Mathematical Introduction for Physicists 2
Dr. Dan Maoz
Course for first-year students, given in the second semester, 3 hours
lecture + 1 hour recitation each week.
Syllabus
- Vector analysis
- Algebra of vectors, components, scalar and vector fields
- Scalar and vector products, triple product
- Derivatives of vectors, continuity and differentiability, partial derivatives
of vectors, differential geometry
- Gradient, divergence, and curl
- Integration of vectors: line, surface, and volume integrals
- Gauss' Theorem, Green's and Stokes' Theorems
- Curvilinear coordinates: unit vectors, gradient, divergence, and curl
- Differential equations
- First order equations
- Linear vs. non-linear first-order equations
- Solution of linear equations
- Separable equations
- Exact differentials and integration factors
- Substitutions and scale invariance
- Second-order equations
- Homogeneous linear equations and linear independence
- Reduction of order
- Constant coefficients
- Particular solutions to inhomogeneous equations
- Systems of linear equations
Textbooks
- M. R. Spiegel, Vector Analysis (Schaum's Outline)
- F. Ayres, Differential Equations (Schaum's Outline)
References
- G. B. Thomas, Calculus and Analytic Geometry (any edition)
- W. E. Boyce and R. C. DiPrima, Elementary Differential Equations
(any edition)
Exams