MATH425/PHYS407 Studio Calculus/Physics Schedule

Fall 2004




Instructors:
Prof. Karsten Pohl (Physics), 302A DeMeritt Hall, 862-4197, Karsten.Pohl@unh.edu
Prof. Joachim Raeder (Calculus), 245G Morse Hall, 862-3412, J.Raeder@unh.edu


Syllabus


Joint Phys/Calc classes are in blue

Physics classes are in green

Calculus classes are in red

(1) SWBAT means: Students Will Be Able To

Week 1

Mon, 08/30/2004 J01 First Day: Introduction, the goals, group work, the subjects, the daily rules
Tue, 08/31/2004 P01 Position, time, and average velocity (Chapter on Describing Motion). SWBAT(1):
  • 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.
Wed, 09/01/2004 C01 Average Rate of Change, MATLAB I. SWBAT:
  • 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.
Thu, 09/02/2004 P02 Representations of Motion (McDermott tutorial). SWBAT:
  • Calculate average acceleration and jerk
  • Go between simple plots of x, v, and a.
  • Go between actual physical motions and plots.
Fri, 09/03/2004 C02 Sequences and Convergence. SWBAT:
  • Definition of a sequence as an ordered list of numbers.
  • Graphical understanding that the slopes of the secant line, as Delta(t) decreases, is a sequence.
  • Formal definition of a limit.
  • Algebraic form of the average rate of change, and the sequence it creates as Delta(t) decreases.

Week 2

Mon, 09/06/2004 N01 Labor Day, no classes
Tue, 09/07/2004 P03 Vector Addition and Subtraction SWBAT:
  • 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.
Wed, 09/08/2004 C03 The derivative of polynomials. SWBAT:
  • 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.
Thu, 09/09/2004 P04 Acceleration in 1-D. SWBAT:
  • 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
Fri, 09/10/2004 C04 More on derivatives. SWBAT:
  • Take derivatives of sums of functions.
  • Derive the general form of the derivative of a polynomial.

Week 3

Mon, 09/13/2004 C05 Anti-derivatives. SWBAT:
  • Recognize anti-derivatives as the inverse of a derivative.
  • Find velocity from acceleration
  • Find position for non-constant acceleration
Tue, 09/14/2004 P05 Acceleration in two dimensions. (Projectile motion lab). SWBAT:
  • Calculate acceleration in 2-D using video data.
  • See that motion in the 2 directions is independent.
  • Gain practice in solving standard projectile problems.
Wed, 09/15/2004 C06 Shifting polynimials . SWBAT:
  • Take derivatives of shifted functions.
  • Take anti-derivatives of shifted functions.
Thu, 09/16/2004 P06 Emily's walk: SWBAT:
  • 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.
Fri, 09/17/2004 J02 Kinematic Problem solving. SWBAT:
  • Apply the GOAL format for problem solving
  • Use GOAL format to solve problems involving anti derivatives, derivatives, and vector additions.

Week 4

Mon, 09/20/2004 C07 Slope and concativity . SWBAT:
  • Understand the relationship between concavity and the second derivative.
  • Go between plots of position, acceleration and velocity.
Tue, 09/21/2004 P07 Relations between velocity and acceleration in 2-D SWBAT:
  • 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.
Wed, 09/22/2004 C08 Calculus review .
Thu, 09/23/2004 P08 Physics review .
Fri, 09/24/2004 J03 First Exam .

Week 5

Mon, 09/27/2004 C09 Quotient and product rules . SWBAT:
  • Apply the product, quotient rules.
  • Take derivatives of quotients and products of polynomials and rational functions.
Tue, 09/28/2004 C10 Composition and chain rule . SWBAT:
  • Take derivatives of composite functions of polynomial or rational functions.
Wed, 09/29/2004 P09 Introduction to Forces (How do forces combine?). SWBAT:
  • Identify some common forces.
  • Add forces as vectors.
  • Begin to draw a correct free body diagram.
Thu, 09/30/2004 P10 Newton's laws. SWBAT:
  • Recognize that a constant velocity requires no net force.
  • Recognize that the acceleration is proportional to the NET force.
Fri, 10/01/2004 P11 Normal Force and Third law pairs. SWBAT:
  • Identify third law pairs.
  • Calculate the normal force in many situations, especially those for which the normal force is not equal to the weight.

Week 6

Mon, 10/04/2004 C11 Exponential functions . SWBAT:
  • 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.
Tue, 10/05/2004 P12 Parts II/III of the foces tutorial SWBAT:
  • Draw free body diagrams.
  • Identify forces that act directly on the body.
Wed, 10/06/2004 C12 General inverse functions and the log function . SWBAT:
  • 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.
Thu, 10/07/2004 P13 Friction . SWBAT:
  • Identify statics and kinetic friction.
  • Identify the direction in which friction acts.
Fri, 10/08/2004 C13 Series, Power series, Taylor-MacLaurin series . SWBAT:
  • Recognize a power series.
  • Understand power series convergence.
  • Calculate Taylor polynimials for rational, log, end exp functions.
  • Linearize a function.
  • Estimate approximation errors.

