Math253 Calculus III | Mike Pierce

Within each section are links to notes, video lectures, practice exercises, problems, and past midterm exams. Chapters enumerated with § refer to Calculus 9E by Stewart.

Week One · August 19

Monday – Syllabus, Orientation, and Introduction

Tuesday – Three-Dimensional Space

§12.1 Three-Dimensional Coordinate Systems
Notes: The 3-D Coordinate System, Paul Dawkins

Exercises

Thursday – Lines and Surfaces

§12.5 Equations of Lines and Planes
§12.6 Cylinders and Quadric Surfaces
Notes: Equations of Lines, Paul Dawkins
Notes: Equations of Planes, Paul Dawkins
Notes: Quadric Surfaces, Paul Dawkins
Lecture: Lines and Planes in 3-D, Professor Leonard
Lecture: Cylinder and Surfaces in 3-D, Professor Leonard

Exercises

Wednesday – Cylindrical and Spherical Coordinates

Notes: Cylindrical Coordinates, Paul Dawkins
Notes: Spherical Coordinates, Paul Dawkins
Lecture: Using Cylindrical and Spherical Coordinates, Professor Leonard

Exercises

Week Two · August 26

Monday – Vectors

§12.2 Vectors
Lecture: An Introduction to Vectors, Professor Leonard
Lecture: Vectors in 3-D Coordinate System, Professor Leonard

Exercises

Tuesday – The Dot Product

§12.3 The Dot Product
Lecture: Using the Dot Product, Professor Leonard
Video: Dot products and duality, 3Blue1Brown
Notes: Understanding the Dot Product, Kalid Azad

Exercises

Wednesday – The Cross Product

§12.4 The Cross Product
Lecture: The Cross Product, Professor Leonard
Video: Cross products, 3Blue1Brown
Video: Cross products in the light of linear transformations, 3Blue1Brown
Notes: Understanding the Cross Product, Kalid Azad

Exercises

Thursday – Lines and Planes Defined by Vectors

§12.5 Equations of Lines and Planes
§12.6 Cylinders and Quadric Surfaces
Notes: Equations of Lines, Paul Dawkins
Notes: Equations of Planes, Paul Dawkins
Notes: Quadric Surfaces, Paul Dawkins
Lecture: Lines and Planes in 3-D, Professor Leonard
Lecture: Cylinder and Surfaces in 3-D, Professor Leonard

Exercises

Week Three · September 2

Monday – Force, Work, Torque, etc

The ends of §12.2 and §12.3 and §12.4
Notes: Force » Combining forces, Wikipedia
Notes: Work (physics), Wikipedia
Notes: Work (physics) » Mathematical calculation, Wikipedia
Notes: Power (physics), Wikipedia
Notes: Torque, Wikipedia
Notes: Moment (physics), Wikipedia
Notes: Chirality (physics), Wikipedia
Notes: Momentum, Wikipedia
Notes: Angular momentum, Wikipedia
Notes: TK, Wikipedia

Exercises

Tuesday – Calculus with Vector-Valued Functions

§13.1 Vector Functions and Space Curves
§13.2 Derivatives and Integrals of Vector Functions
Notes: Vector Functions, Paul Dawkins
Notes: Calculus with Vector Functions, Paul Dawkins
Lecture: An Introduction to Vector Functions, Professor Leonard
Lecture: Derivatives and Integrals of Vector Functions, Professor Leonard

Wednesday – Arclength and Curvature

§13.3 Arc Length and Curvature
Notes: Arc Length with Vector Functions, Paul Dawkins
Notes: Curvature, Paul Dawkins
Lecture: Arc Length/Parameterization, TNB Intro, Professor Leonard
Lecture: TNB Frames, Curvature, Torsion, Encapsulation, Professor Leonard

Exercises

Thursday – The Frenet–Serret Frame

§13.3 Arc Length and Curvature
Notes: Tangent, Normal, and Binormal Vectors, Paul Dawkins
Lecture: Arc Length/Parameterization, TNB Intro, Professor Leonard
Lecture: TNB Frames, Curvature, Torsion, Encapsulation, Professor Leonard

