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Recommended Text

The notes of Dr. Tenti are an excellent alternate source of the matrial in this course:

The recommended texts for MATH 211 are James's Modern Engineering Mathematics and Advanced Modern Engineering Mathematics series. This sequence of two books describes most of the mathematics required by electrical and computer engineering undergraduate students. Ideally these texts will be used in all three 2nd-year courses: MATH 115, MATH 211, and MATH 212.

The sub-sections which currently appear to be relevant to the above descriptions of the course material and the laboratories are emphasized with bold and and italics, respectively; and those sections where the majority of sub-sections are of interest are also emphasized.

Glyn James, Modern Engineering Mathematics, 4th Ed.

The relevant chapters, sections, and subsections are listed here.

10 Introduction to Ordinary Differential Equations

  • 10.1 Introduction
  • 10.2 Engineering Examples
    • 10.2.1 The take-off run of an aircraft
    • 10.2.2 Domestic hot-water supply
    • 10.2.3 Hydro-electric power generation
    • 10.2.4 Simple electrical circuits
  • 10.3 The classification of differential equations
    • 10.3.1 Ordinary and partial differential equation
    • 10.3.2 Independent and dependent variables
    • 10.3.3 The order of a differential equation
    • 10.3.4 Linear and nonlinear differential equations
    • 10.3.5 Homogeneous and nonhomogeneous equations
  • 10.4 Solving differential equations
    • 10.4.1 Solution by inspection
    • 10.4.2 General and particular solutions
    • 10.4.3 Boundary and initial conditions
    • 10.4.4 Analytical and numerical solutions
  • 10.5 First-order ordinary differential equations
    • 10.5.1 A geometrical perspective
    • 10.5.3 Solutions of separable differential equations
    • 10.5.5 Solutions of differential equations of x(1)(t) = f(x/t) form
    • 10.5.7 Solutions of exact differential equations
    • 10.5.9 Solutions of linear differential equations
    • 10.5.11 Solutions of Bernoulli differential equations
  • 10.6 Numerical solution of first-order ordinary differential equations
    • 10.6.1 A simple solution method: Euler's method
    • 10.6.2 Analyzing Euler's method
    • 10.6.3 Using numerical methods to solve engineering problems
  • 10.7 Engineering application: analysis of damper performance
  • 10.8 Linear differential equations
    • 10.8.1 Differential operators
    • 10.8.2 Linear differential equations
  • 10.9 Linear constant-coefficient differential equations
    • 10.9.1 Linear homogeneous constant-coefficient equations
    • 10.9.3 Linear nonhomogeneous constant-coefficient equations
  • 10.10 Engineering applications: second-order linear constant-coefficient differential equations
    • 10.10.1 Free oscillations of elastic systems
    • 10.10.2 Free oscillations of damped elastic systems
    • 10.10.3 Forced oscillations of elastic systems
    • 10.10.4 Oscillations in electrical circuits
  • 10.11 Numerical solutions of second- and higher-order differential equations
    • 10.11.1 Numerical solutions of coupled first-order equations
    • 10.11.2 State-space representation of higher-order systems
  • 10.12 Quantitative analysis of second-order differential equations
    • 10.12.1 Phase-plane plots

Glyn James, Advanced Modern Engineering Mathematics, 3rd Ed.

The relevant chapters, sections, and subsections are listed here.

2 The Laplace Transform

  • 2.1 Introduction
  • 2.2 The Laplace Transform
    • 2.2.1 Definition and notation
    • 2.2.2 Transforms of simple functions
    • 2.2.3 Existence of the Laplace transform
    • 2.2.4 Properties of the Laplace transform
    • 2.2.5 Table of Laplace transforms
    • 2.2.7 The inverse Laplace transform
    • 2.2.8 Evaluation of inverse transforms
    • 2.2.9 Inversion using the first shift theorem
  • 2.3 Solutions of Differential Equations
    • 2.3.1 Transforms of derivatives
    • 2.3.2 Transforms of integrals
    • 2.3.3 Ordinary differential equations
    • 2.3.4 Simultaneous differential equations
  • 2.4 Engineering applications: electric circuits and mechanical vibrations
    • 2.4.1 Electrical circuits
    • 2.4.2 Mechanical vibrations
  • 2.5 Step and impulse functions
    • 2.5.1 The Heaviside step function
    • 2.5.2 Laplace transform of the unit step function
    • 2.5.3 The second shift theorem
    • 2.5.4 Inversion using the second shift theorem
    • 2.5.5 Differential equations
    • 2.5.6 Periodic functions
    • 2.5.8 The impulse function
    • 2.5.9 The sifting property
    • 2.5.10 Laplace transforms of impulse functions
    • 2.5.11 Relationship between the Heaviside step and impulse functions
    • 2.5.13 Bending of beams
  • 2.6 Transfer functions
    • 2.6.1 Definitions
    • 2.6.2 Stability
    • 2.6.3 Impulse response
    • 2.6.4 Initial- and final-value theorems
    • 2.6.6 Convolution
    • 2.6.7 System response to an arbitrary input
  • 2.7 Engineering application: frequency response

4 Fourier Series

  • 4.1 Introduction
  • 4.2 Fourier series expansion
    • 4.2.1 Periodic functions
    • 4.2.2 Fourier's theorem
    • 4.2.3 The Fourier coefficients
    • 4.2.4 Functions of period 2π
    • 4.2.5 Even and odd functions
    • 4.2.7 Even and odd harmonics
    • 4.2.8 Linearity property
    • 4.2.9 Convergence of the Fourier series
    • 4.2.10 Functions of period T
  • 4.3 Functions defined over a finite interval
    • 4.3.1 Full-range series
    • 4.3.2 Half-range cosine and sine series
  • 4.4 Differentiation and integration of Fourier series
    • 4.4.1 Integration of a Fourier series
    • 4.4.2 Differentiation of a Fourier series
    • 4.4.3 Coefficients in terms of jumps at discontinuities
  • 4.5 Engineering application: frequency response and oscillating systems
    • 4.5.1 Response to periodic input
  • 4.6 Complex form of Fourier series
    • 4.6.1 Complex representation
    • 4.6.2 The multiplication theorem and Parseal's theorem
    • 4.6.3 Discrete frequency spectra
    • 4.6.4 Power spectrum
  • 4.7 Orthogonal functions
    • 4.7.1 Definitions
    • 4.7.2 Generalized Fourier series
    • 4.7.3 Convergence of generalized Fourier series
  • 4.8 Engineering application: describing functions

9 Partial-differential Equations

  • 9.1 Introduction
  • 9.2 General discussion
    • 9.2.1 Wave equation
    • 9.2.2 Heat-conduction or diffusion equation
    • 9.2.3 Laplace equation
    • 9.2.4 Other and related equations
    • 9.2.5 Arbitrary functions
  • 9.3 Solutions of the wave equation
    • 9.3.1 D'Alembert solution and characteristics
    • 9.3.2 Separated soluations
    • 9.3.3 Laplace transform solution
    • 9.3.5 Numerical solutions
  • 9.4 Solutions of the heat-conduction/diffusion equation
    • 9.4.1 Separation method
    • 9.4.2 Laplace transform method
    • 9.4.4 Numerical solutions
  • 9.5 Solutions of the Laplace equation
    • 9.5.1 Separated solutions
    • 9.5.3 Numerical solutions
  • 9.6 Finite elements
  • 9.7 General considerations
    • 9.7.1 Formal classification
    • 9.7.2 Boundary conditions
  • 9.8 Engineering application: wave propagation under a moving load
  • 9.9 Engineering application: blood-flow model