Curriculum Syllabus & Outline
Markdown Syllabus# Calculus IV Outline
1. Advanced Vector Calculus
2. Fourier Series & Transforms
3. PDEs (heat, wave, Laplace)
4. Complex Analysis (intro)
5. Variational Calculus (intro)
Educational Context & Standards
Calculus IV tutoring: advanced topics for engineering/physics/math majors.
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 (5 Lessons)
1
Vector Calculus
Divergence, curl, potentials.
2
Fourier Series
Periodic functions, coefficients.
3
PDEs
Separation of variables.
4
Complex Analysis
Analytic functions, Cauchy-Riemann.
5
Variational
Euler-Lagrange equation.
Assessments & Check-for-Understanding
Q1
Fourier coefficient a0?
Answer
(1/L)ā« f(x) dx
Q2
Cauchy-Riemann: āu/āx = ?
Answer
āv/āy
Q3
Heat equation?
Answer
u_t = Ī± u_xx
Q4
Wave equation?
Answer
u_tt = cĀ² u_xx
Q5
Laplace equation?
Answer
āĀ²u = 0
Q6
Analytic function derivative?
Answer
Complex derivative exists