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MATH 3705

Mathematical Methods I

0.5 credit · Undergraduate

Laplace transforms, series solutions of ordinary differential equations, the Frobenius method. Fourier series and Fourier transforms, solutions of partial differential equations of mathematical physics, boundary value problems, applications.

2022

Topics

  • The Laplace Transform
  • 1 Introduction
  • 2 Further Properties and Initial-Value Problems
  • 3 Convolutions and Generalized Functions
  • Series Solutions of Ordinary Differential Equations
  • 1 Basic Concepts
  • 2 Solutions About Ordinary Points
  • 3 Solutions About Regular Singular Points
  • 3.1 Cauchy-Euler Equations
  • 3.3 Bessel’s Equation
  • Fourier Series, Lectures 11 −12
  • 1 Periodic Functions
  • 2 Functions Defined on Finite Intervals
  • Partial Differential Equations, Lectures 13 −17
  • 1 The Heat Equation
  • 1.1 The Bar with Zero Boundary Conditions
  • 1.2 The Bar with Nonzero Boundary Conditions
  • 1.3 The Bar with Insulated Ends

Readings

  • Mathematical Methods and Boundary Value Problems, Fifth Edition, by S.

Prerequisites & course information

Precludes additional credit for PHYS 3808 . This course may be taken for credit as a 3000-level Honours Mathematics course by students in any Honours program in the School of Mathematics and Statistics. Prerequisite(s): i) MATH 1005 or MATH 2404 , and ii) MATH 2002 or MATH 2004 or MATH 2008 or MATH 3009 ; or permission of the School. Lectures three hours a week and one hour tutorial.

Sources