Exercises

Week Four · September 9

Monday – Velocity and Acceleration

§13.4 Motion in Space: Velocity and Acceleration
Notes: Velocity and Acceleration, Paul Dawkins
Lecture: Velocity and Acceleration of Vector Functions, Professor Leonard

Exercises

Tuesday – Kepler’s Laws of Planetary Motion

§13.4 Motion in Space: Velocity and Acceleration

Wednes/Thursday – First Midterm Exam

Past Midterm Exams

2024Fall

Week Five · September 16

Monday – Multivariable Functions

§14.1 Functions of Several Variables
Notes: Functions of Several Variables, Paul Dawkins
Lecture: Intro to Multivariable Functions, Professor Leonard

Exercises

Tuesday – Limits and Continuity

§14.2 Limits and Continuity
Notes: Limits, Paul Dawkins
Lecture: Limits and Continuity of Multivariable Functions, Professor Leonard

Exercises

Wednesday – Partial Derivatives and Tangent Planes

§14.3 Partial Derivatives
§14.4 Tangent Planes and Linear Approximations
Notes: Partial Derivatives, Paul Dawkins
Notes: Interpretations of Partial Derivatives, Paul Dawkins
Notes: Higher Order Partial Derivatives, Paul Dawkins
Notes: Differentials, Paul Dawkins
Lecture: Partial Derivatives, Professor Leonard
Lecture: Finding Differentials of Multivariable Functions, Professor Leonard

Thursday – The Chain Rule

§14.5 The Chain Rule
Notes: Chain Rule, Paul Dawkins
Lecture: The Chain Rule for Multivariable Functions, Professor Leonard

Exercises

Week Six · September 23

Mon/Tuesday – Directional Derivatives and the Gradient Vector

§14.6 Directional Derivatives and the Gradient Vector
Notes: Directional Derivatives, Paul Dawkins
Notes: Tangent Planes and Linear Approximations, Paul Dawkins
Notes: Gradient Vector, Tangent Planes and Normal Lines, Paul Dawkins
Notes: Understanding Pythagorean Distance and the Gradient, Kalid Azad
Notes: Understanding the Gradient, Kalid Azad
Lecture: Finding Directional Derivatives and Gradients, Professor Leonard
Lecture: Finding Tangent Planes and Normal Lines to Surfaces, Professor Leonard

Exercises

Wednes/Thursday – Local and Global Extrema

§14.7 Maximum and Minimum Values
Notes: Relative Minimums and Maximums, Paul Dawkins
Notes: Absolute Extrema, Paul Dawkins
Lecture: Finding Extrema of Functions of 2 Variables, Professor Leonard

Exercises

Week Seven · September 30

Mon/Tuesday – Optimization with Lagrange Multipliers

§14.8 Lagrange Multipliers
Notes: Lagrange Multipliers, Paul Dawkins
Lecture: Constrained Optimization with LaGrange Multipliers, Professor Leonard

Exercises

Wednes/Thursday – Second Midterm Exam

Past Midterm Exams

2024Fall

Week Eight · October 7

Mon/Tuesday – Double Integrals in Rectangular Coordinates

§15.1 Double Integrals over Rectangles
§15.2 Double Integrals over General Regions
Notes: Double Integrals, Paul Dawkins
Notes: Iterated Integrals, Paul Dawkins
Notes: Double Integrals over General Regions, Paul Dawkins
Lecture: Introduction to Double Integrals, Professor Leonard
Lecture: How to Solve Double/Repeated/Iterated Integrals, Professor Leonard

Wednesday – Double Integrals in Polar Coordinates

§15.3 Double Integrals in Polar Coordinates
Notes: Double Integrals in Polar Coordinates, Paul Dawkins
Lecture: Double Integrals over Polar Regions, Professor Leonard

Exercises

Thursday – Applications of Double Integrals

§15.4 Applications of Double Integrals
§15.5 Surface Area
Notes: Surface Area, Paul Dawkins
Lecture: Center of Mass for Lamina in 2-D, Professor Leonard

