MATH 425H / PHYS 407H Studio Calculus/Physics I

Fall 2010

Daily Schedule

Class Schedule:
Teaching Assistants:
Syllabus: pdf

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, 08/30/2010 J01 First Day of Class
  • Introduction, the goals, group work, the subjects, the daily rules
  • Computer Resources: Blackboard, MasteringPhysics
Tue, 08/31/2010 P01 Position, Time, and Average Velocity
  • 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 2e Introduction, Ch. 1 and Ch. 2.1 - 2.2
Activity: Newton - "Describing Motion"
Wed, 09/01/2010 C01 Average Rate of Change
  • 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 MAPLE.
Reading: Hass Ch. 2.1
Activity: Newton 1 & 2
Thu, 09/02/2010 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 2e Ch. 2.2 - 2.7
Activity: Tutorial - "Representations of Motion"
Fri, 09/03/2010 C02 Limits of Average Rates of Change
  • Definition of differentiability.
  • Graphical understanding that the slopes of the secant lines approach a number that is the slope of the tangent line.
  • Algebraic form of the average rates of change over intervals that decrease toward zero.
Reading: Hass Ch. 2.1

Week 2

Mon, 09/06/2010 N01 Labor Day, no classes
Tue, 09/07/2010 P03 Vector Addition and Subtraction
  • 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 2e Ch. 3
Activity: Newton - "Moving in Two Dimensions" and "Subtracting Vectors"
Wed, 09/08/2010 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
Activity: Newton 5 & 6
Thu, 09/09/2010 P04 Acceleration in One Dimension
  • 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 2e Ch. 2.4 - 2.7
Activity: Newton - "Calculating Velocity and Acceleration" and Tutorial - "Acceleration in 1D"
Fri, 09/10/2010 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
Activity: Newton 7 & 8

Week 3

Mon, 09/13/2010 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
Activity: Newton 9 & 10
Tue, 09/14/2010 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 2e Ch. 4.1 - 4.4
Activity: Newton - "Projectile Motion Lab"
Wed, 09/15/2010 C06 Shifting Functions and their Derivatives
  • Take derivatives of shifted functions.
  • Take anti-derivatives of shifted functions.
Reading: Hass Ch. 1.2, 3.1
Activity: Newton 11 & 12
Thu, 09/16/2010 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.
Reading: Knight 2e Ch. 4.1 - 4.4
Activity: Newton - "Emily's Walk" and "Emily's Walk - Redux"
Fri, 09/17/2010 J02 Kinematics Problem Solving
  • Apply the GOAL format for problem solving.
  • Use GOAL format to solve problems involving anti derivatives, derivatives, and vector additions.
Activity: Newton - "Kinematics Problem Solving"

Week 4

Mon, 09/20/2010 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
Activity: Newton 13 & 14
Tue, 09/21/2010 P07 Physics Review - Kinematics
Activity: Newton - "Kinematics Problem Solving" Part 1 and 2
Wed, 09/22/2010 C08 Calculus Review
Thu, 09/23/2010 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 2e figures 4.40 and 4.42
Activity: Newton - "Emily's Walk - Redux" and Tutorial - "Motion in two dimensions"
Fri, 09/24/2010 J03 First Exam
Part 1 - Physics (w/both problem): Friday 9:10am - 11:00am in DeM 301 and 311
Part 2 - Calculus: Tuesday, 9/28, 12:40pm - 2:00pm in TBA

Week 5

Mon, 09/27/2010 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
Activity: Newton 15 & 16
Tue, 09/28/2010 P09 Introduction to Forces
  • Identify some common forces.
  • Add forces as vectors.
  • Begin to draw a correct free body diagram.
Reading: Knight 2e Ch. 5.1 - 5.3, and 5.7
Activity: Newton - "How Do Forces Combine?" and Tutorial - "Forces" Part III
Wed, 09/29/2010 C10 Composition and Chain Rule
  • Take derivatives of composite functions of polynomial or rational functions.
Reading: Hass Ch. 1.2 and 3.5
Activity: Newton 17 & 18
Thu, 09/30/2010 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 2e Ch. 5.4 - 5.6 and 6.1 - 6.3
Activity: Newton - "Investigating Force, Acceleration, and Velocity"
Fri, 10/01/2010 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 2e Ch. 7.1 - 7.4
Activity: Newton - "Atwood Machine Problem", "Banging Cars", and "Third Law Pairs"

