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Martinborough Manor, Flowers, Homesteading and Mathematics/Engineering Mathematics 1 MG5004
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Engineering Mathematics 1 MG5004

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This is THE way to learn Maths for Engineering, a compulsory course for the B Eng Tech
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Contents

Welcome

How it all works!
Student Registration for mymathlab Instructions - don't buy the ebook version, I will supply
MG5004 course outline tri 1 2023.docx
mathematics-for-engineers-fourth-edition-pdf.pdf
MG5004 2023 Formula booklet.pdf
MG5004 test 1 2020.pdf
MG5004 Test 1 2020 Solutions.pdf
MG5004 Dummy test 1 2023.pptx
MG5004 DE5418 Test 2 tri 2 2020.pdf
MG5004 solutions test 2 2020.pdf
Q10 test 1 2020.pptx
MG5004 test 2 2020 as done in class on 31 May 2023
Why I should care about learning maths?

Topic 1 Review of Basic arithmetic

in topic 1 you will learn or revise:
  • how to perform operations on whole numbers
  • how to manipulate whole numbers
  • the order in which operations on whole numbers must be carried out
  • the definition of a prime number and how to find one
Before you start
Lesson 1 Basic arithmetic
MG5004 DE5248 topic 1 class 1
MG5004 Topic 1 Arithmetic T1 C1.pptx
Extra inequality and abs value questions.pdf
Textbook questions
Lesson 2 Decimals and percentages
mg5004 topic 1 class 2
MG5004 Topic 1 Arithmetic T1 C2.pptx
Textbook questions

Topic 2 Review of basic algebra and functions

You will learn or revise
  • properties of numbers and common notation and symbols
  • rules of indices (covering multiplication, division, raising to a power and finding a root) 
  • the degree of a polynomial
  • number bases
  • simplification by collecting like terms, removing brackets, factorising
  • how to work wtih algebraic fractions
  • how to use and rearrange formulae
  • basic concepts of functions
  • how to sketch a graph of a function
  • composition of functions
  • how to check for 1-1 functions and inverse functions
  • parametric representation of a function
  • how to describe functions
  • how to draw and recognise a straight line
  • some common engineering functions
Lesson 1 Basic algebra
mg5004 topic 2 part 1
MG5004 Topic 2 Algebra T2 C1.pptx
Textbook questions
Lesson 2 Functions and graphs
MG5004 De5418 Topic 2 class 2 part 1
mg5004 topic 2 class 2 part 2
MG5004 DE5418 topic 2 class 2 part 3
MG5004 Topic 2 Algebra 1 class (T2 C2).pptx
MG5004 Simple parametric curve sketching
Composite functions
Poles of a rational function
The Unit Step Function
Odd, even or neither functions
Textbook questions
Assignment 1 q19.pptx

Topic 3 Solving equations and inequations

In this topic you will learn (or revise)
  • solving linear equations
  • solving quadratic equations
  • factorising and solving polynomial equations
  • solving simultaneous equations
  • how to solve inequalities
  • how to decompose a fraction in to partial fractions
Lesson 1 solving equations and inequations.
MG5004 Topic 3 class 1 part 1
MG5004 Topic 3 Algebra 2 class 1 p1.pdf
MG5004 Topic 3 class 1 p2
MG5004 Topic 3 Algebra 2 class 1 p2.pdf
Completing the square to solve equations
Applications of solving equations
Application of solving equations at 2:00 in video
Solving equations a tricky one from the video at 2 minutes in.pptx
Solving inequalities involving modulus
Textbook questions
Questions from p276 .pptx
mymathlab exercise
Lesson 2 Partial fractions
MG5004 Topic 3 class 2
MG5004 Topic 3 Algebra 2 class 2.pdf
MG5004 Decomposing a fraction into partial fractions
Partial fractions q6 p270.pptx
Division of polynomials
Textbook questions
mymathlab exercise
MG5504 common errors in topic test 3.pdf
Topic test 3 on mymathlab

Topic 4 Exponential and logarithmic functions

You will learn to
  • manipulate powers of "e"
  • use the rules of exponents to simplify expressions involving "e"
  • convert from a statement in "e" to a statement in natural logs
  • graph equations involving "e"
  • complete problems involving "e" 
  • evaluate, manipulate and apply hyperbolic functions
  • manipulate and simplify logarithms to different bases
  • use the rules of logarithms to simplify expressions involving logs
  • graph the logarithmic functions
  • solve equations involving logarithms
  • use scales on graphs that are not linear, but are related to logs
Lesson 1 - the exponential function
MG5004 topic 4 class 1
MG5004 Topic 4 Exponents T4 C1.pptx
Exponential quesitons Simplification.pptx
Textbook questions
mymathlab exercise
Lesson 2 Logarithms and their laws, and using exponents and logs to solve equations including them
MG5004 topic 4 class 2
MG5004 Topic 4 Logs and Exp class 2.pptx
log_linear_grph.pdf
graphingonloglogpaper.pdf
Textbook questions
mymathlab exercise
Topic test 4 on mymathlab
Solution of part of assignment 2.jpg
Log Graph Paper.pdf
Ass 2 q11.pptx

