MATH 426H / PHYS 408H Studio Calculus/Physics II

Spring 2010

Daily Schedule

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, 01/25/2010 N01
Tue, 01/26/2010 P01 (Classes begin) Review of Equilibrium and Elasticity
  • Define different types of equilibria.
  • Identify forces and torques that balance.
  • Understand that hinges, pins, etc. can provide forces in all direction, but pedestals on push up/down.
  • Solve standard 1D and 2D problems.
  • Define stress and strain.
Reading: Knight 2e Ch. 6.1, 12.8, and 15.6
Wed, 01/27/2010 C01 Complex Numbers I
  • Feel comfortable with the notation.
  • Add, subtract, multiply and divide complex numbers.
  • Represent complex numbers on the plane and think of complex numbers as vectors.
  • Take a complex conjugate.
  • Use "i" to stand for the square root of negative one.
Reading: Fundamentals of Complex Analysis - handout
Thu, 01/28/2010 P02 Introduction to Oscillations
  • Pick off amplitude, period, phase, frequency given x(t).
  • Recall relations between period, frequency, and angular frequency.
  • Understand qualitatively the effect of the mass and the spring constant on the motion.
Reading: Knight 2e Ch. 14.1 - 14.3
Activity: Newton - "Description of Harmonic Motion of Spring" and "Investigating Parameters of Motion of Spring"
Fri, 01/29/2010 C02 Complex Numbers II
  • Express complex numbers in terms of angle and magnitude.
  • Use a Taylor series to derive the Euler formula that links exponentials to sines and cosines.
  • Begin to do operations on complex numbers that are in exponential form.
Reading: Fundamentals of Complex Analysis - handout

Week 2

Mon, 02/01/2010 C03 Complex Numbers III
  • Take roots of complex numbers.
  • Begin to be able to solve linear differential equations with constant coefficients using the guess x = R exp(nt). This is used in the next physics class and an upcoming joint class.
Reading: Fundamentals of Complex Analysis - handout
Tue, 02/02/2010 P03 Dynamics of Oscillations
  • Find the differential equation knowing the forces.
  • Solve the differential equation using x = R exp(nt) which was introduced in Calculus.
  • Go back and forth between exponential and trigonometric functions.
  • See the role of initial conditions in the solution.
Reading: Knight 2e Ch. 14.4 - 14.6
Activity: Newton - "Forces for Object on a Spring" and "Physical Pendulum"
Wed, 02/03/2010 C04 Differential Equation and Taylor Series

Students see the differential equation for simple harmonic motion solved using Taylor series. Also students see that the solution does not always converge.

Reading: Hass Ch. 8.8
Thu, 02/04/2010 P04 Introduction to Waves
  • Distinguish between different types of waves.
  • Distinguish between wave and particle motion.
Reading: Knight 2e Ch. 20.1 - 20.3
Activity: Newton - "Wave Velocity/Particle Velocity"
Fri, 02/05/2010 C05 Differential Equation and Taylor Series

Students see the differential equation for simple harmonic motion solved using Taylor series. Also students see that the solution does not always converge.

Reading: Hass Ch. 8.8

Week 3

Mon, 02/08/2010 C06 Trigonometric Integrals
  • Integrate products of two sine or cosine functions as is needed for the calculation of Fourier coefficients.
Reading: Hass Ch. 7.2
Tue, 02/09/2010 P05 Mathematical Description of Waves
  • Translate between words, plots and/or equations description of waves.
Reading: Knight 2e Ch. 20.3 - 20.5 (20.6 - 20.7 recommended for Physics majors)
Activity: Newton - "Understanding the Sign in the Phase", HRW7 Problems 16: 19 and 79
Wed, 02/10/2010 C07 Introduction to Series and Sequences

Students are introduced to sequences of numbers and the question of convergence. They look at a few sequences and try to determine convergence.

Reading: Hass Ch. 8.1 and 8.2
Thu, 02/11/2010 P06 Kinetic Theory of Gases
  • Make a connection between temperature and average kinetic energy.
Reading: Knight 2e Ch. 16 and 18.1 - 18.3
Activity: Newton - "What is Temperature?"
Fri, 02/12/2010 J01 Fourier Series & Superposition of Waves

Students will be introduced to the idea of Fourier series and get a bit of experience in calculating Fourier coefficients. This will be followed up with integration of trigonometrical functions in the next calculus class.

