Mathematica代写-MSIN0011
时间:2022-04-30
MSIN0011 Exam Preparation Checklist
2021 - 2022
Sets, functions and limits
Sets and intervals - be familiar with the notation (p. 1 - 3)
Functions
how to define a function (p. 4 - 10)
properties such as increasing, decreasing, continuity (p. 10, 13)
Limits
find the limit of a continuous function with justification (p. 13-15)
understand when limits don’t exist (p. 15)
L’Hopital’s rule including justification of when to use it (p. 21-22)
evaluate and justify the limit at infinity (p. 28 - 30)
Differentiation
Basic calculus - you must be able to differentiate
Derivatives
you simply need to know || is not differentiable at = 0 (p. 17-20)
understand and appreciate the importance of different levels of smoothness (p. 22)
calculating partial derivatives of a multivariate function(p. 35 - 37)
finding the derivative of a multivariate function (p. 37 - 38)
finding the gradient of a multivariate function (p. 38)
finding the directional derivative of a multivariate function(p. 39)
know that minus the gradient points in the direction of greatest descent (p. 40)
know the justification that minus the gradient points in the direction of greatest descent (p. 40)
same for greatest ascent
Integration
Know how to integrate anything in one variable
Know how to calculate an improper integral (p. 26 - 30)
Know and understand the Fundamental Theorem of Calculus (p. 25)
Integrating a multivariate function over a set (p. 89 - 102)
Recognise the technique for evaluating integrals from the set
Integrating over unbounded sets
Changing variable - know and be able to use the technique of changing variables
1
Optimization models
Know the difference between constrained and unconstrained optimisation (p. 47, 48, 51, 64)
Critical points - what they are, how to find them and why we care (p. 50)
Stationary points - what they are and how to find them (p. 50)
Know the algorithm to solve a constrained optimisation problem in one-variable (p. 50)
Be able to use the algorithm to solve a constrained optimisation problem in one-variable (p. 50 - 51,
also seminar 4)
Finding the stationary points of a multivariate function (p. 51 - 56)
Classifying the stationary points of a multivariate function (p. 51 - 56)
Understand the importance of convexity in optimisation - why does it make optimisation easier (p.
56 - 61)
Know basic examples of convex function - e.g. quadratic functions etc. (do not need to justify this
using the Hessian) (p. 57, 58)
Gradient Descent Algorithm (p. 61 - 64 and Seminar 5)
learn and understand how it works
understand the parameters
know when and when not to use it
know what convergence means
Constrained optimisation for a multivariate function (p. 64 - 70)
Recognise a constrained optimisation problem
Set up a problem as a constrained optimisation problem
Know how to solve problems using Lagrange multipliers
Differential Equations
Recognise the type of differential equation - first order, second order, linear, etc.
Solving first order equations
Integrating (p. 74)
Separtating variables (p. 75 - 77)
Integrating factors (p. 77 - 79)
Know the difference, and when to use each (p. 74 - 79)
Solving second order equations
Know the terms: linear, homogeneous, etc. (p. 81 - 82, 84)
Know and be able to solve any equation (p. 81 - 88)
2


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