## PHYS1160 Differential Calculus and Infinite Series

### 10 creditsClass Size: 100

Module manager: Professor M D Savage
Email: m.d.savage@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2005/06

### Pre-requisite qualifications

A Level Mathematics or equivalent

### Pre-requisites

PHYS1150 or equivalent

This module is not approved as an Elective

### Objectives

On completion of this module you should be able to:
- solve second order, linear, ordinary differential equations with constant coefficients;
- solve the SHM equation and the damped and forced SHM equations;
- determine the limit of a sequence;
- sketch the graphs of simple functions;
- test a series for convergence;
- determine the Taylor/Maclaurin series for a function of a single variable;
- determine the Fourier half range and full range series for a function, f(x);
- determine the partial derivatives of functions of two and three variables;
- apply the chain rule;
- determine the maxima, minima and saddle points of a function of two variables.

Skills outcomes
Basic mathematical skills in pure mathematics
Ability to solve differential equations
ability to model a physical problemBasic mathematical skills in pure mathematics
Ability to solve differential equations
ability to model a physical problem

### Syllabus

Ordinary Differential Equations:
Second order, linear ODE's, principle of superposition. Solution of homogeneous equations with constant coefficients; the complementary function. Solution of inhomogeneous equations; finding particular integrals; the general solution as a combination of the complementary function and a particular integral. Application to Newtonian mechanics; simple harmonic motion, forced and damped oscillations.
Limits and Curve Sketching
Concept of a limit; L'hopital's rule; limit of a sequence and a series. Convergence of sequences and series
Curve sketching by finding stationary points, asymptotes and various limits of functions.
Series
Power series, Maclaurin series, Taylor series and Taylor's theorem. Fourier series, half and full range series.
Several Variable Calculus
Functions of two and three variables, partial differentiation, chain rule. Maxima , minima and saddle points of functions of several variables.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Lectures: 22 x 1 hour;

Example classes: 10 x 1 hour.

### Private study

Examples: 40 hours.

5 assignments.

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

1 x 2 hour written examination at the end of the semester: 85%;
5 assignments submitted during the semester: 15%.