General Course Information and Documents...

High-School Course Syllabus and Detailed Course Topics Description:
 Honors CalcIII/DiffEq HS Course Syllabus
 Honors CalcIII/DiffEq Detailed Course Topics Description

If you take this course for Rio Salado credit, you are also subject to the Rio Salado syllabus rules:
 Rio Salado Course Syllabus - MAT241
 Rio Salado Course Syllabus - MAT277

Week 36 Schedule: April 29 - May 5...

Date		Daily lesson materials		Homework
M 4/29		Ch8 Review   Ch8 Blank Notes   Ch8 Filled-In Notes		Use the Test Review problems...   Ch8 Required Practice Packet   Ch8 Required Practice Packet - ANSWERS   Ch8 Extra Practice Packet   Ch8 Extra Practice Packet- FULL SOLUTIONS   Ch8 formula sheet   Ch8 Test Review - SOLUTIONS
T 4/30		** Ch8 Test **
W 4/31		Introduction to MATLAB/OCTAVE   OCTAVE Classwork Packet   OCTAVE follow-on Mayfair Packet (required, not extra credit) You'll need these functions to copy...   testfunction.m   testscript.m		Bring your laptop every day until we are done with OCTAVE :)
Th 5/1		OCTAVE work time
F 5/2		OCTAVE work time

Calculus III/DiffEq announcements...

Semester 2 Final Exam...

•   DiffEq Practice Final
•   DiffEq Practice Final - SOLUTIONS
•   Final Exam Formulas

DiffEq - MATLAB/OCTAVE...

•   OCTAVE Classwork Packet
•   OCTAVE Extra Credit problem: Murder at the Mayfair Diner
• Lesson Videos:
  •   OCTAVE day 1 Lesson video
  •   OCTAVE day 2 Lesson video
  •   OCTAVE day 3 (and 4) Lesson video

DiffEq - Ch8: Systems of Differential Equations...

•   Ch8 Blank Notes
•   Ch8 Filled-In Notes
•   Ch8 Required Practice Packet
•   Ch8 Required Practice Packet - ANSWERS
•   Ch8 Extra Practice Packet
•   Ch8 Extra Practice Packet- FULL SOLUTIONS
•   Ch8 Formula Sheet
• Lesson Videos:
  •   8.1: Intro to Systems of Differential Equations
  •   8.2 day 1: Eigenvalues, Eigenvectors, solving a DE system
  •   8.2 day 2: Repeated Eigenvalues
  •   8.2 day 3: Complex Eigenvalues
  •   8.2 day 3 Derivations
  •   8.2 day 4: Phase Portraits
  •   8.3 day 1: Solving Non-Homogeneous DE systems: Method of Undetermined Coefficients
  •   8.3 day 2: Solving Non-Homogeneous DE systems: Method of Variation of Parameters
  •   8.3 day 3: Solving Non-Homogeneous DE Systems with Initial Conditions
  •   8.3 day 4: Higher-Order Single DEs as Systems

DiffEq - Ch7: Laplace Transforms...

•   Ch7 Blank Notes
•   Ch7 Filled-In Notes
•   Ch7 Required Practice Packet
•   Ch7 Required Practice Packet - ANSWERS
•   Ch7 Extra Practice Packet
•   Ch7 Extra Practice Packet- FULL SOLUTIONS
•   Ch7 formula sheet
• Lesson Videos:
  •   7.1: Laplace Transforms (by definition and table)
  •   7.1 (extra): extra info about Laplace Transforms in general
  •   7.2 day 1: Finding Inverse Laplace Transforms
  •   7.2 day 2: Laplace Transforms of Derivatives, Solving DEs using Laplace Transforms
  •   7.3 day 1: Laplace Transform Properties: Translation in s
  •   7.3 day 2: The Unit Step Function
  •   7.3 day 3: Laplace Transform Properties: Translation in t
  •   7.4: Derivative of a Transform
  •   7.5: The Dirac Delta Function (Impulse response)
  •   7.5 Derivations

DiffEq - Ch5: Modeling using Higher-Order Differential Equations

•   Ch5 Blank Notes
• (no filled in notes - all problems are worked in the 'blank' notes)
•   Ch5 Required Practice Packet
•   Ch5 Required Practice Packet - ANSWERS
•   Ch5 Extra Practice Packet
•   Ch5 Extra Practice Packet - SOLUTIONS
•   Ch5 Formula Sheet
• Lesson Videos:
  •   5.1 Lesson video

