PHY120 and PHY165

Introductory mathematics for physicists and astronomers


Department of Physics and Astronomy

University of Sheffield

Academic year 2015-2016




Dr. Vitaly Kudryavtsev (module leader) E45, tel.: 2224531;

Dr. Matthew Mears D29, tel.: 2224289;

Mr. Jim Weston F25, tel.: 2224547;

Dr. Emiliano Cancellieri E13a, tel.: 2223550;

Dr. Francesco Hautmann D19, tel.: 2223544;

Prof. David Whittaker E12b, tel.: 2223537;

Dr. Maxim Makhonin E13, tel.: 2223522;




PHY120 is a year-long module worth 30 credits.  Out of these, 20 credits (44 lectures) are in the autumn semester and 10 credits (22 lectures) are in the spring semester. The module is core for all students taking any programme in the Department of Physics and Astronomy except Theoretical Physicists who opted for taking MAS110 in the School of Mathematics and Statistics in the Autumn semester. Those theorists are taking PHY165 instead of PHY120. They will need to attend Unit 2 (Vectors) of PHY120 in the Autumn semester (3 lectures) and take a test that will contribute 5% to their PHY165 module mark. They will also attend all lectures, problem classes and the exam in the Spring semester.


In the first semester there will be 4 lectures, 2 hours of problem classes, one homework and one online exercise per week.  Homework and online exercises each contribute 10% to the total module mark.  Formal written examinations at the end of the semesters contributes 80% to the total mark for the semester. The 1st semester (exam and the coursework) contributes 2/3 to the total module mark, whereas the 2nd semester contributes 1/3.



Units and lecture notes for the 1st semester:


Unit 1: Functions and differentiation – Dr. Vitaly Kudryavtsev, notes.

Unit 2: Introduction to vectors – Dr. Emilliano Cancellieri, notes.

Unit 3: Complex numbers. – Dr. Francesco Hautmann, notes, slides.

Unit 4: Integration – Dr. Matthew Mears.

Unit 5: Differential equations – Dr. Vitaly Kudryavtsev, notes.

Unit 6: Matrices – Mr. Jim Weston, notes.



Compulsory textbook:

“Introductory Maths for Physicists and Astronomers”, compiled by David Mowbray (ed. Pearson) – The book will be purchased by the Department and given to the students at the beginning of the term.



Semester 2


Units for the 2nd semester:


Unit 7: Vectors and differentiation; gradient, divergence and curl – Prof. David Whittaker, notes.

Unit 8: Multiple integrals and vector calculus – Dr. Francesco Hautmann, notes.

Unit 9: Probability – Dr. Maxim Makhonin, notes.