12/07/2006 C30 Hyperbolic Functions and L'Hopital's Rule
Fri, 12/08/2006 C31 (Last day of classes) Calculus Review

Week 16

Mon, 12/11/2006 N06 Reading day
Tue, 12/12/2006 N07 Finals
Wed, 12/13/2006 N08 Calculus Final
8:00am - 10:00am in KING S145
Thu, 12/14/2006 N09 Finals
Fri, 12/15/2006 N10 Physics Final
3:30pm - 5:30pm in KING S145

last update: Tue Dec 5 22:08:50 EST 2006