DiffEq - Ch4: Methods of Solving Higher-Order Differential Equations

•   Ch4 Blank Notes
•   Ch4 Filled-In Notes
•   Ch4 Required Practice Packet
•   Ch4 Required Practice Packet - ANSWERS
•   Ch4 Extra Practice Packet
•   Ch4 Extra Practice Packet - SOLUTIONS
•   Ch4 Formula Sheet
• Lesson Videos:
  •   4.1: Intro to Higher Order DEs, use of the Wronskian to show solutions are linearly independent
  •   4.2: Reduction of Order (finding a 2nd solution from a given 1st solution)
  •   4.3: Use auxiliary equation roots to solve linear DEs with constant coefficients
  •   Derivations for 4.3
  •   4.4: Solving non-homogeneous DEs using Undetermined Coefficients
  • (4.5 is skipped)
  •   4.6: Solving non-homogeneous DEs using Variation of Parameters
  •   Derivations for 4.6
  •   4.7: Solving Cauchy-Euler form DEs
  •   Derivations for 4.7

DiffEq - Ch3: Modeling using First-Order Differential Equations

•   Ch3 Blank Notes
• (no filled in notes - all problems are worked in the 'blank' notes)
•   Ch3 Formula Sheet
•   Ch3 Required Practice Packet
•   Ch3 Required Practice Packet - ANSWERS
•   Ch3 Extra Practice Packet
•   Ch3 Extra Practice Packet - SOLUTIONS
• Lesson Videos:
  •   3.1 Lesson video
  •   3.2 Lesson video

DiffEq - Ch1/Ch2: Intro/Methods of solving first-order DEs

•   Ch1/2 Blank Notes
•   Ch1/2 Filled-In Notes
•   Ch1-2 Required Practice Packet
•   Ch1-2 Required Practice Packet - ANSWERS
•   Ch1-2 Extra Practice Packet
•   Ch1-2 Extra Practice Packet - SOLUTIONS
•   Ch1-2 Test Formula Sheet
• Lesson Videos:
  •   1.1: Intro to Differential Equations, Terminology
  •   1.2: Initial Value Problems
  •   2.1: Slope fields, solution curves, 1D-phase portraits
  •   2.2: Separable Variables
  •   2.3: Linear equations - Integrating Factor Method
  •   Derivations - 2.3: linear equations
  •   2.4: Exact Equations
  •   Derivations - 2.4: exact equations
  •   2.5: Substitutions for Bernoulli and Composite forms
  •   2.6: Numerical Methods (Euler)

Calc3 - Semester 1 Final Exam

•   Calc 3 Final Exam Review
•   Calc 3 Final Exam Review - SOLUTIONS
•   Calc 3 Final Exam Formula Sheet

Calc3 - Ch16: Vector Calculus

•   Ch16 Blank Notes
•   Ch16 Filled-In Notes
•   Ch16 Required Practice Packet
•   Ch16 Required Practice Packet - ANSWERS
•   Ch16 Extra Practice Packet
•   Ch16 Extra Practice Packet- FULL SOLUTIONS
•   Ch16 Review Packet
•   Ch16 Review Packet - SOLUTIONS
•   Ch16 Test Formulas
•   Ti92 online emulator
• Lesson Videos:
  •   16.1: Vector Fields
  •   16.2 part 1: Line Integrals (for Scalar and Vector integrands)
  •   16.2 part 2: Line Integrals (parametrizing with respect to x,y,z instead of t), intuitively interpretation of work
  •   16.3: Conservative Vector Fields, The Fundamental Theorem of Line Integrals
  •   16.4: Green's Theorem, Circulation
  •   16.5: Curl and Divergence
  •   16.6 part 1: Parametric Surfaces and their areas, Tangent Planes
  •   16.6 part 2: Parametric Surfaces and their areas, Tangent Planes
  •   16.7: Surface Integrals of Scalar Functions
  •   Using the Ti-92 online calculator emulator
  •   16.8: Stokes' Theorem
  •   16.9: The Divergence (Gauss') Theorem

Ch15: Multiple Integrals...

