General information

• Module Info
• Module Schedule
• Laplace transforms formulae

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Selected slides

• Intro to matrices & determinants
• Inverse trigonometric functions
• Partial fractions
• Integration (I)
• Intro to definite integration
• Finding areas
• Numerical integration
• Complex numbers (2)
• Intro to Laplace transforms
• IVPs & Laplace transforms
• Discrete random variables
• Continuous random variables

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Selected vids

• Laplace Transform (ex.1)
• Laplace Transform (ex.2)
• Laplace Transform (ex.3)

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Tutorials

• Practice Questions 1
  
  Review of algebra (index laws, simplification of algebraic expressions, changing the subject in a formula).
  Quadratics; vertex; roots; the squared form of a quadratic.
  Functions (definition + terminology; function composition, etc).
  
• Practice Questions 2
  
  Polynomials; long division; rational functions; partial fraction decomposition.
  The exponential and logarithmic functions; equations involving these functions.
  Trigonometric functions (SIN, COS, TAN, COTAN); basic trig identities.
  
• Practice Questions 3
  
  Differentiation; definition; operations with derivatives; the product and quotient rules; the chain rule.
  Trigonometric equations.
  
• Practice Questions 4
  
  Minima and maxima of functions of one variable; stationary (or critical points) & their classification; practical applications.
  Indefinite integrals; integration by substitution;integration by parts.
  
• Practice Questions 5
  
  Definite integrals; area below the graph of a function; fundamental theorem of calculus.
  Evaluation of definite integrals.
  
• Practice Questions 6a
  
  Taylor and Maclaurin series.
• Practice Questions 6b
  
  Vectors; scalar and vector products; mixed products.
• Practice Questions 7
  
  Complex numbers; complex conjugate; Cartesian and polar form; operations withcomplex numbers. De Moivre's formula. Roots of unity.
• Practice Questions 8
  
  Matrices; addition, subtraction, and multiplication of matrices. The inverse of a square matrix.
  Determinants; the cofactor expansion theorem; Cramer's rule.
  
• Practice Questions 9
  
  Introduction to ODEs; first-order ODEs; separable equations; integrating factors.
  Second-order ODEs; initial-value problems; applications to simple harmonic motion.
  
• Practice Questions 10
  
  The Laplace transform.
  Applications of the Laplace transform to the solution of initial-value problems.
  
• Practice Questions 11
  
  Basic concepts from probability theory and statistics.
  

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Page created by Ciprian Coman
Last updated: Dec 2023