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Martinborough Manor, Flowers, Homesteading and Mathematics/Engineering Mathematics 1 DE4102
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Engineering Mathematics 1 DE4102

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Welcome

DE4102 is THE maths course for the New Zealand Diploma of Engineering.  The course is for students of Wellington Institute of Engineering (WelTec).

To contact me please email me at penelope.deboer@weltec.ac.nz
How it all works!
DE4102 course outline tri 1 2022.pdf
DE4102 lesson timetable trimester 1 2022.xlsx
Textbook information
All courses 2022 Trimester 1 2022 Student text registration Instructions.pptx
Student_Registration_Handout_deboer16984 DE4102.pdf
mymathlab sign in link
Why should I care about learning maths?

Topic 1 Review of Basic arithmetic

In this topic we will quickly go over the basic arithmetic skills you will need to be able to complete the course.
  • Operations on numbers
  • Operations on Fractions
  • Decimals, Percentages and approximations
Before you start
Why do engineers need maths.pptx
Lesson 1 Operations on numbers
DE4102 Topic 1 part 1
Topic 1 Review of basic arithmetic skills p1.pptx
HCF and LCM
Lesson 2 Operations on fractions
Topic 1 Class 2 Arithmetic of fractions
Topic 1 Review of basic arithmetic skills p2.pdf
Lesson 3 Decimals, percentages and approximations
Topic 1 class 3 Review of basic arithmetic
Topic 1 Review of basic arithmetic skills p3.pdf
DE4102 Topic 1 mega hard problems.pptx
Ever wondered why? mega hard questions
Decimals etc and Excel
DE4102 T1 C1 2022.pptx
DE4102 T1 C2 2022.pptx

Topic 2 Review of basic algebra

In order to be able to apply mathematics to any discipline, it is necessary to use symbols to represent physical quantities.  Then we use Algebra to manipulate these symbols.  We need to be able to manipulate the symbols, in order that we develop the necessary foundation to use techniques later in the course, and in other courses, and in engineering itself.

in this topic you will learn (or revise how) to :
  • use mathematical notation and symbols
  • use the laws of powers
  • simplify by collecting like terms
  • simplify by removing brackets
  • simplify by factorising
  • add, subtract, multiply and divide algebraic fractions
  • manipulate (transpose) formulae
Lesson 1 Simplification
Ever wondered why topic 2 part 1.pdf
Topic 2 - Reveiw of basic alegbraic skills 2020 p1.pdf
Lesson 2 Algebraic fractions
Topic 2 - Review of basic algebraic skills 2021 p2
Crazy fractions
Lesson 3 Formulae and transposition
Topic 2 - Reveiw of basic alegbraic skills 2021 p3.pdf
Working with variables in spreadsheets
Assignment 1 Otago 2022.pdf
DE4102 T2 C1 and C2 otago 2022.pptx
DE4102 T2 C3 Otago 2022.pptx

Topic 3 Functions

In topic 3 (chapter 6) you will learn:
  • the basic concepts of a function
  • how to sketch a graph of a function
  • how to find the result of a function on another function (composition of functions)
  • how to find the inverse of a function
  • how to describe a function in words and how to write a function from words
  • how to describe a linear function in equation form, and identify the key components of a straight line
  • how to find the equation of a line given information on various variables
  • to find the distance between two points
  • to identify polynomials of different orders
  • how to use Excel to draw a straight line
Lesson 1 Functions
Topic 3 p1 Functions.pdf
One-to-one functions - a tricky question
Lesson 2 Straight lines
Topic 3 part 2
Textbook questions
Topic 3 p2 Straight lines.pdf
Study plan
Finding the equation of a line and finding the distance between two points.pdf
Distance between 2 points, equation of a line given 2 points, the answers
Lesson 3 producing straight lines in Excel
Topic 3 class 3 Producing a straight line in excel
DE4102 Topic 3 class 3 Producing straight lines in excel.pdf
Lesson 4 Common engineering functions
DE4102 topic 3 class 4
Topic 3 p4 Common engineering functions.pdf
Applications of parabolas etc.pdf, the questions
Applications of parabolas etc (the answers)
Poles of a rational function
Polynomials
Finding the vertex and axis of symmetry of a quadratic