•   Ch15 Blank Notes
•   Ch15 Part 1 Required Practice Packet
•   Ch15 Part 1 Required Practice Packet - ANSWERS
•   Ch15 Part 1 Extra Practice Packet
•   Ch15 Part 1 Extra Practice Packet- FULL SOLUTIONS
•   Ch15 Part 2 Required Practice Packet
•   Ch15 Part 2 Required Practice Packet - ANSWERS
•   Ch15 Part 2 Extra Practice Packet
•   Ch15 Part 2 Extra Practice Packet- FULL SOLUTIONS
• Lesson Videos:
  •   15.1-15.2: 2D Riemann Sums, Double Integrals over Rectangular Domain Regions, Iterated Integrals (Fubini's Theorem)
  •   15.3: Double Integrals over General Domain Regions
  •   15.4: Double Integrals in Polar Coordinates
  •   15.5: Applications of Double Integrals (density/mass, moments/center-of-mass, moment of inertia, probability density functions - expected value, variance, skewness, kurtosis)
  •   15.6 Part 1: Triple Integrals
  •   15.6 Part 2: Triple Integrals (additional examples)
  •   15.7: Triple Integrals in Cylindrical Coordinates
  •   15.8: Triple Integrals in Spherical Coordinates

Ch14: Multivariable Functions...

•   Ch14 Blank Notes
•   Ch14 Filled-In Notes
•   Ch14 Part 1 Required Practice Packet
•   Ch14 Part 1 Required Practice Packet - ANSWERS
•   Ch14 Part 1 Extra Practice Packet
•   Ch14 Part 1 Extra Practice Packet- FULL SOLUTIONS
•   Ch14 Part 2 Required Practice Packet
•   Ch14 Part 2 Required Practice Packet - ANSWERS
•   Ch14 Part 2 Extra Practice Packet
•   Ch14 Part 2 Extra Practice Packet- FULL SOLUTIONS
• Lesson Videos:
  •   14.1: Multivariable Functions, Level Curves/Surfaces, Contour Maps
  •   14.2: Limits of Multivariable Functions
  •   14.3: Partial Derivatives
  •   14.4: Tangent Planes, Linear Approximations, Differentials
  •   14.5: The Chain Rule for Multivariable Functions
  •   14.6: Directional Derivatives, Gradient Vector
  •   14.7: Multivariable Function Optimization (Max/Min/Saddle Points using the Hessian Determinant, with and without domain constraints)
  •   14.8: Multivariable Function Optimization with constraints - Method of Lagrange Multipliers
  •  More About Why: Directional Derivative and Gradient Derivations
  •  More About Why: Derivation of the equations for computing an LSRL

Ch13: Vector Functions...

•   Ch13 Blank Notes
•   Ch13 Filled-In Notes
•   Ch13 Required Practice Packet
•   Ch13 Required Practice Packet - ANSWERS
•   Ch13 Extra Practice Packet
•   Ch13 Extra Practice Packet- FULL SOLUTIONS
•   Ch13 Test Formula Sheet
• Lesson Videos:
  •   13.1: Vector Functions, Space Curves, Parametrization of Lines/Line Segments and Circles/Ellipses, Limits of Vector Functions
  •   13.2: Derivatives and Integrals of Vector Functions, Tangent vectors
  •   13.3 part 1: Arc Length, Arc Length Functions, Parametrization with respect to arc length
  •   13.3 part 2: Curvature, Osculating Circles, Unit Tangent/Normal/Binormal Vectors and the TNB Frame
  •   13.4: Velocity and Acceleration

Ch12: Vectors and the Geometry of Space...

•   Ch12 Blank Notes
•   Ch12 Filled-In Notes
•   Ch12 Required Practice Packet
•   Ch12 Required Practice Packet - ANSWERS
•   Ch12 Extra Practice Packet
•   Ch12 Extra Practice Packet- FULL SOLUTIONS
•   Ch12 Test Review - FULL SOLUTIONS
•   Ch12 Test Formula Sheet
• Lesson Videos:
  •   12.1: 3D Coordinate System
  •   12.2 part 1: Vectors (definition, addition/subtraction, colinear vectors)
  •   12.2 part 2: Vectors (unit vectors, properties of vectors)
  •   12.2 part 3: Applications of Vectors (Forces, Work)
  •   12.3: Dot Product, Angle between vectors, Projections of one vector onto another, Work
  •   12.4: Cross Product, Triple Product, Area of parallelogram, Determine if vectors are parallel/perpendicular, Torque
  •   12.5 part 1: Equations of Lines in space
  •   12.5 part 2: Equations of Planes in space
  •   12.6: Cylinders and Quadric Surfaces

(Note: all information in the future is tentative and may change.)

