Curriculum Syllabus & Outline
Markdown Syllabus# Advanced Calculus Outline
1. Multivariable Functions
2. Partial Derivatives & Gradients
3. Multiple Integrals
4. Vector Calculus
- Line & surface integrals
- Green's, Stokes', Divergence theorems
5. Sequences & Series of Functions
6. Fourier Series (intro)
7. PDEs (intro)
Educational Context & Standards
Advanced calculus for upper-level students: multivariable differentiation/integration, vector calculus theorems, and series of functions.
Cross-Curriculum Equivalents
Canada/BC: BC University Calculus Prep & Tutoring
CA-BC-TUT
Canada/ON: Ontario Collegiate Advanced Tutoring
CA-ON-TUT
US/National: AP & Collegiate Advanced Mathematics
US-ADV-MTH
Structured Lesson Modules (6 Lessons)
1
Partial Derivatives
f_x, f_y. Clairaut's theorem.
2
Gradient & Directional Derivative
∇f · u. Max rate of change.
3
Double/Triple Integrals
Fubini, change of variables, Jacobian.
4
Line Integrals
Work along curve. Conservative fields.
5
Surface Integrals
Flux through surface.
6
Green/Stokes/Divergence
Relate integrals over regions/boundaries.
Assessments & Check-for-Understanding
Q1
Gradient of f?
Answer
∇f = (f_x, f_y, f_z)
Q2
Directional derivative formula?
Answer
∇f·u
Q3
Green's theorem relates?
Answer
Line integral around boundary to double integral over region
Q4
Divergence theorem?
Answer
Flux through closed surface = triple integral of div F
Q5
Jacobian for polar?
Answer
r
Q6
Stokes' theorem?
Answer
Line integral around boundary = surface integral of curl