Physics 4031  Mathematical Physics I (Ubriaco)
 Number of Credits: 3
 Prerequisites: Mate 3152
 Marcelo R. Ubriaco

Office: C318 (ext 88424)
University of Puerto Rico  Rio Piedras Campus
Department of Physics
Text
 Advanced Engineering Mathematics, Erwin Kreyszig, (Wiley) 9th Edition
Minimum Required Facilities
 Traditional lecture room
Instructional Strategy
 Lectures
Grading
 Grading is based on four exams, with each exam having a 25% weight. Problems in the exams will be based on examples done in the class, suggested problems, and exercises given throughout the course.
Description
This is the first part of the introductory course on Mathematical Physics for undergraduate Physics students.
Objectives
After completing this course the student will have a good background to understand the mathematical formalism required in more advanced physics courses.
Contents

Vector differential calculus
 Vectors
 Inner and vector product
 Gradient, divergence and curl

Vector Integral Calculus
 Line integrals
 Green's theorem
 Surface integrals, triple integrals
 Divergence theorem and its applications
 Stoke's Theorem

Ordinary differential equations
 First order equations
 Exactness, integrating factors
 Linear equations
 Bernoulli equations
 Secondorder equations
 Homogeneous equations
 EulerCauchy equations
 Wronskian
 Nonhomogeneous equations

Linear algebra
 Matrices
 Matrix multiplication
 Linear independence, vector space
 Solutions of linear systems
 Determinants
 Inverse of a matrix
 Eigenvalues, eigenvectors
 Twodimensional rotations
 Symmetric, skewsymmetric and Orthogonal matrices
 Diagonalization
 Quadratic forms
 Complex matrices