ENGR1180 - Engineering Mathematics I
Credits: 03

Lecturers:
Dr. Shanaz Wahid email:Shanaz.Wahid@sta.uwi.edu
Mr. Oral Robertson email:Oral.Robertson@sta.uwi.edu


Online Textbooks and References

Vector Calculus (Corral)

Linear Algebra (Dawkins)

Calculus II (Dawkins)

Just the Maths (Hobson)

Differential Equations (Dawkins)

 

Note: the three Dawkins texts may also be obtained from Paul's Online Math Notes.



Target Delivery Schedule (using above online references)


Week
Topics
References
1
Plane and space vectors, vector equations of lines and planes, dot product, cross product Sections 1.1-1.5 of Vector Calculus (Corral)
2
Geometric interpretation of linear equations, Gaussian elimination,  n-dimensional space, definition of a vector space Pages 3-26, 126-135, 154-155, 183-184 of Linear Algebra (Dawkins)
3
Span and subspace, linear dependence, basis, dimension, basic properties of matrices Pages 193-228, 27-38  of  Linear Algebra (Dawkins)
4
Transpose, determinants, rank and its application to linear systems, matrix inversion by cofactors Pages 43-52, 107-114  of  Linear Algebra (Dawkins)
5
Convergence of series, comparison and ratio tests, Maclaurin and Taylor series Pages 179-201, 211-218, 230-234, 254, 269-278  of  Calculus II (Dawkins)
6
Definition and properties of a complex number, complex roots of a quadratic equation, complex numbers as vectors, modulus and argument, product and quotients Units 6.1, 6.2, 6.3 of Just the Maths (Hobson)
7
De Moivre’s theorem, exponential form, hyperbolic functions, loci in the Argand diagram Units 6.4, 6.5, 6.6 of Just the Maths (Hobson)
8
Definitions, direction fields, linear first order differential equations, separable differential equations Pages 2-18, 21-44 of  Differential Equations (Dawkins)
9
Modelling with first order equations, exact equations, numerical approximations, homogeneous second order equations with constant coefficients Pages 77-84, 45-55, 94-101, 104-112 of  Differential Equations (Dawkins)
10
Fundamental solutions, complex and repeated roots of the characteristic equation, reduction of order, method of undetermined coefficients Pages 113-130, 137-155 of  Differential Equations (Dawkins)
11
Variation of parameters, mechanical and electrical vibrations, higher order homogeneous differential equations Pages 156-173, 350-354 of  Differential Equations (Dawkins)




Assignments:


Assignment 1 Vectors
Assignment 2 Gaussian Elimination and Vector Spaces
Assignment 3 Matrices
Assignment 4 Series and Taylor Series (updated Sep 2 2011)
Assignment 5 Complex Numbers I
Assignment 6 Complex Numbers II
Assignment 7 Differential Equations I (updated Sep 2 2011)
Assignment 8 Differential Equations II (updated Sep 5 2011)
Assignment 9 Differential Equations III


Sample Examination

Sample final examination Solutions


Past Examinations

Dec 2012 Solutions
July 2012 Solutions
Dec 2011 Solutions


Online lectures for ENGR1180 topics


Vectors

Basic revision of vectors -- component form, length of a vector, vector addition and scalar multiplication, dot product, angle between two vectors, orthogonal vectors, scalar and vector projections, cross product, scalar triple product Tisdell Vectors I
Visually understanding basic vector operations Khan Vectors I
Parametric equations of lines Khan Vectors II
Defining a plane in R^3 with a point and normal vector Khan Vectors III
Figuring out a normal vector to a plane from its equation Khan Vectors IV
Distance between a point and a plane in three dimensions Khan Vectors V

 

Linear Algebra

Geometric interpretation of a linear system in two dimensions Khan Linear Algebra I
Geometric interpretation of a linear system in three dimensions Khan Linear Algebra II
Solving a system of linear equations by using an augmented matrix (infinite number of solutions) Khan Linear Algebra III
Another example of using an augmented matrix (unique solution) Khan Linear Algebra IV
A third example of using an augmented matrix (no solution) Khan Linear Algebra V
Linear combinations and spans of vectors Khan Linear Algebra VI
Introduction to linear independence Khan Linear Algebra VII
More on linear independence Khan Linear Algebra VIII
Determining whether 3 vectors are linearly independent and/or span R^3 Khan Linear Algebra IX
Introduction to linear subspaces of R^n Khan Linear Algebra X
Understanding the definition of a basis of a subspace Khan Linear Algebra XI

 

Matrices

What a matrix is. How to add and subtract them. Khan Matrices I
Multiplying two 2x2 matrices Khan Matrices II
More on multiplying matrices Khan Matrices III
Identity matrix; introduction to matrix inverses; formula for inverse of a 2 x 2 matrix; determinant of a 2 x 2 matrix Khan Matrices IV
Determinants of 2 x2 and 3 x 3 matrices Khan Matrices V
Inverting a 3x3 matrix Khan Matrices VI
Using the inverse of a matrix to solve a system of equations Khan Matrices VII
Transpose of a matrix Khan Matrices VIII
Taking the transpose of the product of two matrices Khan Matrices IX
Transposes of sums and inverses Khan Matrices X

 

Series

Sigma notation, introduction to series, n^th partial sum, convergence, geometric series, telescoping series, n^th term test, integral test (not required) Tisdell Series I
Comparison, limit comparison and ratio tests for series Tisdell Series II
Taylor polynomials (a.k.a. polynomial approximations); material after the 24^th minute is not required Tisdell Series I
Taylor and Maclaurin series Tisdell Series I

 

Complex numbers

i and Imaginary Numbers Khan Complex Numbers I
Adding, subtracting and multiplying complex numbers Khan Complex Numbers II
Dividing complex numbers; argument of a complex number Tisdell Complex Numbers I
Calculations using the polar form of complex numbers Tisdell Complex Numbers II
Sketching regions in the complex plane Tisdell Complex Numbers III
n^th roots of a complex number Tisdell Complex Numbers IV
Application of complex numbers to trigonometric identities Tisdell Complex Numbers V

 

Differential equations

Introduction to ordinary differential equations Tisdell Differential Equations I
First order linear differential equations Tisdell Differential Equations II
Separable differential equations Tisdell Differential Equations III
Modelling with differential equations (an example of a mixing problem) Tisdell Differential Equations IV
Geometric interpretation of y'=f(x,y), direction fields, integral curves, plotting direction fields via isoclines, integral curves don't cross, integral curve cannot touch because of uniqueness, consequence of noncontinuity in uniqueness and existence Mattuck Differential Equations I
Euler method (modified Euler methods such as Runge-Kutta are not required) Mattuck Differential Equations II
Introduction to first order homogenous equations Khan Differential Equations I
Exact differential equations Tisdell Differential Equations V
Second order differential equations (homogeneous) Tisdell Differential Equations VI
Solution to a 2nd order, linear homogeneous ODE with repeated roots Tisdell Differential Equations VII
Second order differential equations (inhomogeneous) using the method of undetermined coefficents Tisdell Differential Equations VIII
An example of the reduction of order method Khan Differential Equations II
Mechanical vibration example; variation of parameters example Tisdell Differential Equations IX
Second-order linear homogeneous ode's: superposition, uniqueness, Wronskians Mattuck Differential Equations III




Method of Evaluation

Element Required to pass course Weighting Number of Assessment Artefacts
Final Exam No 60% 1
Assignments No 5% 9
Midterms No 35% 2
TOTAL Yes 100% 12