Topic 5 Trigonometry

In this topic you will learn to:
  • measure angles in degrees and radians, and to be able to convert between them, when these angles are from a full rotation (or more) of the quadrants
  • define the major trig ratios, and the inverse trig ratios
  • use these in an engineering context
  • consider the trig ratios as generating trig functions
  • draw trig graphs and to transform them horizontally, vertically
  • use common trig identities in order to simplify trig expressions
  • solve trigonometrical equations
  • sketch, manipulate and use in an engineering context, engineering waves
  • add waves of the same frequency
Lesson 1 Trig ratios, trig functions and their graphs
MG5004 topic 5 class 1
MG5004 Topic 5 Trig functions class 1.pptx
Textbook questions
mymathlab exercise
Lesson 2 trigonometric identities and solving trig equations
mg5004 topic 5 class 2
MG5004 Topic 5 Trig functions class 2.pptx
Proving a trig identity without using a trig identity!
Cupid's curves
Compound angles 1
Compound angles 2
Circular functions - crank shaft example
How do I know which trig identity to use?
MG5004 Elliptical gear question.pptx
Textbook questions
text questions p 349.pptx
MG5004 Why bcos.pptx
CH9 HW
mymathlab exercise
Test 5 Q14 worked answer.pptx
Topic test 5 on mymathlab

Topic 6 Complex numbers

In this topic you will learn to:
  • define complex numbers
  • add, subtract, multiply and divide complex numbers
  • draw complex numbers on an Argand diagram
  • recognize complex numbers in rectangular and polar form and to be able to convert between them
  • manipulate and recognize the exponential form of a complex number
  • compute and sketch roots and powers of complex numbers using de Moivre's theorem
  • solve equations where roots are imaginary, and find roots of complex numbers
Lesson 1 Introduction to complex numbers and the forms of complex numbers
mg5004 topic 6 part 1
MG5004 Topic 6 class 1 Complex numbers.pptx
Finding the natural log of a complex number
Textbook questions
mymathlab exercise
Lesson 2 de Moivre's theorem, using this theorem to prove trig identities and solving equations involving complex numbers
MG5004 DE5418 Topic 6 class 2
MG5004 Topic 6 Class 2 Complex numbers.pptx
Solving complex equations #1
Solving complex equations #2
Find sine theta to the power of 3.pptx
Find sin^4 theta.pptx
Pascal's triangle, the what, the why and the how
Textbook questions
mymathlab exercise
Topic test 6 on mymathlab
MG5004 Assignment 3 question 6.pptx
Assignment 3 Question 1.pptx
MG5004 Written assignment 3.pdf
Ass 3 help.pptx

Topic 7 Matrices

In topic 7 you will learn to:
  • multiply matrices
  • find the determinant of a matrix
  • find the inverse of a matrix
  • use Cramer's rule
  • use the inverse matrix to solve simultaneous equations
  • complete a Gaussian elimination
  • find the eigenvalues and eigenvectors of a given matrix
Lesson 1 Matrices and determinants
The applications of matrices
MG5005 Topic 7 class 1
MG5004 Topic 7 Matrices class 1.pptx
Using excel for matrices.xlsx
SIngularity of a matrix
Textbook questions
mymathlab exercise
Lesson 2 Using matrices and determinants to solve equations
MG5004 Topic 7 class 2
MG5004 Topic 7 Matrices class 2.pptx
eigenvalues in real life.pdf
Linear equations - gaussian elimination method
Eigenvalues and eigenvectors #1
Eigenvalues and eigenvectors #2
Textbook questions
mymathlab exercise

Topic 8 Vectors

In this topic you will learn:
  • the basic concepts of vectors
  • how to describe vectors wtih reference to various coordinate systems
  • how to compute the scalar product (or dot product) of two vectors
  • how to compute the vector product (or cross product) of two vectors 
  • how to find the vector equation of a line and a plane
Introductory basic vector material.pdf
A useful website for vector introduction
Lesson 1 The basic concepts of vectors
MG5004 topic 8 class 1
MG5004 Topic 8 Class 1 Matrices and vectors.pptx
Textbook questions
mymathlab exercise
Lesson 2 Multiplication of vectors and the vector equation of a line and a plane
MG5004 Topic 8 class 2
MG5004 Topic 8 Class 2 Matrices and vectors.pptx
Planes and lines
More planes and lines
Intersecting lines
Textbook questions
mymathlab exercise