Week 6

Mon, 10/04/2010 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
Activity: Newton 19 & 20
Tue, 10/05/2010 P12 Examining more Forces
  • Draw free body diagrams.
  • Identify forces that act directly on the body.
Reading: Knight 2e Ch. 7.5
Activity: Newton - "Examining Forces", "Atwood Machine Problem" and Tutorial - "Forces" Part III
Wed, 10/06/2010 C12 Exponential Functions II
  • 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
Activity: Newton 19 & 20
Thu, 10/07/2010 P13 Investigating Friction
  • Identify statics and kinetic friction.
  • Identify the direction in which friction acts.
Reading: Knight 2e Ch. 6.4 - 6.6
Activity: Newton - "Thinking about Friction"
Fri, 10/08/2010 J04 Newton's Method
  • Apply Newton's method to find roots.
  • Estimate the approximation error.
Reading: Knight 2e Ch. 4.4 and Hass Ch. 4.7
Activity: Newton - "Newton's Method" and "Nasty Canasty vs. Monty Gue"

Week 7

Mon, 10/11/2010 C13 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
Activity: Newton 21 & 22
Tue, 10/12/2010 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 2e Ch. 4.5 - 4.7 & 8.1 - 8.7
Activity: Newton - "Moving in a Circle at Constant Speed" and "Forces and Circular Motion at Constant Speed"
Wed, 10/13/2010 C14 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 and Newton p. 177-179
Thu, 10/14/2010 J05 Terminal Velocity
  • Measure drag force on a coffee filter.
Reading: Knight 2e Ch. 6.5
Activity: Newton - "Drag Force on a Coffee Filter"
Fri, 10/15/2010 N02 (Mid-semester) Fall break, no classes

Week 8

Mon, 10/18/2010 P15 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 2e Ch. 12.2
Activity: Newton - "Balance Point"
Tue, 10/19/2010 C15 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
Activity: Newton 23 & 24
Wed, 10/20/2010 C16 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
Activity: Newton 25 & 26
Thu, 10/21/2010 C17 Calculus Review
Fri, 10/22/2010 P16 Physics Review - Dynamics

Week 9

Mon, 10/25/2010 J06 Second Exam
Part 1 - Calculus (w/both problem): Monday 9:10am - 11:00am in DeM 301 & 311
Part 2 - Physics: Tuesday, Oct. 26, 12:40pm - 2:00pm in DeM 301 & 311
Tue, 10/26/2010 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 2e Ch. 9.1 - 9.6
Activity: Newton - "Proof of Conservation of Momentum" and "Recognizing Conservation of Momentum"
Wed, 10/27/2010 C18 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
Activity: Newton 27 & 28
Thu, 10/28/2010 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 2e Ch. 10.1 - 10.2 and Ch. 11.1 - 11.3
Activity: Tutorial - "Work and the Work-Energy Theorem"
Fri, 10/29/2010 C19 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. 5.1 -5.3, and 6.7
Activity: Newton 31 & 32

Week 10

Mon, 11/01/2010 C20 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, 11/02/2010 P19 (Election day) 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 2e Ch. 10.3 - 10.5 and 11.4 - 11.7
Activity: Newton - "Forces and Work" and "Proof of Work-Energy Theorem"
Wed, 11/03/2010 C21 Unconstrained Optimization
Thu, 11/04/2010 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 2e Ch. 10.6 - 10.7 and 11.8 - 11.9
Activity: Newton - "Proof of Conservation Laws" and "Contrasting Work-Energy Theorem and Newton's 2nd Law"
Fri, 11/05/2010 J07 Project Day