Reading: Knight 2e Ch. 21.1 - 21.6 (21.7 - 21.8 recommended for Physics majors)
Activity: Newton - "Fourier Series"

Week 4

Mon, 02/15/2010 C08 Geometric Series
  • Recognize geometric series.
  • Be able to determine if a geometric series converges or diverges.
Reading: Hass 8.2
Tue, 02/16/2010 P07 Specific Heat and Heat Transfer
Students get another chance to look at conservation of energy through the lens of heat transfer and phase change.

Reading: Knight 2e Ch. 17
For a more fundamental description of specific heat and statistical physics consult Ch. 18.4 - 18.6.
Activity: HRW7 Problems 18.31 and 40, and Sample Problem 18-5
Wed, 02/17/2010 C09 Integral Test and u-Substitution
  • Use the integral test to show convergence or divergence.
  • Understand the value of u-substitution in integration.
Reading: Hass 5.5, 5.6, and 8.3
Thu, 02/18/2010 P08 Introduction to Electrostatics
  • Define "same charges".
  • Explain and give evidence for the principle of superposition.
  • Understand induced charge and its effects.
  • Solve a three body equilibrium problem.
Reading: Knight 2e Ch. 26
Activity: Tutorial - "Charge" I, II, and III
Fri, 02/19/2010 J02 Problem Solving: Damped Simple Harmonic Motion (SMH)

Students try to find the smallest value of magnetic damping that meets certain design specifications. This is a chance to solve a slightly more difficult differential equation.
Knowledge of the details of magnetic damping are not needed.

Reading: Knight 2e Ch. 14.7 and 14.8
Activity: Newton - "Damped Harmonic Motion"

Week 5

Mon, 02/22/2010 C10 Direct and Limit Comparison Test
  • Use these two tests to check for series convergence.
Reading: Hass 8.4
Tue, 02/23/2010 P09 Physics Review - Oscillations & Waves & Thermodynamics
Wed, 02/24/2010 C11 Calculus Review
Complex Numbers, Differential Equations and Taylor Series, Trigonometric Integrals, Sequences and Series.
Thu, 02/25/2010 P10 Coulomb Force and Gravitational Force
  • Apply Newton's laws to situations that include Coulomb and/or Gravitational Forces.
  • Students know how to find the net force on a charged particle/planet using vector addition.
Reading: Knight 2e Ch. 13
Activity: Tutorial - "Charge" IV
Activity: Newton - "Electrostatic Equilibrium" and "Net Electrostatic Force"
Fri, 02/26/2010 J03 First Exam - Storm Day
Part 1 - Calculus: Thursday 12:40pm - 2:00pm in Kingsbury S145
Part 2 - Physics: Tuesday 12:40pm - 2:00pm in DeMeritt 301 & 311
Both Problem: Wednesday 10:35am - 11:00am in DeMeritt 301 & 311

Week 6

Mon, 03/01/2010 C12 u-Substitution and Change of Variables
  • Use this technique to integrate.
Reading: Hass 5.6
Tue, 03/02/2010 P11 Introduction to E field

This conceptual introduction to flux should be done before the mathematical calculations of flux.
  • Define the electric field.
  • Interpret electric field lines.
  • Point out incorrectly drawn field lines.
  • Estimate flux through a surface.
Reading: Knight 2e Ch. 27.1 - 27.3 and Ch. 28.1 - 28.3
Activity: Newton - "Electric Field"
Activity: Tutorial - "Electric Field and Flux" I and III
Wed, 03/03/2010 C13 Trigomometric Substitution & 1st Exam Both Problem
  • Use this technique to integrate.
Reading: Hass 7.3
Thu, 03/04/2010 J04 Electric Field due to a Bar of Charge
Hand in one write-up per group.
  • Use superposition and knowledge of Reimann sums and integrals to calculate the E field due to a uniform charge distribution.
Reading: Knight 2e Ch. 27.3 - 27.4
Activity: Newton - "E field due to bar of charge"
Fri, 03/05/2010 J05 Comet Problem - Part I

Students get a chance to put together gravitational force and work-kinetic energy theorem to solve a problem.