Week Nine · October 14

Monday – Triple Integrals in Rectangular Coordinates

§15.6 Triple Integrals
Notes: Triple Integrals, Paul Dawkins
Lecture: How to Solve Triple Integrals, Professor Leonard

Exercises

Tuesday – The Jacobian, and Change of Coordinates

§15.9 Change of Variables in Multiple Integrals
Notes: Change of Variables, Paul Dawkins
Lecture: How to Change Variables in Multiple Integrals, Professor Leonard

Exercises

Wednes/Thursday – Triple Integrals in Cylindrical/Spherical Coordinates

§15.7 Triple Integrals in Cylindrical Coordinates
§15.8 Triple Integrals in Spherical Coordinates
Notes: Triple Integrals in Cylindrical Coordinates, Paul Dawkins
Notes: Triple Integrals in Spherical Coordinates, Paul Dawkins
Notes: Area and Volume Revisited, Paul Dawkins
Lecture: Triple Integrals […] with Cylindrical or Spherical Coord., Professor Leonard

Week Ten · October 21

Mon/Tuesday – Applications of Triple Integrals

TK: TK

Exercises

Wednes/Thursday – Third Midterm Exam

Past Midterm Exams

2024Fall

Week Eleven · October 28

Mon/Tuesday – Vector Fields

§16.1 Vector Fields
Notes: Vector Fields, Paul Dawkins
Notes: Understanding Circulation and Curl, Kalid Azad
Notes: Understanding Divergence, Kalid Azad
Lecture: Introduction to Vector Fields, Professor Leonard
Lecture: How to Find Divergence and Curl of Vector Fields, Professor Leonard
Video: Divergence and curl: The language of Maxwell's equations, fluid flow, and more, Grant Sanderson

Exercises

Wednes/Thursday – Line Integrals

§16.2 Line Integrals
§16.3 The Fundamental Theorem of Line Integrals
Notes: Line Integrals - Part I, Paul Dawkins
Notes: Line Integrals - Part II, Paul Dawkins
Notes: Line Integrals over Vector Fields, Paul Dawkins
Notes: Fundamental Theorem for Line Integrals, Paul Dawkins
Lecture: How to Compute Line Integrals, Professor Leonard
Lecture: Line Integrals on Conservative Vector Fields, Professor Leonard

Week Twelve · November 4

Mon/Tuesday – Green’s Theorem

§16.4 Green’s Theorem
Notes: Conservative Vector Fields, Paul Dawkins
Notes: Green’s Theorem, Paul Dawkins
Lecture: Green’s Theorem, Professor Leonard

Exercises

Wednesday – Curl and Divergence

§16.5 Curl and Divergence
Notes: Curl and Divergence, Paul Dawkins

Exercises

Week Thirteen · November 11

Monday – Surface Area

§16.6 Parametric Surfaces and Their Areas
Notes: Parametric Surfaces, Paul Dawkins

Exercises

Tuesday – Surface Integrals

§16.7 Surface Integrals
Notes: Surface Integrals, Paul Dawkins
Notes: Surface Integrals over Vector Fields, Paul Dawkins
Notes: Understanding Flux, Kalid Azad
Lecture: Surface And Flux Integrals, […], Divergence/Stoke's Theorem, Professor Leonard

Exercises

Wednes/Thursday – Stoke’s Theorem

§16.8 Stoke’s Theorem
Notes: Stokes’ Theorem, Paul Dawkins

Exercises

Week Fourteen · November 18

Mon/Tuesday – The Divergence Theorem

§16.9 The Divergence Theorem
Notes: Divergence Theorem, Paul Dawkins

Exercises

Wednes/Thursday – Fourth Midterm Exam

Past Midterm Exams

2024Fall

Week Fifteen · November 25

Thanksgiving Break, No Class

Week Sixteen · December 2

Revision Week, No Lecture

Final Exam

Wednesday Dec 11 @ 10am