•   Ch12 Calendar
•   Ch13 Calendar
•   Ch14 Calendar
•   Ch15 Calendar
•   Ch16 Calendar
•   Final Exam Calendar
•   DiffEq Ch1/Ch2 Calendar
•   DiffEq Ch3 Calendar
•   DiffEq Ch4 Calendar
•   DiffEq Ch5 Calendar
•   DiffEq Ch7 Calendar
•   DiffEq Ch8 Calendar
•   OCTAVE/Final Exams Calendar

Taking Honors Calculus III/Differential Equations for college credit

You can optionally choose to take this course for college credit by enrolling in the two 3-credit Rio Salado courses MAT240-Calculus with Analytic Geometry III and MAT276-Modern Differential Equations.

THE SHORT VERSION...

• Rio Salado registration occurs now, so if you want to take the course for Rio Salado Dual-Enrollment credit, you should start the process soon.
  
  In order to take this course for Rio Salado credit you must have college credit in Calc1/Calc2 (AP Calculus BC). There are two ways Rio Salado will accept to demonstrate that you have college credit in the prerequisite course:
  1. You took AP Calculus BC in a previous year for Rio Salado Dual-Enrollment credit (so that it appears on your Rio Salado transcript.
  2. You took AP Calculus BC in a previous year, did not take it for Rio Salado credit, but took the AP Calculus BC exam and scored a 4 or a 5. For this option, Desert Vista must send a record of your AP scores to Rio Salado for confirmation for you to complete enrollment in Calc III at Rio Salado.
  Use these section numbers when registering for Mr. Felling's Honors Calculus III/Differential Equation class:
     Fall semester: MAT241 Calculus w/Analytic Geometry III (4 credits), section 23311
     Spring semester: MAT277 Modern Differential Equations (3 credits), section 11019
  
  In past years, students have registered only for the Fall semester course now and we register later in the year for 2nd semester, but you may have the option to register for both semesters at the beginning of the year (new this year).

MORE DETAILS / IF YOU NEED HELP DECIDING WHAT TO DO...

•  Deciding whether to take this course for college credit
•  Rio Salado's Enrollment Flyer

What to do if you are struggling or behind due to absences...

Try not to miss class, and try to catch up to the class as quickly as possible. When you aren't caught up to the class, it makes it difficult to understand what is going on, so even though you're in class, you aren't getting the maximum benefit from attending. As soon as you realize you are behind, try to catch up as quickly as possible.

Things you can do at home to improve your understanding:

• Watch my lesson videos: During the COVID year, I recorded lesson videos for all topics. These are great for review if you need to hear something again or needed to miss a class.
• Read your textbook: Your textbook contains complete explanations with good, worked-out examples for all (or nearly all) topics in class.
• Look at the filled-in notes on this website: You can see the lecture notes and worked examples in the filled-in notes pdf document for the chapter.
• Do all homework to the best of your ability and check your answers whenever possible: Practice is not effective if it is done incorrectly.
• Ask your friends in class to explain ideas to you: Your friends are a great resource and can sometimes explain things more plainly than a teacher would explain.
• Find and watch internet videos on the topic: A general internet search on a topic will always lead to useful information. The video sites YouTube, and Khan Academy are particularly useful. You can learn a lot from watching a 15 minute video, especially when you pause/rewatch sections until you understand.
• Tutoring: There are many options for various levels of math tutoring...
  • Free math teacher tutoring: You can get tutoring from me online during my tutoring office hours. No appointment is necessary, just login to the class chat at the scheduled time. If you are unable to get online during my tutoring hours, please email me and we can try to make other arrangements.
  • Professional tutoring: If you are feeling extremely far behind and/or other tutoring options will not work for you, we maintain a list of professional tutors who can work with you at home (or the library, Starbucks, etc.) This option is very effective, but is expensive (typically $25-$65 per hour). Email me if you want a list of professional tutors you can contact.

Most important: If you are not understanding, don't wait to get help. Find a way to improve your understanding as soon as possible by using the above ideas.