Topic 4 Solving equations

In topic 4 (chapter 7), you will learn to:
  • solve linear equations
  • solve quadratic equations
  • factorise polynomial equation, and thus solve them
  • solve a set of simultaneous equations
Lesson 1 Solving linear equations
Topic 4 p1 Linear equations 2021.pdf
Solving LINEAR equations
Study plan
Textbook questions
Study plan
mymathlab exercise
Lesson 2 Solving linear equations in Excel
DE4102 T4 C2 using excel to solve linear equations.xlsx
Lesson 3 Solving quadratic equations
Topic 4 p3 Quadratic equations 2021.pdf
DE4102 topic 4 part 3
Solving equations - solving a quadratic equation
Textbook questions
mymathlab exercise
Lesson 4 Solving quadratic equations part 2
DE4102 T4 C4 Otago 2022.pptx
Lesson 5 Plotting quadratic equations in excel
DE4102 Topic 4 class 5 drawing quadratic functions in spreadsheets.pptx
Lesson 6 Solving simultaneous equations
Topic 4 p6 Simultaneous equations 2021.pdf
DE4102 topic 4 part 6 Simultaneous equations
Solving equations - solving simultaneous equaitions
Study plan
Textbook questions
mymathlab exercise
Lesson 7 Simultaneous equations part 2, including using excel
Assignment 2 Otago 2022.pdf

Topic 5 Exponents and logarithms

In topic 5 (chapter 8), you will learn to:
  • manipulate expressions involving the exponential constant, "e"
  • sketch exponential functions
  • use exponential functions in an engineering context
  • define logarithms, and rewrite exponential statements in terms of logarithms, and vice versa
  • use the "laws" of logarithms to simplify logarithmic expression
  • sketch logarithmic functions
  • solve equations involving logarithms and exponents in a pure sense and in an engineering context
Lesson 1 The exponential function
Topic 5 class 1 - Exponential functions
topic 5 p1 The exponential function 2021.pdf
Study plan
Textbook questions
mymathlab exercise
Lesson 2 Logarithms and their laws
DE4102 topic 5 part 2 Logarithmic functions
topic 5 p2 Logarithms 2021.pdf
Study plan
Textbook questions
mymathlab exercise
Lesson 3 producing exponential graphs in Excel
Lesson 4 Producing logarithmic graphs in spreadsheets
Lesson 5 Solving equations involving logarithms and exponentials
DE4102 topic 5 class 5 Solving equations with logs and exponents
topic 5 p5 Solving log equations pdf
Study plan
Textbook questions
mymathlab exercise
Lesson 6 Solving log equations part 2

Topic 6 Trigonometry

In topic 6 (chapter 9) you will learn to:
  • describe angles in either degrees or radians
  • convert angle measures from degrees to radians and vice versa
  • find the trigonometric ratios in all four quadrants
  • describe the ratios in terms of functions
  • sketch the trigonometrical functions
  • recognize the need for and be able to use trigonometrical identities
  • solve trigonometrical equations
  • apply trigonometrical functions in an engineering context.  
Why do we need to know about trigonometry.pdf
Lesson 1 Trigonometrical ratios
Topic 6 - Trigonometry p1 trig ratios.pdf
DE4102 topic 6 part 1
MG5004/DE4102 Fractional and surd forms of trig ratios
Study plan
Textbook questions
mymathlab exercise
Lesson 2 Finding the inverse trig ratios using a calculator
Lesson 2 Topic 6 class 2 Finding inverse trig ratios
DE4102 Topic 6 class 2 Finding inverse trig ratios using a calculator.pdf
Lesson 3 Circular definition of the trigonometric functions
Topic 6 class 3 Circular definitions of the trigonometric functions
DE4102 Topic 6 class 3 Circular defintion of the trigonmetrical functions.pdf
Lesson 4 Trig functions and their graphs
DE4102 topic 6 class 4
Topic 6 - Trigonometry class 4 Trig functions and their graphs.pdf
Study plan
Sinusoidal waveforms #1
Sinusoidal waveforms #2
Sinusoidal waveforms extra questions.pdf
sinusoidal waveforms solutions.pdf
Textbook questions
mymathlab exercise
Lesson 5 Trig functions and their graphs part 2
DE4102 T6 C5.pdf
Lesson 6 Trigonometry and Excel
DE4102 Topic 6 class 6 Trigonometry and Excel
DE4102 Topic 6 class 6 Trigonometry and excel.pdf
Lesson 7 Trig identities and solving trig equations
DE4102 topic 6 part 7
Topic 6 - Trigonometry p7 Trig equations.pdf
Solving trig equations #1
Solving trig equations #2
Rewriting sin4t+3cos4t
Study plan
Textbook questions
DE4102 Topic 6 class 8
DE4102 Extra questions to be done before trig 3 on mymathlab
Tricky question in trig 3
mymathlab exercise
Radians or degrees?
DE4102 Assignment 3 Otago 2022 to be done after topic 6 trig is finished