Reading: Knight 2e Ch. 13
Activity: Newton - "How fast in the Comet going?"

Week 7

Mon, 03/08/2010 C14 Flux through a Surface of Revolution
  • Calculate the flux through a surface of revolution due to a point charge.
Reading: "Flux through a Surface", Activity Book pages 137-145, Hass 6.1
Tue, 03/09/2010 C15 Flux through a Plane due to a Point Charge
  • Calculate the electric flux through an infinite plane.
  • Calculate the electric field through an infinite uniform plane of charge.
Reading: "Flux through a Surface", Activity Book pages 137-145
Wed, 03/10/2010 P12 Gauß' Law I
  • Estimate flux through a surface using Gauss' law.
  • See why Gauß' law still holds even if the charge is outside the surface.
Reading: Knight 2e Ch. 27.7 and Ch. 28.4
Activity: Newton - "Electric Dipole"
Activity: Tutorial - "Gauß' Law" I and II
Thu, 03/11/2010 P13 Gauß' Law II
  • Explain why symmetry plus Gauß' law can help us calculate E in a few special cases.
  • Understand why it is useful in ONLY these three cases for finding E.
Reading: Knight 2e Ch. 27.5 and 28.5 - 28.6
Activity: Newton - "Gauß' Law and Symmetry" and "E field calculations using Gauß' Law"
Fri, 03/12/2010 J06 (Mid-semester) Motion in an Electric Field and Comet Problem - Part II

Students will get a chance to see again that the motion is not necessarily in the direction of the force, and see how to solve a differential equation numerically and check the answers for reasonableness.

Reading: Knight 2e Ch. 27.6
Activity: Newton - "Motion in an Electric Field (17)" and "When will the Comet hit?"

Week 8

Mon, 03/15/2010 N02 Spring Break
Tue, 03/16/2010 N03 Spring Break
Wed, 03/17/2010 N04 Spring Break
Thu, 03/18/2010 N05 Spring Break
Fri, 03/19/2010 N06 Spring Break

Week 9

Mon, 03/22/2010 C16 Partial Fractions
  • Decompose a ratio into a partial fraction.
  • Use partial fractions to integrate.
Reading: Hass 7.4
Tue, 03/23/2010 P14 Electric Potential I
  • Calculate the electric potential for groups of point charges, simple charge distributions and symmetric charge distributions.
Reading: Knight 2e Ch. 29.1 - 29.4 and Ch. 29.6 and Ch. 30.1 - Ch. 30.2
Activity: Newton - "Motion in an Electric Field (23)", "Motion in a Gravitational Field", "Calculating V due to Point Charges", and "Calculating V due to Charge Distributions"
Wed, 03/24/2010 C17 Integration by Parts I
  • Use integration be parts to calculate center of mass.
  • Use integration be parts to find Fourier coefficients.
Reading: Hass 7.1
Thu, 03/25/2010 P15 Electric Potential II
  • Interpret equipotential curves.
  • Calculate V for an infinite cylinder.
  • Verify V between two concentric hoops.
Reading: Knight 2e Ch. 29.5 and 29.7 and Ch. 30.3 - 30.4.
Activity: Newton - "Visualizing the Potential" and "Electric Potential for a Cylinder"
Fri, 03/26/2010 P16 Capacitance I
  • Understand the role of a capacitor in a circuit.
  • Explain why capacitance depends only on geometry and not on charge or voltage.
Reading: Knight 2e Ch. 30.4 - Ch. 30.5 (review Ch. 27.5. and Ch. 29.5)
Activity: Newton - "Infinite Sheets of Charge" and Tutorial "Capacitance" II

