Universitat Politècnica de Catalunya · BarcelonaTech

Vector Calculus and Differential Equations (2500012) – Course 2025/26 PDF

Contents

Parametrised curves Arc length and reparametrisation Path integrals and line integrals Examples and exercises

Dedication

5h Large group + 5h Medium group + 15h Self Study
Total: 25h

Parametrized surfaces Surface area Integrals of scalar and vector fields Examples and exercises

Dedication

5h Large group + 5h Medium group + 15h Self Study
Total: 25h

Review of differential operators Physical interpretation Examples and exercises

Dedication

2h Large group + 2h Medium group + 6h Self Study
Total: 10h

Green's theorem Stokes' theorem Gauss' theorem Application: Faraday's law Application: mass conservation Examples and exercises

Dedication

4h Large group + 4h Medium group + 12h Self Study
Total: 20h

1D heat equation Boundary conditions Heat equation in multiple dimensions Derivation of the heat equation using integral theorems

Dedication

2h Large group + 2h Medium group + 6h Self Study
Total: 10h

Separation of variables Non-homogeneous case Examples and exercises

Dedication

5h Large group + 5h Medium group + 15h Self Study
Total: 25h

Derivation of the Laplace equation Separation of variables Examples and exercises

Dedication

2h Large group + 2h Medium group + 6h Self Study
Total: 10h

Derivation of the wave equation Method of characteristics Examples and exercises

Dedication

5h Large group + 5h Medium group + 15h Self Study
Total: 25h