Previous tests and exams

DE4102 Engineering Maths 1 Formulae Sheet - FINAL (1).pdf
DE4102 Test 1 tri 1 2021 Q1
DE4102 test1 tri 1 2021 Q2
DE4102 test 1 tri1 2021 q3
DE4102 Test 1 tri 1 2021 Q4
DE4102 Test 1 tri 1 2021 Q5
DE4102 Test 1 tri 1 2021 Q6
DE4102 Test 1 tri 1 2021 Q7
DE4102 test 1 tri 1 2021 Q8 and Q9
DE4102 Engineering Maths test 2 trimester 1 2021.pdf
DE4102 test 2 trimester 1 2021 Q1.pdf
DE4102 test 2 trimester 1 2021 Q2.pdf
DE4102 test 2 trimester 1 2021 Section B Q1.pdf
DE4102 test 2 Trimester 1 2021 Section B Q2.pdf
DE4012 test 2 trimester 1 2021 Section B Q3.pdf
DE4102 test 2 trimester 1 2021 Section B Q4.pdf
DE4102 Engineering Mathematics Final Exam June 2013 FINAL VERSION.pdf
DE4102 Engineering Maths S1, 2018 - Exam.pdf
DE4102 Engineering Maths June 2019 Exam - FINAL.pdf
DE4102 Engineering Maths Semester 2 2020 - Exam - FINAL (1).pdf
DE4102 Q1 test 1 trimester 2 2021
DE4102 q2 test 1 trimester 2 2021
DE4102 q3 test 1 trimester 2 2021
DE4102 q4 test 1 trimester 2 2021
DE4102 q5 test 1 trimester 2 2021
DE4102 q6 test 1 trimester 2 2021
DE4102 q1 test 2 trimester 2 2021
DE4102 q2 test 2 trimester 2 2021
DE4102 section C q1 test 2 tri 2 2021
DE4102 section C q2 test 2 tri 2 2021
DE4102 section C q3 test 2 tri 2 2021
DE4102 section C q4 test 2 tri 2 2021
DE4102 Engineering Maths Semester 1 2021 - Exam - FINAL.pdf
DE4102 Engineering Maths Semester 1 2021 - Marking Guide.pdf

Topic 7 Introduction to differentiation

In topic 7 you will what a derivative is, how to use a table of derivatives and how to find the derivative of a function several times (finding higher derivatives).
DE4102 topic 7 part 1
Basic understanding of calculus, without using big words
Topic 7 Differentiation class 1.pdf
Study plan
etext problems
Topic 7 class 2 Using excel to show a derivative
DE4102 topic 7 class 3
Topic 7 Differentiation class 3.pdf
DE4102 topic 7 class 3 part 2
Topic 7 Differentiation class 3 part 2.pdf
Study plan
Textbook questions
mymathlab exercise