Week 10

Mon, 03/29/2010 C16 Integration by Parts II
  • Practice with integration by parts.
  • Use it twice to solve an integral.
Reading: Hass 7.1
Tue, 03/30/2010 P17 Physics Review - Electrostatics
Wed, 03/31/2010 C17 Calculus Review
Thu, 04/01/2010 P18 Capacitance II
  • Recognize capacitors in series and in parallel, even if the circuit is drawn in a messy way.
  • Find the equivalent capacitance for a complicated circuit.
  • Understand the role of a dielectric material in a capacitor.
Reading: Knight 2e Ch. 30.5 - 30.7
Activity: Newton - "Untangling circuits", "Capacitors w/ dialectric", and problems on Equivalent Capacitance
Fri, 04/02/2010 J09 Second Exam
Part 1 - Physics: Thursday 12:40pm - 2:00pm in DeMeritt 112
Part 2 - Calculus (w/ both problem): Friday 9:10am - 11:00am in DeMeritt 301 & 311

Week 11

Mon, 04/05/2010 C18 Root and Ratio Test
  • Prove convergence or divergence of a series using root, ratio, and previously discussed convergence tests.
Reading: Hass 8.5
Tue, 04/06/2010 P19 Introduction to Resistors and Kirchhoff's Laws
  • Understand the basics of resistors in series and parallel.
  • Understand that current is not used up.
  • Understand that Kirchhoff's laws are really conservation of energy and charge.
Reading: Knight 2e Ch. 31 and Ch. 32.1.
Activity: Tutorial "A model for circuits Part 1: Current and resistance"
Wed, 04/07/2010 C19 Power Series and Alternating Series
  • Be able to check the interval of convergence of a power series, including checking the endpoints.
Reading: Hass 8.6 and 8.7
Thu, 04/08/2010 P20 Resistors and Kirchhoff's Laws II
  • Conceptually use the loop rule to predict circuit behavior.
  • Find the equivalent resistance.
Reading: Knight 2e Ch. 32.2 - 32.5
Activity: Newton - "Amperemeters and Voltmeters", Tutorial "A model for circuits Part 2: Potential difference", and problems on Equivalent Resistance
Fri, 04/09/2010 J10 Neon Lights

Students use their understanding of energy and the electric potential to understand energy transitions in a neon atom.

Activity: Newton - "Neon Lights"

Week 12

Mon, 04/12/2010 C20 Differential Equation for RC Circuits I
  • Write down the differential equation for a multi loop RC circuit.
Find qualitative solutions only for such systems of equations.
Reading: Hass 15.2 (on Blackboard under Course Documents)
Tue, 04/13/2010 P21 Kirchhoff's Laws III
  • Analyze a moderately complicated circuit (two to three loops) using Kirchhoff's laws.
Reading: Knight 2e Ch. 32.6 - 32.8
Activity: Newton - Standard book problems on Kirchhoff's laws
Wed, 04/14/2010 C21 Differential Equation for RC Circuits II
  • Write down the differential equation for a single loop RC circuit.
Solve the inhomogeneous differential equation using integrating factors.
Reading: Hass 15.2 (on Blackboard under Course Documents)
Thu, 04/15/2010 J11 Charging and Discharging RC Circuits I
  • Understand an RC circuit conceptually and mathematically.
Reading: Knight 2e Ch. 32.9
Activity: Newton - "Discharging an RC circuit" and "Charging an RC circuit"
Fri, 04/16/2010 P22 Charging and Discharging RC Circuits II
  • Understand an RC circuit experimentally.
Reading: Knight 2e Ch. 32.9
Activity: Hand-out "Kirchhoff's Law and RC circuits" (revised Newton - "Designing an RC circuit")

Week 13

Mon, 04/19/2010 C22 Polar Coordinates I
  • Convert a function from carthesian to polar coordinates.
  • Plot a function in polar coordinates.
Reading: Hass 9.1 and 9.2
Tue, 04/20/2010 P23 Physics Review - Circuits
Wed, 04/21/2010 C23 Polar Coordinates II
  • Calculate arc length and work in polar coordinates.
Reading: Hass 9.3
Thu, 04/22/2010 P24 Introduction to Magnetism
  • Draw distinctions between electrostatics and magnetism.
  • Sketch the lines of magnetic force.
  • See the effect of a magnet on the motion of a beam of electrons.
Reading: Knight 2e Ch. 33.1 - 33.2
Activity: Newton - "Investigating Magnets"
Fri, 04/23/2010 J12 Third Exam
Part 1 - Calculus: Thursday 12:40pm - 2:00pm in TBA
Part 2 - Physics (w/ both problem): Friday 9:10am - 11:00am in DeMeritt 301 & 311

Week 14

Mon, 04/26/2010 C24 Limits Redux I

Students revisit the idea of limits in a more rigorous way than before, using the electric potential due to a bar of charge as a specific example.

