Brooks Emerick

matH 283 — Calculus III

Fall 2025 — Section 010

Course Materials:

• Schedule (updated Aug 24)

• Syllabus (updated Aug 24)

Hawkes Learning:

• Purchase Access/Login

• Training Videos

• Hawkes Learning Support

lecture notes:

• Chapter 11 — Vectors and the Geometry of Space

• Chapter 12 — Vector Functions

• Chapter 13 — Partial Derivatives

• Chapter 14 — Integration

• Chapter 15 — Vector Calculus

• Summary of Integration (ongoing updates)

Videos and Desmos:

• Using GeniusScan to Upload Homework to D2L

• Distance Between Two Spheres

• Graphing Surfaces with Cross-Sections — Paraboloid

• Graphing Surfaces with Cross-Sections — Hyperbolic Paraboloid

• Lines in Three-Dimensional Space

• Skew Lines

• Planes in Three-Dimensional Space

• Intersection of Two Planes

• Quadric Surfaces

• Vector-Valued Functions

• Tangent Line to Vector Functions

• Two Variable Functions

• Contour Maps

• Limits of Two Variable Functions

• Partial Derivatives and Tangent Lines

• Directional Derivatives and Gradients

• Tangent Lines and Tangent Planes

• Gradients and Tangent Planes

• Double Integrals as Riemann Sums

• Double Integrals over General Regions

• Average Value

• Triple Integral Solid

• Two-Dimensional Vector Fields

• Three-Dimensional Vector Fields

• Gradient Vector Fields

Worksheets:

• S.11.1: Three-Dimensional Cartesian Space (Solutions)

• S.11.2: Vectors (Solutions)

• S.11.3: The Dot Product (Solutions)

• S.11.4: The Cross Product (Solutions)

• S.11.5.P1: Lines (Solutions)

• S.11.5.P2: Planes (Solutions)

• S.11.6: Cylinders and Quadric Surfaces (Solutions)

• S.12.1: Vector-Valued Functions (Solutions)

• S.12.2: Arc-Length and the Unit Tangent Vector (Solutions)

• S.13.1: Two Variable Functions (Solutions)

• S.13.2.P1: Limits of Multivariable Functions (Solutions)

• S.13.2.P2: Limits and Continuity (Solutions)

• S.13.3.P1: Partial Derivatives (Solutions)

• S.13.3.P2: Implicit Differentiation and Tangent Lines (Solutions)

• S.3.4: The Chain Rule (Solutions)

• S.13.5: Directional Derivatives and Gradient Vectors (Solutions)

• S.13.6: Tangent Planes (Solutions)

• S.13.7: Extreme Values (Solutions)

• S.14.1.P1: Double Integrals over Rectangular Regions (Solutions)

• S.14.1.P2: Double Integrals over General Regions (Solutions)

• S.14.2: Applications of Double Integrals (Solutions)

• S.14.3: Double Integrals in Polar Coordinates (Solutions)

• S.14.4.P1: Triple Integrals (Solutions)

• S.14.4.P2: Triple Integrals (Solutions)

• S.14.5.P1: Triple Integrals in Cylindrical Coordinates (Solutions)

• S.14.5.P2: Triple Integrals in Spherical Coordinates (Solutions)

• S.14.5.P3: Rectangular, Cylindrical, and Spherical Coordinates (Solutions)

• S.15.1: Vector Fields (Solutions)

• S.15.2.P1: Line Integrals of Scalar Functions (Solutions)

• S.15.2.P2: Line Integrals of Vector Fields (Solutions)

• S.15.3: Fundamental Theorem for Line Integrals (Solutions)

• S.15.4.P1: Curl and Divergence Operators (Solutions)

• S.15.4.P2: Green’s Theorem, Tangential Curl Form (Solutions)

• S.15.4.P3: Green’s Theorem, Normal Divergence Form (Solutions)

Problem Sets:

• Problem Set I (Solutions)

• Problem Set II (Solutions)

• Problem Set III (Solutions)

• Problem Set IV (Solutions)

• Problem Set V (Solutions)

• Problem Set VI (Solutions)

• Problem Set VII (Solutions)

• Problem Set VIII (Solutions)

Desmos Labs:

• Desmos Lab I — Vectors, Lines, Planes, and Quadrics (Solutions)

  • Part 1 — Three Points Make a Plane

  • Part 2 — Distance Between Two Lines

  • Part 3 — Quadric Surfaces

• Desmos Lab II — Vector-Valued Functions, Limits, and Tangents (Solutions)

  • Part 1 — Vector-Valued Functions

  • Part 2 — Domains and Limits of Two-Variable Functions

  • Part 3 — Tangent Lines and Tangent Plane

• Desmos Lab III — Optimization and Center of Mass (Solutions)

  • Part 1 — Optimization

  • Part 2 — Center of Mass

• Desmos Lab IV — Parametric Surface (Solutions)

  • Part 1 — Surface Area as a Surface Integral

Exams:

• Exam I (Solutions)

• Exam II (Solutions)

• Exam III (Solutions)