Week 7

Mon, 10/11/2004 C14 More on Taylor series and applications . SWBAT:
  • Use the binomial theorem.
  • Calculate series expressions for basic trig functions.
  • Estimate approximation errors.
Tue, 10/12/2004 P14 Problem solving session, or possibly a day off .
Wed, 10/13/2004 C15 Riemann sums and integrals I . SWBAT:
  • Understand Riemann sums as the area under a curve.
  • Calculate Riemann sums for simple functions.
  • Recognize the definition of an integral.
Thu, 10/14/2004 P15 Moving in a circle at constant speed .
  • 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.
  • Fri, 10/15/2004 N02 Fall break, no classes

    Week 8

    Mon, 10/18/2004 C16 Newton's Method. SWBAT:
  • Apply Newton's method to find roots.
  • Estimate the approximation error.
  • Tue, 10/19/2004 P16 Terminal Velicity. SWBAT:
    • Measure drag force on a coffee filter.
    Wed, 10/20/2004 C17 Calculus review .
    Thu, 10/21/2004 P17 Physics review .
    Fri, 10/22/2004 J04 Second Exam .

    Week 9

    Mon, 10/25/2004 C18 Riemann sums, integrals, and the Fundamental Theorem of Calculus II . SWBAT:
  • Approximate integrals.
  • Understand integral through the limit process.
  • Understand the relationship between integration and differentiation.
  • Tue, 10/26/2004 P18 Balance point, center of mass .
    Wed, 10/27/2004 C19 Center of Mass. SWBAT:
  • 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.
  • Thu, 10/28/2004 P19 Conservation of momentum. SWBAT:
  • 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.
  • Fri, 10/29/2004 P20 Work and dot product. SWBAT:
    • 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 axba+ or ab-cos[theta].

    Week 10

    Mon, 11/01/2004 C19 Work integrals. SWBAT:
    • Recognize parametric curves.
    • Calculate the work due to a constant force on a parametric curve using ds = sqrt(dx2+dy2).
    • Show that the work due to gravity is always mgh regardless of the path taken.
    Tue, 11/02/2004 C20 (Election day) Constrained optimization I. SWBAT:
    • Minimize or maximize a function subject to a constraint.
    • Be able to "solve" constrained optimization "by eye"
    Wed, 11/03/2004 P21 Forces and work and Proof of work-energy theorem. SWBAT:
    • Explain the distinction between conservative and non-conservative forces.
    • Use calculus to prove the work-energy theorem
    Thu, 11/04/2004 P22 Conservation Laws - when do I use what method? SWBAT:
    • Recognize when work-energy theorem is appropriate to solve a problem
    • Recognize when Newton's second law is appropriate to solve a problem
    Fri, 11/05/2004 J05 Conservation Lab I (Momentum). SWBAT:
    • Recognize that momentum is conserved.
    • Verify that momentum is nearly conserved.

    Week 11

    Mon, 11/08/2004 C21 Constrained Optimization II.
    Tue, 11/09/2004 P23 Conservation Lab II (Energy).
    Wed, 11/10/2004 N02 No Class.
    Thu, 11/11/2004 N03 Veterans Day, no classes
    Fri, 11/12/2004 C22 Impuulse-Momentum Theorem.

    Week 12

    Mon, 11/15/2004 J06 Euler's method and air drag. SWBAT:
    • Numerically solve simple differential equations.
    • Solve the differential equation for air drag.
    • Recognize Euler's method as the numerical equivalent to slope fields.
    Tue, 11/16/2004 P24 Introduction to rotation SWBAT:
    • 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.
    Wed, 11/17/2004 C24 Calculus review.
    Thu, 11/18/2004 P25 Physics review.
    Fri, 11/19/2004 J10 Third Exam

    Week 13

    Mon, 11/22/2004 C25 Trigonometric functions and the unit circle SWBAT:
    • 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 2. order differential equation y'' = - ω ^2 y.
    • Relate radius vector, velocity vector, and acceleration vector in a circular motion.
    Tue, 11/23/2004 P26 Introduction to moment of inertia and torque
    Wed, 11/24/2004 C26 Derivatives and antiderivatives of trigonometric functions (all of them).
    Thu, 11/25/2004 N03 Thanksgiving, no classes
    Fri, 11/26/2004 N04 Thanksgiving, no classes

    Week 14

    Mon, 11/29/2004 C27 Working with vectors. SWBAT:
    • 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, 11/30/2004 P27
    Wed, 12/01/2004 C28 Inverse trigonometric functions, hyperbolic functions I. SWBAT:
    • Recognize the inverse trig and hyp functions.
    • Take the derivative of inverse trig/hyp funtions.
    • Recognize inverse trig functions as atiderivatives of some rational and trancentental functions.
    Thu, 12/02/2004 P28
    Fri, 12/03/2004 P29

    Week 15

    Mon, 12/06/2004 C29 Inverse trigonometric functions II. SWBAT:
    • Know what to do with them.
    • Recognize sinh/cosh as solution of differential equation.
    Tue, 12/07/2004 P30
    Wed, 12/08/2004 C30 Calculus review.
    Thu, 12/09/2004 P31
    Fri, 12/10/2004 J11 (Last day of classes)

    Week 16

    Mon, 12/13/2004 N05 Reading day
    Tue, 12/14/2004 N06 Calculus final, 8-10am, Kingsbury 317.
    Wed, 12/15/2004 N07 Finals
    Thu, 12/16/2004 N08 Finals
    Fri, 12/17/2004 N09 Saturday, 12/18, 1-3pm, Physics final in Kingsbury 135.

    last update: Thu Jul 7 18:40:23 EDT 2005