Topic 9 Differentiation

In this topic you will learn to (or revise):
  • the meaning of a derivative
  • use a table of derivatives
  • find higher derivatives
  • use the product and quotient rules to differentiate functions not in the table of derivatives
  • use the chain rule to differentiate a composite function
  • differentiate an expression that is expressed implicitly
  • differentiate an expression that is expressed parametrically
  • use logarithmic differentiation to deal with functions that are too complicated to use the quotient or product rule for
  • find the tangent or he normal to a curve
  • find the optimum values of a function and the nature of those optimums
Lesson 1 Differentiation - an introduction
MG5004 Topic 9 class 1
MG5004 Topic 9 Class 1 Differentiation.pptx
The Chain rule
The product rule
Differentiating from first principles
difficult product rule question.pdf
Implicit differentiation - tangents to a curve
Lesson 2 Logarithmic differentiation, tangents and normals and optimising a function
MG5004DE5418 Topic 9 class 2
MG5004 Topic 9 Class 2 Differentiation.pptx
MG5004 Optimising handout Topic 9 class 2.pdf
MG5004 Written assignment 4 2022.pdf
The quotient rule
MG5004 ch16 worked examples.pdf

Topic 10 Integration

In topic 10 (chapter 17) you will learn to:
  • integrate by treating the process as the reverse of differentiation
  • calculate definite integrals
  • find the area under a curve
  • use Simpson's rule and the trapezoidal rule to find area where you can't easily use integration
  • integrate a product, by parts
  • make an algebraic substitution that will allow you to then integrate
  • to simplify algebraic fractions into partial fractions so you can then integrate them
  • integrate trigonometrical functions

Lesson 1
MG5004 topic 10 class 1 integration
MG5004 Topic 10 Class 1 Integration.pptx
Related rates question
Lesson 2
MG5004 topic 10 class 2
MG5004 Topic 10 Class 2 Integration.pptx
MG5004 More Techniques of integration

Topic 11 Applications of integration

In topic 11 (chapter 18) you will learn to apply integration.  You will learn to:
  • find volumes of revolution
  • calculate the centres of mass
  • find the moment of inertia
  • find the length of a curve and the area of a surface of revolution
  • find the mean value and root mean square value of a function
MG5004 Topic 11 class 1
MG5004 Topic 11 Class 1 Applications of integration.pptx
MG5004 topic 11 class 2
MG5004 Topic 11 Class 2 Applications of integration.pptx
Integration by substituion from T11 C2.pptx
MG5004 centroid question where y=x^2, y=2.pdf
Not in the course but maybe useful

Topic 12 Differential Equations

In this topic (chapter 20) you will learn:
  • the basic concepts of differential equations
  • how to separate variables
  • how to solve first-order linear equations using an integrating factor
  • how to solve second order linear constant-coefficient equations
Lesson 1
MG5004 Topic 12 class 1
MG5004 Topic 12 Class 1 Differential equations.pptx
MG5004 Topic 12 class 2
MG5004 Topic 12 class 2.pptx
Extra video 1
Extra video 2
Extra video 3
Extra video 4
2021 MG5004 Written Assignment 5.pdf
ass 5 q2.pptx
Ass 5 q1(a).pptx

Notes from "live" classes

These will be posted on the Friday of every week, for the classes during that week
MG5004 T8 C2 otago 2023.pptx
MG5004 T9 C 1 Otago 2023.pptx
MG5004 T9 C2 Otago 2 2022.pptx
MG5004 T10 C1 Otago 2 2022.pptx
MG5004 T10 C2 Otago 2023.pptx
MG5004 T11 C1 Otago 2023.pptx
MG5004 integration by parts, T10 C2 2023.pdf
MG5004 T11 C2 Otago 2023.pptx
MG5004 T12 C1 2023.pptx
MG5004 T12 C2 Otago 2023.pptx

Past exams

MG5004 Engineering Mathematics 1 Final Examination WelTec November 2016.pdf
MG5004 2016 tri 2 exam q1 and q2
MG5004 tri 2 2016 exam q3 and q4
MG5004 tri 2 2016 exam q5 and q6
MG5004 tri 2 2016 exam q7 and q8
MG5004 solutions test 2 2020.pdf
MG5004 past exam.pptx
past exam MG5004 part 2.pptx