Topic 8 Techniques of differentiation 2021 last time offering

In topic 8 you will learn to use techniques for differentiating functions that are not directly listed in the list of common derivatives (list in textbook and on your formula sheet).  These will include:
  • the product rule
  • the quotient rule
  • the chain rule
DE4102 topic 8 part 1
Topic 8 - Differentiation techniques p1.pdf
Study plan
Textbook questions
mymathlab exercise
DE4102 topic 8 part 2
Topic 8 - Differentiation techniques p2.pdf
DE4102 topic 8 part 3
Topic 8 - Differentiation techniques p3.pdf

Topic 9 Applications of differentiation last time offered 2021

In topic 9 you will learn to apply differentiation in an engineering context, not limited to:
  • tangents
  • distance problems
  • velocity problems
  • acceleration problems
Topic 9 - Differentiation applications p1.pdf
DE4102 topic 9 part 1
Rapid Learning: Problem Solving In Calculus - How To Solve Calculus Problems
Quadratic keywords for appplied problems
Hand out 1 Topic 9 class 1.pdf
DE4102 T9 C1 handout 1 solutions
DE4102 topic 9 part 2
Topic 9 class 2 problems DE4102 Applications of differentiation and dynamics - problems for topic 9 class 2
Question 6 Handout Topic 9 class 2
Topic 9 Class 3 Applications of differentiation part 2
DE4102 test preparation for test 9
DE4102 test 9 questions.pdf
Q 8 handout Topic 9 class 3

Topic 8 2022 onwards Using differentiation to optimise functions

In topic 8 (second part of chapter 16) you will learn to:
  • locate the turning points of a function
  • to identify these turning points as a maximum or a minimum
  • show where a function is decreasing or increasing
  • find the points where a function's concavity changes
Maximums and minimums, the intuition
Questions on max and mim using the first derivative test
DE4102 topic 8 class 1 2022
DE4102 Topic 8 - Maxima and minima of functions class 1.pdf
Study plan
Textbook questions
mymathlab exercise
DE4102 topic 8 2022 onwards class 2
Topic 8 2022 onwards - Maxima and minima of functions.pdf
Optimal values of functions.pdf
Optimum values of "real" functions
mymathlab exercise
DE4102 Topic 8 questions.pdf
Application of max and Min - voltage question
Applied question

Topic 9 Introduction to integration 2022 onwards

You will learn to:
  • see integration as a process that is the reverse of differentiation
  • use a table of integrals
  • use the rules of integration
  • calculate definite integrals

Lesson 1
Topic 9 part 1
Topic 9 - Integration p1.pdf
study plan
textbook questions
mymathlab
Lesson 2
Topic 9 part 2
Topic 9 - Integration p2.pdf
study plan
textbook questions
mymathlab
Finding a definite integral with an infinite limit
Topic 9 class 3 Simpson's rule #1
Simpson's rule #2

Topic 12 Techniques and applications of integration

In topic 12 (second half of chapter 17, and parts of chapter 18) you will learn to:
  • find the area bounded by a curve
  • use Simpson's rule to find an area when integration is not possible
  • integrate by substitution when the function is too complicated for the table of integrals
  • integrate trigonometrical functions
  • use integration for other applications in an engineering context
Topic 12 C1
Topic 12 – Integration part 2 p1.pdf
integration of 3^x.pdf
Study plan
etext
mymathlab
Topic 12 C2
Topic 12 – Integration part 2 p2.pptx
Study plan
etext
mymathlab
Finding the area between two curves
Topic 12 C3
Topic 12 – Integration part 2 p3.pptx
Designing a soup bowl - application of integration
Study plan
etext
mymathlab
Numerical integration using Excel

Topic 13 An introduction to statistics

In topic 13, you will learn to:
  • find the mean, median and mode of a data list (on your calculator)
  • use simple regression analysis and correlation to make predictions from given data
Topic 13 – Basic Statistics .pdf
Topic 13 Class 1 1 Basic statistics
Topic 13 Basic statistics 2
Statistics wtih the Casio fx-82AU+
Class limits and boundaries
Using statistics to find descriptive statistics
Using casio fx-82AU PLUS II to find standard deviation
Data presentation.pdf
Statistical Averages and Measure of Spread.pdf
Class work for Topic 13.docx
DE4102 Assignment 13 2021.pdf
Lesson

