You may find that you want to look something up and revisit topics you've learned in this class. To make this easier for you, I've compiled all of the color lesson notes, plus the worked examples, into a single PDF file with a table of contents for you to take to college:
CalcIII/DiffEq Entire Course Notes
| Date | Daily lesson materials | Homework | ||
| W 7/22 | Welcome to Honors Calculus III/Differential Equations! Info about the course and about taking this course for college credit. | |||
| Th 7/23 | School wide activities | |||
| F 7/24 | An intro to 12.1 - working and sketching in 3D | |||
Welcome to Honors Calculus 3 / Differential Equations!
This course is my very favorite course to teach...it is a truly fascinating course!
First semester is Calculus III w/Analytic Geometry, a continuation of the main ideas we learned in AP Calculus BC, but in 3 and higher dimensions, and is the mathematics that is the foundation of really understanding fields as diverse as physics and economics.
Second semester is Modern Differential Equations where we will learn many additional techniques for solving differential equations besides Separation of Variables, learn about real-world applications of differential equations, and finish with a short MATLAB programming unit to explore things when they get too complicated to solve by hand.
I look forward to sharing this interesting area of mathematics with you!
You can optionally check a textbook out from the DV bookstore
All our practice work will be using practice packets (and not out of the textbook) and I will be teaching from my own notes, so having a physical textbook is not really required for this course.
However, this course textbook's explanations are particularly good and in some cases provide more detail than I include in our class lessons. If you are the kind of student who wants to see proofs of why certain formulas work, or to understand the underlying concepts really thoroughly (for example, if you are planning to major in mathematics you may wish to check out the textbook(s) from the bookstore. More about this during the first week of class.
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
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...
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 Review Supplement Ch12 Test Formula Sheet
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 SurfacesCh13: 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 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 AccelerationCh14: 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 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 LSRLCh15: 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 - FULL SOLUTIONS Ch15 Part 2 Extra Practice Packet Ch15 Part 2 Extra Practice Packet- FULL SOLUTIONS 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 CoordinatesCalc3 - 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 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') TheoremCalc3 - Semester 1 Final Exam
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 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)DiffEq - Ch3: Modeling using First-Order Differential Equations
Ch3 Blank Notes Ch3 Formula Sheet Ch3 Required Practice Packet Ch3 Required Practice Packet - ANSWERS Ch3 Required Practice Packet - FULL SOLUTIONS Ch3 Extra Practice Packet Ch3 Extra Practice Packet - SOLUTIONSDiffEq - 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 Required Practice Packet - FULL SOLUTIONS Ch4 Extra Practice Packet Ch4 Extra Practice Packet - SOLUTIONS Ch4 Formula Sheet 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 4.6: Solving non-homogeneous DEs using Variation of Parameters Derivations for 4.6 4.7: Solving Cauchy-Euler form DEs Derivations for 4.7DiffEq - Ch5: Modeling using Higher-Order Differential Equations
Ch5 Blank Notes Ch5 Required Practice Packet Ch5 Required Practice Packet - ANSWERS Ch5 Extra Practice Packet Ch5 Extra Practice Packet - SOLUTIONS Ch5 Formula SheetDiffEq - Ch7: Laplace Transforms...
Ch7 Blank Notes Ch7 Filled-In Notes Ch7 Required Practice Packet Ch7 Required Practice Packet - FULL SOLUTIONS Ch7 Extra Practice Packet Ch7 Extra Practice Packet- FULL SOLUTIONS Ch7 formula sheet 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 But what is the Fourier Transform? A visual introduction What does the Laplace Transform really tell us? A visual explanation (plus applications) Free Online Intro to MATLAB Programming Course
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 DerivationsDiffEq - Ch8: Systems of Differential Equations...
Ch8 Blank Notes Ch8 Filled-In Notes Ch8 Required Practice Packet Ch8 Required Practice Packet - FULL SOLUTIONS Ch8 Extra Practice Packet Ch8 Extra Practice Packet- FULL SOLUTIONS Ch8 Formula Sheet Ch8
Test Review - FULL SOLUTIONS 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 SystemsDiffEq - MATLAB/OCTAVE...
Semester 2 Final Exam...