Week 11

Mon, 11/08/2010 J08 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: "Air Drag and Euler's Method"
Tue, 11/09/2010 P21 Conservation Lab I (Momentum)
  • Recognize that momentum is conserved.
  • Verify that momentum is nearly conserved.
Reading: Knight 2e Ch. 9.5 - 9.6
Activity: Newton - "Conservation Lab I"
Wed, 11/10/2010 C22 Constrained Optimization I
  • Minimize or maximize a function subject to a constraint.
  • Be able to "solve" constrained optimization "by eye".
Thu, 11/11/2010 N03 Veterans Day, no classes
Fri, 11/12/2010 P22 Conservation Lab II (Energy)
  • Recognize that mechanical energy is conserved.
  • Verify that mechanical energy is nearly conserved.
Reading: Knight 2e Ch. 10.6
Activity: Newton - "Conservation Lab II"

Week 12

Mon, 11/15/2010 C23 Constrained Optimization II
Tue, 11/16/2010 P23 Physics Review - Conservation Laws
Wed, 11/17/2010 C24 Calculus Review
Thu, 11/18/2010 P24 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 2e Ch. 8.2 - 8.4 (review) and 12.1
Activity: Tutorial - "Rotational Motion" (parts I and II only!)
Fri, 11/19/2010 J09 Third Exam
Part 1 - Calculus: Thursday 12:40pm - 2:00pm in DeM 301 & 311
Part 2 - Physics (w/both problem): Friday 9:10am - 11:00am in DeM 301 & 311

Week 13

Mon, 11/22/2010 C25 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.

Activity: Newton 31 & 32
Tue, 11/23/2010 P25 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 2e Ch. 12.2 - 12.6 and 12.9
Activity: Newton - "Rotational Analogs to Force and Mass" and "Moment of Inertia"
Wed, 11/24/2010 C26 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.
Activity: Newton 41 & 42
Thu, 11/25/2010 N04 Thanksgiving Break, no classes
Fri, 11/26/2010 N05 Thanksgiving Break, no classes

Week 14

Mon, 11/29/2010 C27 Derivatives and Antiderivatives of Trigonometric Functions

Activity: Newton 43 & 44
Tue, 11/30/2010 P26 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 2e Ch. 12.7
Activity: Newton - "Problem using Torque and Moment of Inertia" and "Atwood Machine Problem - Redux"
Wed, 12/01/2010 C28 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.
Activity: Newton 45 & 46
Thu, 12/02/2010 P27 Torque Lab I and Equilibrium
  • Determine the modified atwood machine with a massive pulley.
  • Several standard equilibrium problems.
Reading: Knight 2e Ch. 12.8
Fri, 12/03/2010 P28 Torque Lab II
  • Use (1) rotational dynamics and (2) geometry to find the moment of inertia for a large pulley.
Reading: Knight 2e Ch. 12.3 - 12.4 and 12.7
Activity: Newton - "Moment of Inertia Experiment"

Week 15

Mon, 12/06/2010 C29 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.
Activity: Newton 47 & 48
Tue, 12/07/2010 P29 Angular Momentum
  • Apply conservation of angular momentum to explain some everyday phenomena.
  • Apply conservation of angular momentum in problem solving.
Reading: Knight 2e Ch. 12.10 - 12.11
Activity: Newton - "Spinning our selves!"
Wed, 12/08/2010 P30 Physics Review
Thu, 12/09/2010 C30 Inverse Trigonometric Functions and Hyperbolic Functions II
  • Know what to do with them.
  • Recognize sinh/cosh as solution of differential equation.
Fri, 12/10/2010 C31 (Last day of classes) Calculus Review

Week 16

Mon, 12/13/2010 N06 Reading Day
Tue, 12/14/2010 N07 Finals
Wed, 12/15/2010 N08 Calculus Final
10:30am - 12:30pm in TBA
Thu, 12/16/2010 N09 Physics Final
3:30pm - 5:30pm in TBA
Fri, 12/17/2010 N10 Finals

last update: Thu Nov 4 09:51:17 EDT 2010