Topic 11 An Introduction to complex numbers

In topic 11 (some of )chapter 11 you will learn to:
  • add, subtract, multiply and divide complex numbers
  • write complex numbers in both rectangular and polar form
  • represent a complex number on an Argand diagram
  • use excel with complex numbers
Topic 11 Class 1
Topic 11 p 1 Complex numbers.pdf
Topic 11 Class 2
Topic 11 p2 2 Polar, rectangular forms, Argand diagrams.pdf
DE4102 T11 C3 Using excel for complex numbers.pptx
DE4102 Assignment 4 Otago 2022.pdf

Notes from the "live" classes

These will be added on the Friday of each week for anyone who has missed a class
DE4102 T6 C2.pptx
DE4102 T6 C3.pptx
DE4102 T6 C1.pptx
DE4102 T7 C1.pptx
DE4102 T7 C2 and C3.pptx
DE4102 T8 C1.pptx
DE4102 T8 C2.pptx
DE4102 T8 C3.pptx
DE4102 T9 C1.pptx
DE4102 T9 C2 2021.pptx
DE4102 T9 C3.pptx
DE4102 T10 C1.pptx
DE4102 T10 C2.pptx
DE4102 T10 C3.pptx
DE4102 T11 C1.pptx
DE4102 T12 c2.pptx
DE4102 T12 c3.pptx
DE4102 T13 C3.pptx
DE4102 T14 C1.pptx
DE4102 T14 C2.pptx
DE4102 T1 C1 2022.pptx
DE4102 T1 C2 2022.pptx
DE4102 T2 C1 and C2 otago 2022.pptx
DE4102 T2 C3 Otago 2022.pptx
DE4102 T3C1 2022 Otago.pptx
DE4102 T3 C2 and C3 otago 2022.pptx
DE4102 T3 c3 Using Excel to produce a straigth line graph.xlsx
DE4102 T4 C1 Solving linear functions Otago 2022.pptx
DE4102 T4 C2 using excel to solve linear equations.xlsx
DE4102 T4 C3 Solving quadratics Otago.pptx
DE4102 T4 C4 Otago 2022.pptx
DE4102 topic 4 class 5. Sketching a quadratic in excel.xlsx
DE4102 T4 C6 Otago 2022.pptx
DE4102 T4 C7 otagi 2022.pptx
DE4102 T5 C1 Otago 2022.pptx
DE4102 T5 C2 Graphing exponential functions in spreadsheets.xlsx
DE4102 T5C2 Otago 2022.pptx
DE4102 T5 C3 oTAGO 2022.pptx
DE4102 T5 C4 Graphing logarithmic functions in spreadsheets.xlsx
DE4102 T5 C4 Otago.pptx
DE4102 T5 C5 Otago 2022.pptx
DE4102 T6 C1 Otago 2022.pptx
DE4102 T6 C2 and C3 Otago 2022.pptx
DE4102 T6 C4 otago 2022.pptx
DE4102 T6 C5.pptx
DE4102 T6 C6 Otago 2022.pptx
DE4102 topic 6 class 6 Trig and excel.xlsx
DE4102 T6 C7 Otago 2022.pptx
DE4102 T6 C8 Otago 2022.pptx
DE4102 T7 C1 Otago 2022.pptx
DE4102 T7 C2 Otago 2022.xlsx
DE4102 T7 C3 parts 1 and 2 Otago 2022.pptx
DE4102 T8 Class 1 Otago 2022.pptx
DE4102 T8 C2 Otago 2022.pptx
DE4102 T9 C1.pptx
DE4102 T9 c2 Otago 2022.pptx
DE4102 T9 C3 otago 2022.pptx
DE4102 T9 C3 excel Simpson's rule.xlsx
DE4102 T11 C1 complex numbers otago 2022.pptx
DE4102 T11 C2 Argand diagrams and polar notation otago 2022.pptx
DE4102 T11 C3 Using excel for complex numbers.pptx