Reading: Hass 2.2 - 2.6
Tue, 04/27/2010 P25 Motion in a Magnetic Field
  • Explain why a charged particle will move in a circle in a constant B field.
  • Explain how we know from the Hall effect that the electrons carry current, and not the protons.
Reading: Knight 2e Ch. 33.7
Activity: Newton - "Motion in a constant B field"
Wed, 04/28/2010 C25 Limits Redux II

Students are introduced to the ε-δ definition of limits, using graphs as an aid to understanding. They see some pathological examples in dealing with limits.

Reading: Hass 2.2 - 2.6
Thu, 04/29/2010 P26 Current Loop as a Magnetic Dipole
  • See that current loops create magnetic fields similar to bar magnets.
  • See that current loops behave like bar magnets when placed near another magnet.
  • Understand that there are current loops inside all materials.
Reading: Knight 2e Ch. 33.3 - 33.5
Activity: Newton - Tutorial "Magnetic interactions"

Magnetic Fields and Current-carrying Wires
  • Calculate the torque on a current loop.
  • Calculate the B field due to a straight piece of wire or an arc of wire.
  • Calculate the force between two straight current-carrying wires.
Reading: Knight 2e Ch. 33.8 - 33.9
Activity: Newton - "Torque on a current loop" and "B field due to a wire"
Fri, 04/30/2010 J13 LRC Circuit

Students use their knowledge of circuits and differential equations to solve for the time evolution of an LC and an LRC circuit. At this point the inductor is a black box, since inductors are the last thing they learn about this year.

Reading: Knight 2e Ch. 34.8 - 34.10
Activity: Newton - "A new circuit element"

Week 15

Mon, 05/03/2010 C26 Michel Rolle and Joseph-Louis Lagrange - The Mean Value Theorem for Derivatives

Reading: Hass 4.6 and 8.1
Tue, 05/04/2010 P27 Ampere's Law and Faraday's Law
  • Use Ampere's law in situations of high symmetry to calculate the B field.
  • See that changing magnetic flux induces a current.
  • Calculate how much current is induced in a given situation.
Reading: Knight 2e Ch. 33.6 and Ch. 34.1 - 34.5
Activity: Newton - "Applying Ampere's law"
Wed, 05/05/2010 C27 John Bernoulli, Guillaume de l'Hospital, and Augustin-Louis Cauchy - l'Hospital's Rule

Students are introduced to the rule and practice using it determine the limit of a function h(t)/g(t) when both h and g go to zero.

--> Reading: Hass 4.6 and 8.1
Thu, 05/06/2010 P28 Lenz' Law & Maxwell's Equations
  • Predict the direction of induced current in a given situation.
  • Understand the role of inductors in a circuit.
Reading: Knight 2e Ch. 34.6 - 34.10 and Ch. 35.1 - 35.5
Activity: Newton - Tutorial "Lenz' law"
Fri, 05/07/2010 J15 Physics Review - Magnetism

Week 16

Mon, 05/10/2010 C28 (Last day of classes) Calculus Review
Tue, 05/11/2010 N07 Reading Day
Wed, 05/12/2010 N08 Reading Day
Thu, 05/13/2010 N09 Physics Final
13:00 - 15:00 in DeM 301 & 311
Fri, 05/14/2010 N10 Calculus Final
10:30 - 12:30 in TBA

Week 17

last update (KP): Tue May 4 15:02:05 EDT 2010
Mon, 05/17/2010 N11 Finals
Tue, 05/18/2010 N12 Finals
Wed, 05/19/2010 N13 Finals
Thu, 05/20/2010 N14 Finals